Fermi surface and van Hove singularities in the itinerant metamagnet Sr3Ru2O7
铜氧化物高温超导体电子结构与临界温度关系研究
铜氧化物高温超导体电子结构与临界温度关系研究陈宁1，季飞1，范本勇1,汪纯1，李福燊11北京科技大学材料科学与工程学院无机非金属系(100083)E-mail: nchen@摘 要：量子化学电子结构计算（CASTEP方法）结果发现，对于所有已发现的27个铜氧化物超导体系，铜氧面的最近邻阳离子A（内层p轨道）与O离子（内层2s轨道），在E f以下约20e V深处，均存在着的内层轨道作用，这种作用产生的内层耦合电子分布在铜氧面上的相对强度与超导临界温度（T c）成正比。
这一定量关系证明，内层轨道是导致高温超导现象最重要原因之一；同时还揭示，处于最外层轨道上的载流子与内层轨道耦合的联系可能是通过铜氧面上O的内层2s轨道的改变来实现的。
关键词：电子结构、氧化物超导体引言高温超导体有许多令人吃惊的性质，从发现高温超导现象至今十几年的研究热潮中，人们已经在确证、充实及理解那些奇特的现象上花费了巨大的精力。
这些课题任务之所以极其重大的，除了巨大的实际应用价值外，在凝聚态物理理论上也是非常特别的，因为这些体系中电子的行为与通常费米液体行为的金属有很大不同，电子-电子强关联效应似乎占据非常重要的部分。
但是为什么这些体系具有强关联呢？传统的研究中我们忽略了哪些重要的因素呢？因此，我们首先要搞清楚这些体系的电子结构特点。
自高温超导体问世以来，就有很多科研小组对氧化物超导体的电子结构进行了深入研究。
徐建华等[1]、Pickett等[2]用能带理论对La2CuO4体系（La系）进行了计算。
虽然不同的研究组在计算时使用的晶格参数、收敛精度等略有差别，但所得结果在大体上是一致的。
计算结果表明，La的5d带处于E f以上1e V处，而它的4f带则处于E f以上约3e V处。
O的2s带和La的5p带则分别处于E f以下（约-20~-14e V处）。
因而在E f附近，主要是Cu的3d和O的2p形成的一个十分复杂的p-d杂化带。
此外，对于YBa2Cu3O7（Y系）至少有Krakauer、Massidda以及Mattheiss等三个不同的研究小组3]计算了这种体系的能带结构。
Fermi-surfaces-and-Luttinger’s-theorem-in-paired-fermion-systems
out even for non-interacting fermions. We hope that by manipulating the form of the trap potential, its effect can be minimized so that discontinuities in momentum distribution associated with Fermi surfaces can be detected in future experiments; this would probably require a trap potential that is flat inside the trap and rises very fast near the boundary.
We note that Luttinger’s theorem for Bose-Fermi mixtures has also been investigated in recent work [4, 5] in which a boson and a fermion bind to form a fermionic molecular state. Here we will show that these results can be straightforwardly extended to the case of interest to the recent atomic experiments: two fermions binding to form a bosonic molecular state. We also use nonperturbative arguments similar to those of Yamanaka, Oshikawa and Affleck [6] to establish analogous results in one dimension.
A computer movie simulating urban growth in the Detroit region
A Computer Movie Simulating Urban Growth in the Detroit Region †Waldo R. ToblerUniversity of MichiganIn one classification of models the simulation to be described would be considered a demographic model whose primary objectives are instructional. The model developed here may be used for forecasting, but was not constructed for this specific purpose, and it is a demographic model since it describes only population growth, with particular emphasis on the geographical distribution of this growth.As a premise, I make the assumption that everything is related to everything else. Superficially considered this would suggest a model of infinite complexity; a corollary inference often made is that social systems are difficult because they contain many variables; numerous people confuse the number of variables with the degree of complexity. Because of closure, however, models with infinite numbers of variables are in fact sometimes more tractable than models with a finite but large number of variables [27]. My point here is that the utmost effort must be exercised to avoid writing a complicated model. It is very difficult to write a simple model but this, after all, is one of the objectives. If one plots a graph with increasing complexity on the abscissa, and increasing effectiveness on the other axis, it is well known that science is only asymptotic to one hundred percent effectiveness. No scientist claims otherwise. But the rate at which this effectiveness is achieved is extremely important, ceterus paribus. In other words, the objective is high success with a simple model. Statistical procedures that order the eigenvalues are popular for just this reason. Because a process appears complicated is also no reason to assume that it is the result of complicated rules, examples are: the game of chess, the motion of the planets before Copernicus; evolution before Darwin and the double helix, geology before Hutton, mechanics before Newton, geography before Christaller, and so on. The plausibility of models also varies, but this is known to be an incomplete guide to the scientific usefulness of a model. The model I describe, for example, recognizes that people are born, migrate, and die. It does not explain why people are born, migrate, and die. Some would insist that I should incorporate more behavioral notions, but then it would be necessary to discuss the psychology of urban growth; to do this properly requires a treatise on the biochemistry of perception, which in turn requires discussion of the physics of ion interchange, and so on. My attitude, rather, is that since I have not explained birth, migration, or death, the model might apply to any phenomenon that has these characteristics, e.g., people, plants, animals, machines (which are built, moved, and destroyed), or ideas. The level of generality seems inversely related to the specificity of the model. A model of urban growth should apply to all 92,200 cities [9, p. 81] (not just to one city), now and in the future, and to other things that grow. These are rather ambitious aims. Conversely, the model attempts to relate population totals only on the basis of prior populations, and neglects employment opportunities, topography, transportation, and other distinctions between site qualities. Consequently the only difference between places in the model is their population density, and other demographic differences are ignored. Similarly, the population model attempts to relate population growth only to population in the immediately proceeding time period. Since, by assumption, everything is related to everything else, such a neglect of history may prove disastrous. To include all history, however, is known to require integral equations of the Volterra type [37] and these complicate the presentation. We may also determine empirically whether a neglect of history has serious consequences, at least in the short run. In summary, the manysimplifications of the model are acknowledged as advantages, particularly for pedagogic purposes.Conceptually, I have been influenced by Borchert’s model of the twin city region [2]. This was later applied to Detroit by Deskins, and I have used his data [8]. As formulated by Borchert and Deskins the model is in graphical form and suggests that the lines of growth coincide with extrapolations, modified by local conditions, of the orthogonal trajectories to the level curves of population density. The difficult step is to estimate the amount of growth along these trajectories, Presumably this is proportional to the population pressure, or the gradient of the population density [23].Following Pollack [26] specific equations may now he postulated, letting dP/dt denote population growth at any location:dP/dt = k, constant regional growth, ordP/dt = kP, proportional growth, ordP/dt = k(1- α)P, logistic growth, ordP/dt = k[(dP/dx)2 + (dP/dy)2]1/2 , growth is proportional to the population gradient, ordP/dt = k(d2P/dx2 + d2P/dy2), growth is proportional to the rate of change of the population gradient, ord2P/dt2 = k(d2P/dx2 + d2P/dy2), the acceleration of growth is proportional to the population curvature, and so on.Each of these equations could now be examined in some detail, or converted to finite difference form for empirical estimation purposes, but I prefer to generalize in a different direction.The simulation of urban growth raises questions of geographical syntax. As an example, recall that many predictive models are of the formC = BAwhere A is an n by 1 vector of known observations, B is an m by n transformation matrix of coefficients or transition probabilities, and C is the m by 1 vector to be predicted. This scheme seems inadequate as a geographical calculus. The geographical situation is better represented, in a simplified special case, asD = NGEwhere G and D are now m by n matrices, isomorphic to maps of the geographical landscape [32], and N and E are coefficient matrices representing North-South and East-West effects. The matrix D could of course be converted into a long column vector (mn by 1) by partitioning along the columns and the placing of these one above the other. But this destroys the isomorphism to the geographical situation. Since “the purpose of computing is insight, not numbers,”[13] I aim for a simple structure. Using geographical state matrices seems more natural than using state vectors. To some extent attempts to simulate urban growth are also related to the problem of comparing geographical maps, a question which occurs frequently in geography [30]. Let me clarify this analogy. Suppose I have a map showing the 1930 distribution of population in the Detroit region,and a map of the 1940 distribution. I would like to measure the degree of similarity of these two maps. Some type of correlation coefficient is needed. Certainly this is necessary to evaluate an urban growth model, which can be considered a means of predicting a map of population distribution. In order to evaluate the coefficient of correlation properly, I should have some notion of the probability of two randomly selected maps being similar. This requires some information concerning the distribution of actual population maps over the set of all possible population maps. Suppose that the population data are assembled by one-degree quadrilaterals of latitude and longitude, of which there are approximately 360 by 180 on a sphere. If only land areas are considered, say 90 by 180 ≈ 1.6 x 104 cells. If a maximum population density of 5000 persons per square-mile is allowed, each quadrilateral can contain from zero to roughly 17.5 x 106 people. The number of possible population maps is then the number of states raised to the number of cells, that is, (17.5 x 106)1.6 x 10 ^ 4 ≈ 1051. Not all of these are equally likely, and a prediction much better than random can be made by asserting that there will be no change from the present. This suggests that, from an information-theoretic point of view, a prediction does not contain a great deal of information! This unhappy conclusion is avoided by recognizing that geographical predictions must be discounted for the effect of persistence.The usual measure of association is the Pearsonian correlation coefficient. This not only serves as a measure of similarity, but also provides, via the linear regression equation, a means of prediction. Most discussions of methods of comparing maps overlook this important feature. This clearly suggests predicting the 1940 population of a cell as a linear function of the 1930 population of that cell, that is, P1940ij = A + B P1930ij . Now this, as a model, has advantages and disadvantages. For example, discrepancies between the model and the actual situation might be used as a measure of the perceived suitability of a site for occupation. More cogently, a major disadvantage is that it ignores the premise “everything is related to everything else.” The geographical interpretation of this premise should be that population growth at place A depends not only on the previous population at place A but also on the population of all other places. More concretely, population growth in Ann Arbor from 1930 to 1940 depends not only on the 1930 population of Ann Arbor, but also on the 1930 population of Vancouver, Singapore, Cape Town, Berlin, and so on. Stated as a giant multiple regression, the 1940 population of Ann Arbor depends on the 1930 population of everywhere else; that is, it is a function of about 1.6 x 104 variables, if population data are given by one-degree quadrilaterals. Note that the meteorologist has a similar problem when attempting to predict the weather, and solves it in the following ingenious manner [10, 11, 14, 15, 25 pp. 233-56; 96].The world wide (or hemispheric) distribution of the pertinent weather elements are summarized by an approximating equation. The coefficients of this equation are then used as surrogate variables, much reduced in number, representing the actual distribution. Geographers have also recently used such trend equations [6], but not in this interesting manner. The global distribution of population could now be approximated by an equation with a modest number of coefficients. Alternately, the world population potential [29]could serve as a single surrogate for the 1.6 x l04 variables. Instead of using this approach I invoke the first law of geography: everything is related to everything else, but near things are more related than distant things. The specific model used is thus very parochial, and ignores most of the world.There is merit in considering urban growth from yet another point of view. Think of it as a linear input-output system; that is, the 1930 population distribution serves as input to a black box, the output of which is the 1940 population distribution.Two points of view can be taken: (a) given the inputs and outputs, calculate the characteristics of the black box, i.e., infer theprocess; or (b) design the system to achieve a specific output. The latter is what an engineer does when he builds a radio, or what some urban planners hope to do. The present intent is to deduce some characteristics of the process.A convenient method of studying linear, origin invariant black boxes is by means of the response to a unit impulse:In the present instance the input and output are both two-dimensional distributions, and it is assumed that the system consists of a linear, positionallv invariant, local operator. Such processes are less familiar to engineers hut occur in the study of optical systems [20, 17 pp. 278-281, 28].The equivalent to the unit impulse is the unit inhabitant. Let us see what happens to him in a decade:(a) he has 0.3 children,(b) 0.2 of him dies,(c) 0.05 of him moves to California,(d) 0.4 of him moves to the suburbs,(c) 0.6 of him does nothingThese data are fictitious, hut observe that they include, birth, death, and migration. The net result is 1.15 inhabitants, geographically distributed some what more widely than originally. This then is the final model presented.The population of a cell, 1.5 miles on a side, is estimated as a linear function of the same and neighboring cells in the preceding time period, i.e., where the unit inhabitant came from, rather than where he went. This result can be visualized in several equivalent fashions. Consider the following Gedanken experiment. Randomly sample the population of the region under study and plot a map showing the locations of individuals in 1930 connected by a directed line to their locations in 1940. Now translate each line to a common origin, thus creating a migration rose. The end points of the migration vectors constitute a probability density surface. A comparable result could be achieved by a random sample of select cells and a study of the behavior of all of the inhabitants of these cells, followed by an averaging over all of the sampled cells. The net result should not differ appreciably from the present more indirect inferential procedure of comparing maps. Mathematically the distribution in, say, 1930 can he considered to be described by P(x,y}, that in 1940 by P’(x,y), and the spread of the unit inhabitant by W(u,v). The assumption is that each individual in P(x,y) undergoes an identical spreading W(u,v)P(x+u,y+v) and the final result is the sum of the individual effects, i.e., ΙΙW(u,v)P(x+u,y+v) du dv. Now if F(W) denotes the Fourier transform of W(u,v), F(W) = ΙΙW(u,v) exp(2πi(au + bv)) du dv then, by the two dimensional convolution theorem F(P’) =F(W)F(P). Thus, by converting to the frequency domain there exists a convenient procedure for calculating the spread function. Specific computational details, and application to other geographical situations are given in anearlier paper [33]. The similarity to Hägerstrand’s Mean Information Fields [12], and to an approximately 1000-region input-output study [18] should be apparent. A stochastic model can be written along similar lines [1].For the initial computer movie [19] the equations used are P1930+∆t ij = ΣΣ W pq P1930i+p,j+q , with p and q ranging from –2 to +2, and with W pq = A pq + B pq∆t where ∆t is measured in years from 1930. A pq and B pq were obtained from the coefficients given in the earlier paper [33] by weighting the 1950/60 coefficients twice as much as the 1930/40 and 1940/50 values. An additional movie, giving equal weight to all of the time periods by using W pq = A pq + B pq ∆t + C pq(∆t)2 may be more realistic. Both of these models describe time variant systems [3]. The movies simulate from 1910 to 2000 in time steps of ∆t = 0.5 and ∆t = 0.05 years. A time step of one frame per month would appear to be the most appropriate speed, assuming viewing at 16 frames per second. An interesting question is whether the same coefficients could he used for some other urban region of the United States since the exogenous conditions are obviously relatively constant.The expectation of course is that the movie representations of the simulated population distribution in the Detroit region will provide insights, mostly of an intuitive rather than a formal nature, into the dynamics of urban growth. Comparison of the simulated values for 1930, 1940,1950, and 1960 with the actual values for these dates shows that the model differs from a simple interpolation, which could in fact be made to provide an exact fit to the data and its time derivatives. Viewing the movies suggests that the model introduces an excessive amount of smoothing, and that the decline in population of the CBD does not seem to have been adequately captured by the equations. These inadequacies may he due to several factors. For example, theneighborhood over which the spread function was estimated may have been too small, or the8200 square-mile region over which it is averaged too large. Both of these deficiencies could beexplored by additional computations using the available data. Since there is some evidence thatdiffusion waves occur in city growth [24, 22, 35 pp. 326-340], an equation somewhat moregeneral than those postulated earlier may be proposed to characterize geographical change, namely,n m3 A nΜn P/Μt n = 3 k m(Μm P/Μx m + Μm P/Μy m)o owhere k is a variable function of x, y, and t. This is clearly an attempt to adapt the linear differential equation commonly encountered in systems analysis to take into account the geographical aspects of the problem. It can also be viewed as a statistical procedure for predicting a univariate geographical series, the usual exponential time discounting being extended to include exponential-like space discounting, each observation being related to aspace-time cone of previous and nearby observations. There is no assurance, of course, thaturban growth can be described by positionally invariant linear equations; eventual extension to interactive multivariate geographical forecasting is also required. From a pedagogic point ofview the model presented here has the distinct advantage that its shortcomings are obvious. Themodel given here, for example, uses translationally invariant two-dimensional Fourier transforms, but a rotationally invariant Mellin-Fourier transform would seem more appropriatefor cities. This would allow the spreading of the unit inhabitant to depend on his distance fromthe CBD, and this seems a more realistic approximation to the true, situation.LITERATURE CITED1. Bailey, N. “Stochastic Birth, Death, and Migration Processes for Spatially DistributedPopulations,” Biometrika, 55 (1968), pp. 189—98.2. Borchert, J. “The Twin Cities Urbanized Area: Past, Present, Future,” The Geographical Review, 51 (1961), pp. 47-70.3. Brown, B. M. The Mathematical Theory of Linear Systems. London: Chapman and Hall(Science Paperback), 1965.4. Brown, B. C. Smoothing, Forecasting and Prediction, Englewood Cliffs: Prentice Hall, 1962.5. Bunge, M. “The Weight of Simplicity in the Construction and Assaying of ScientificTheories,” Philosophy of Science, 28 (1961), pp. 120-19.6. Chorley, H. and P. Haggett, “Trend Surface Mapping in Geographical Research,”Transactions and Papers, Institute of British Geographers, 37 (1965), pp. 47-67.7. Connelly, D. S. “The Coding and Storage of Terrain Height Data: an Introduction toNumerical Cartography,” Unpublished thesis, Cornell University, September, 1968.8. Deskins, D. R., Jr., “Settlement Patterns for the Detroit Metropolitan Area: 1930-1970,”Unpublished paper, Department of Geography, University of Michigan, 1963.9. Doxiadis, C. A. Ekistics. New York: Oxford University Press, 1968.10. Epstein, E. S. “Stochastic Dynamic Prediction,” Tellus, forthcoming.11. Friedman, D. “Specification of Temperature and Precipitation in Terms of CirculationPatterns,” journal of Meteorology, 12 (1965), pp. 428—35.12. Hägerstrand, T., Innovation Diffusion as a Spatial Process. Translated by A. Pred.Chicago: Chicago University Press, 1967.13. Hamming, R. Numerical Methods for Scientists and Engineers. New York: McGraw-Hill,1962.14. Hare, F. “The Quantitative Representation of the North Polar Pressure Fields,” PolarAtmosphere Symposium. New York: Pergamon Press, 1958.15. Haurwitz B. and R. Craig, “Atmospheric Flow Patterns and Their Representation bySpherical Surface Harmonics,” Geophysical Research Paper No. 1-1, Cambridge Research Center, 1952.1.6.Highway Research Board, Urban Development Models, HRB-Special Report 97,Washington, D.C., NRC, 1968.17. Hsu, H. P. Outline of Fourier Analysis. New York: Simon and Schuster, 1967.18. Isard, W. Methods of Regional Analysis, Cambridge: MIT Press, 1960.19. Knowlton, K. “Computer Produced Movies,” Science, 150 (1965), pp. 116-20.20. Kovasznay, L. and H. Joseph, “Image Processing,” Proceedings, Institute of Radio Engineers(May, 1955), pp. 560-570.21. Lee, D. Models and Techniques for Urban Planning, Cornell Aeronautical Laboratory ReportVY-2474-G-1, September, 1968.22. Morrill, R., “Waves of Spatial Diffusion.” Journal of Regional Science, (1969), pp.1-18.23. Muehrcke, P. “Population Slope Maps,” Unpublished MA. thesis, Department of Geography, University of Michigan, 1966.24. Newling, .B. “The Spatial Variation of Urban Population Densities,” Geographical Review, 59 (1969), pp. 242-232;25. Petterssen, S. Weather Analysis and Forecasting. 2nd ed. Vol. 2, New York; McGraw-Hill, 1956.26. Pollack, H. “On the Interpretation of State Vectors and Local Transformation Operators,” Colloquium on Simulation, University of Kansas Computer Contribution 22, Lawrence, 1968, pp. 43-6.27. Robinson, E. An Introduction to Infinitely Many Variates. New York, Hafner, 1959.28. Rosenfeld, A. Picture Processing by Computer. New York; Academic Press, 1969.29. Stewart, J. Q. and W. Warntz, “Physics of Population Distribution,” Journal of Regional Science, 1 (1958), pp. 99-123.30. Tobler, W., “Computation of the Correspondence of Geographical Patterns,” Papers, Regional Science Association,15 (1965), pp. 131-39.31. Tobler, W. “Spectral Analysis of Spatial Series,” Proceedings, Fourth Annual Conference on Urban Planning Information Systems and Programs, University of California, Berkeley, 1966. pp. 179-86.32. Tobler, W. “Of Maps and Matrices.” Journal of Regional Science, 7 (Supplement, 1967); pp. 276-80.33. Tobler, W., “Geographical Filters and Their Inverses,” Geographical Analysis, 1 (1969), pp. 234-53.34. Volterra, V. Theory of Functionals and of Integral and Integro-Differential Equations. Dover: New York, 1959.35. Watt, K. Ecology and Resource Management. New York; McGraw-Hill, 1968.36. White, R. M. and W. C. Palson, Jr. “On the Forecasting Possibilities of Empirical Influence Functions,” Journal of Meteorology, 12 (1955), pp. 478—85.†W. Tobler, 1970, “A Computer Movie Simulating Urban Growth in the Detroit Region”, Economic Geography, 46, 2 (1970), pp. 234-240. (The ‘first law of geography’ is at the bottom of page 236 in the original).。
FermiSurfaces,De...
Degenerate Black Holes
These are all states with the maximal SU(2) but different Jz. We can scan over them.
In particular the extremal state with Jz=0 has zero entropy. Ie, the state
Degenerate Black Holes
Explicitly – since the bosons are not charged under this SU(2) fermions (in pairs) and bosons can mix only if the fermions combine to an SU(2) singlet rep. For example
This sector has one interesting property which is that it has an
additional SU(2) symmetry, not present in the full N=4 SYM
under which all the pairs
is a doublet for every k.
Degenerate Black Holes
There is, however, a problem – the corresponding BH has finite entropy. So the state above is “contaminated” by many other states.
Which is gauge invariant, with easy to compute charges under the both SU(2)L*SU(2)R and under the 3 U(1)’s: 1. These are the ground states of the Fermionic PSU(1,1) sector
费米面ppt课件
r rr
E (k )i J (0 ) J (R m )e ik • R m
n .n .
其中
J ( 0 ) V ( r r ,0 ) |i( r r ) |2 d
r
r r r rr
J ( R m ) i * ( r ) V ( r , R m ) i ( r R m ) d
一、能态密度函数 （function of energy state density）
二、费米面（Fermi surface）
本节思路：用定义模式密度的方法引入能态密度，具体给出 几个模型的能态密度；在此基础上给出费米面的定义以及费 米能、费米动量、费米速度等概念。
Physics Department, Northwest University
Kittel: The Fermi surface is the surface of constant energy F in k space. The Fermi surface separates the unfilled orbitals from the filled orbitals, at absolute zero.
—— 费米能量
EF
51.1eV (rs /a0)2
Solid State Physics
EF
h
2
k
2 F
2m
a0 0.529 1010 m n ~ 1023 / cm 3 rs / a0 2 ~ 6
EF 1.5eV~15eV
Physics Department, Northwest University
二、晶体能带的对称性
En(k)=En(αk) En(k)=En(-k)
En(k)=En(k＋Gn)
费米面ppt课件
§6-7 能态密度和费密面
Solid State Physics
一、 能态密度函数 1、能态密度函数的定义
—— 固体中电子的能量由一些准连续的能级形成的能带
—— 能量在E ~ E+E之间
E
能态数目Z
能态密度函数
N(E) lim Z E0 E
Physics Department, Northwest University
Physics Department, Northwest University
能带重叠
3) 紧束缚模型的电子能态密度
Solid State Physics
—— 简单立方格子的s带
E s(k ) E 0 2 J 1 (c k x a o csk o y a s ck o z a )s
—— k=0附近
kE 2 a1J (s2k ixa n s2 ik n ya s2 ik n za )
能态密度
N(E)
V
43
dS kE
N (E )8V 3 a J1等 能 面(sin2kxasin d 2 S kyasin2kza)
Physics Department, Northwest University
Solid State Physics
kE 2 a1J (s2k ixa n s2 ik n ya s2 ik n za ) 带底 EE06J1和 EE02J1
出现微商不连续的奇点 —— 等能面与布里渊区相交
X点 k ( , 0, 0)
a EX E02J1
Physics Department, Northwest University
1、费米面： 费米面是指绝对零度时， k 空间电子占据态与未占据态之间的分界面.
Phase_noise_and_frequency_stability_in_oscillators-Rubiola_2009
More informationPhase Noise and Frequency Stability in OscillatorsPresenting a comprehensive account of oscillator phase noise and frequency stability,this practical text is both mathematically rigorous and accessible.An in-depth treatmentof the noise mechanism is given,describing the oscillator as a physical system,andshowing that simple general laws govern the stability of a large variety of oscillatorsdiffering in technology and frequency range.Inevitably,special attention is given to am-plifiers,resonators,delay lines,feedback,andflicker(1/f)noise.The reverse engineeringof oscillators based on phase-noise spectra is also covered,and end-of-chapter exercisesare given.Uniquely,numerous practical examples are presented,including case studiestaken from laboratory prototypes and commercial oscillators,which allow the oscillatorinternal design to be understood by analyzing its phase-noise spectrum.Based on tuto-rials given by the author at the Jet Propulsion Laboratory,international IEEE meetings,and in industry,this is a useful reference for academic researchers,industry practitioners,and graduate students in RF engineering and communications engineering.Additional materials are available via /rubiola.Enrico Rubiola is a Senior Scientist at the CNRS FEMTO-ST Institute and a Professorat the Universit´e de Franche Comt´e.With previous positions as a Professor at theUniversit´e Henri Poincar´e,Nancy,and in Italy at the University Parma and thePolitecnico di Torino,he has also consulted at the NASA/Caltech Jet PropulsionLaboratory.His research interests include low-noise oscillators,phase/frequency-noisemetrology,frequency synthesis,atomic frequency standards,radio-navigation systems,precision electronics from dc to microwaves,optics and gravitation.More informationThe Cambridge RF and Microwave Engineering SeriesSeries EditorSteve C.CrippsPeter Aaen,Jaime Pl´a and John Wood,Modeling and Characterization of RF andMicrowave Power FETsEnrico Rubiola,Phase Noise and Frequency Stability in OscillatorsDominique Schreurs,M´a irt´ın O’Droma,Anthony A.Goacher and Michael Gadringer,RF Amplifier Behavioral ModelingFan Y ang and Y ahya Rahmat-Samii,Electromagnetic Band Gap Structures in AntennaEngineeringForthcoming:Sorin V oinigescu and Timothy Dickson,High-Frequency Integrated CircuitsDebabani Choudhury,Millimeter W aves for Commercial ApplicationsJ.Stephenson Kenney,RF Power Amplifier Design and LinearizationDavid B.Leeson,Microwave Systems and EngineeringStepan Lucyszyn,Advanced RF MEMSEarl McCune,Practical Digital Wireless Communications SignalsAllen Podell and Sudipto Chakraborty,Practical Radio Design TechniquesPatrick Roblin,Nonlinear RF Circuits and the Large-Signal Network AnalyzerDominique Schreurs,Microwave Techniques for MicroelectronicsJohn L.B.Walker,Handbook of RF and Microwave Solid-State Power AmplifiersPhase Noise and Frequency Stability in OscillatorsENRICO RUBIOLAProfessor of Electronics FEMTO-ST Institute CNRS and Universit´e de Franche Comt´e Besanc ¸on,FranceMore informationMore informationCAMBRIDGE UNIVERSITY PRESSCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521886772C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryISBN978-0-521-88677-2hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationContentsForeword by Lute Maleki page ixForeword by David Leeson xiiPreface xv How to use this book xviSupplementary material xviii Notation xix 1Phase noise and frequency stability11.1Narrow-band signals11.2Physical quantities of interest51.3Elements of statistics91.4The measurement of power spectra131.5Linear and time-invariant(LTI)systems191.6Close-in noise spectrum221.7Time-domain variances251.8Relationship between spectra and variances291.9Experimental techniques30Exercises33 2Phase noise in semiconductors and amplifiers352.1Fundamental noise phenomena352.2Noise temperature and noisefigure372.3Phase noise and amplitude noise422.4Phase noise in cascaded amplifiers492.5 Low-flicker amplifiers522.6 Detection of microwave-modulated light62Exercises65 3Heuristic approach to the Leeson effect673.1Oscillator fundamentals673.2The Leeson formula72More informationvi Contents3.3The phase-noise spectrum of real oscillators753.4Other types of oscillator824Phase noise and feedback theory884.1Resonator differential equation884.2Resonator Laplace transform924.3The oscillator964.4Resonator in phase space1014.5Proof of the Leeson formula1114.6Frequency-fluctuation spectrum and Allan variance1164.7 A different,more general,derivation of the resonatorphase response1174.8 Frequency transformations1215Noise in delay-line oscillators and lasers1255.1Basic delay-line oscillator1255.2Optical resonators1285.3Mode selection1305.4The use of a resonator as a selectionfilter1335.5Phase-noise response1385.6Phase noise in lasers1435.7Close-in noise spectra and Allan variance1455.8Examples1466Oscillator hacking1506.1General guidelines1506.2About the examples of phase-noise spectra1546.3Understanding the quartz oscillator1546.4Quartz oscillators156Oscilloquartz OCXO8600(5MHz AT-cut BV A)156Oscilloquartz OCXO8607(5MHz SC-cut BV A)159RAKON PHARAO5MHz quartz oscillator162FEMTO-ST LD-cut quartz oscillator(10MHz)164Agilent10811quartz(10MHz)166Agilent noise-degeneration oscillator(10MHz)167Wenzel501-04623(100MHz SC-cut quartz)1716.5The origin of instability in quartz oscillators1726.6Microwave oscillators175Miteq DRO mod.D-210B175Poseidon DRO-10.4-FR(10.4GHz)177Poseidon Shoebox(10GHz sapphire resonator)179UWA liquid-N whispering-gallery9GHz oscillator182More informationContents vii6.7Optoelectronic oscillators185NIST10GHz opto-electronic oscillator(OEO)185OEwaves Tidalwave(10GHz OEO)188 Exercises190Appendix A Laplace transforms192References196Index202More informationForeword by Lute MalekiGiven the ubiquity of periodic phenomena in nature,it is not surprising that oscillatorsplay such a fundamental role in sciences and technology.In physics,oscillators are thebasis for the understanding of a wide range of concepts spanningfield theory and linearand nonlinear dynamics.In technology,oscillators are the source of operation in everycommunications system,in sensors and in radar,to name a few.As man’s study ofnature’s laws and human-made phenomena expands,oscillators have found applicationsin new realms.Oscillators and their interaction with each other,usually as phase locking,and withthe environment,as manifested by a change in their operational parameters,form thebasis of our understanding of a myriad phenomena in biology,chemistry,and evensociology and climatology.It is very difficult to account for every application in whichthe oscillator plays a role,either as an element that supports understanding or insight oran entity that allows a given application.In all thesefields,what is important is to understand how the physical parametersof the oscillator,i.e.its phase,frequency,and amplitude,are affected,either by theproperties of its internal components or by interaction with the environment in whichthe oscillator resides.The study of oscillator noise is fundamental to understanding allphenomena in which the oscillator model is used in optimization of the performance ofsystems requiring an oscillator.Simply stated,noise is the unwanted part of the oscillator signal and is unavoidablein practical systems.Beyond the influence of the environment,and the non-ideality ofthe physical elements that comprise the oscillator,the fundamental quantum nature ofelectrons and photons sets the limit to what may be achieved in the spectral purity of thegenerated signal.This sets the fundamental limit to the best performance that a practicaloscillator can produce,and it is remarkable that advanced oscillators can reach it.The practitioners who strive to advance thefield of oscillators in time-and-frequencyapplications cannot be content with knowledge of physics alone or engineering alone.The reason is that oscillators and clocks,whether of the common variety or the advancedtype,are complex“systems”that interact with their environment,sometimes in waysthat are not readily obvious or that are highly nonlinear.Thus the physicist is needed toidentify the underlying phenomenon and the parameters affecting performance,and theengineer is needed to devise the most effective and practical approach to deal with them.The present monograph by Professor Enrico Rubiola is unique in the extent to which itsatisfies both the physicist and the engineer.It also serves the need to understand bothMore informationx Forewordsthe fundamentals and the practice of phase-noise metrology,a required tool in dealingwith noise in oscillators.Rubiola’s approach to the treatment of noise in this book is based on the input–output transfer functions.While other approaches lead to some of the same results,this treatment allows the introduction of a mathematical rigor that is easily tractable byanyone with an introductory knowledge of Fourier and Laplace transforms.In particular,Rubiola uses this approach to obtain a derivation,fromfirst principles,of the Leesonformula.This formula has been used in the engineering literature for the noise analysisof the RF oscillator since its introduction by Leeson in1966.Leeson evidently arrivedat it without realizing that it was known earlier in the physics literature in a differentform as the Schawlow–Townes linewidth for the laser oscillator.While a number ofother approaches based on linear and nonlinear models exist for analyzing noise inan oscillator,the Leeson formula remains particularly useful for modeling the noisein high-performance oscillators.Given its relation to the Schawlow–Townes formula,it is not surprising that the Leeson model is so useful for analyzing the noise in theoptoelectronic oscillator,a newcomer to the realm of high-performance microwave andmillimeter-wave oscillators,which are also treated in this book.Starting in the Spring of2004,Professor Rubiola began a series of limited-timetenures in the Quantum Sciences and Technologies group at the Jet Propulsion Labo-ratory.Evidently,this can be regarded as the time when the initial seed for this bookwas conceived.During these visits,Rubiola was to help architect a system for themeasurement of the noise of a high-performance microwave oscillator,with the sameexperimental care that he had previously applied and published for the RF oscillators.Characteristically,Rubiola had to know all the details about the oscillator,its principleof operation,and the sources of noise in its every component.It was only then that hecould implement the improvement needed on the existing measurement system,whichwas based on the use of a longfiber delay in a homodyne setup.Since Rubiola is an avid admirer of the Leeson model,he was interested in applyingit to the optoelectronic oscillator,as well.In doing so,he developed both an approachfor analyzing the performance of a delay-line oscillator and a scheme based on Laplacetransforms to derive the Leeson formula,advancing the original,heuristic,approach.These two treatments,together with the range of other topics covered,should makethis unique book extremely useful and attractive to both the novice and experiencedpractitioners of thefield.It is delightful to see that in writing the monograph,Enrico Rubiola has so openlybared his professional persona.He pursues the subject with a blatant passion,andhe is characteristically not satisfied with“dumbing down,”a concept at odds withmathematical rigor.Instead,he provides visuals,charts,and tables to make his treatmentaccessible.He also shows his commensurate tendencies as an engineer by providingnumerical examples and details of the principles behind instruments used for noisemetrology.He balances this with the physicist in him that looks behind the obvious forthe fundamental causation.All this is enhanced with his mathematical skill,of which healways insists,with characteristic modesty,he wished to have more.Other ingredients,missing in the book,that define Enrico Rubiola are his knowledge of ancient languagesMore informationForewords xi and history.But these could not inform further such a comprehensive and extremelyuseful book on the subject of oscillator noise.Lute MalekiNASA/Caltech Jet Propulsion Laboratoryand OEwaves,Inc.,February2008More informationForeword by David LeesonPermit me to place Enrico Rubiola’s excellent book Phase Noise and Frequency Stabilityin Oscillators in context with the history of the subject over the pastfive decades,goingback to the beginnings of my own professional interest in oscillator frequency stability.Oscillator instabilities are a fundamental concern for systems tasked with keeping anddistributing precision time or frequency.Also,oscillator phase noise limits the demod-ulated signal-to-noise ratio in communication systems that rely on phase modulation,such as microwave relay systems,including satellite and deep-space parablyimportant are the dynamic range limits in multisignal systems resulting from the mask-ing of small signals of interest by oscillator phase noise on adjacent large signals.Forexample,Doppler radar targets are masked by ground clutter noise.These infrastructure systems have been well served by what might now be termedthe classical theory and measurement of oscillator noise,of which this volume is acomprehensive and up-to-date tutorial.Rubiola also exposes a number of significantconcepts that have escaped prior widespread notice.My early interest in oscillator noise came as solid-state signal sources began to beapplied to the radars that had been under development since the days of the MIT RadiationLaboratory.I was initiated into the phase-noise requirements of airborne Doppler radarand the underlying arts of crystal oscillators,power amplifiers,and nonlinear-reactancefrequency multipliers.In1964an IEEE committee was formed to prepare a standard on frequency stability.Thanks to a supportive mentor,W.K.Saunders,I became a member of that group,whichincluded leaders such as J.A.Barnes and L.S.Cutler.It was noted that the independentuse of frequency-domain and time-domain definitions stood in the way of the develop-ment of a common standard.To promote focused interchange the group sponsored theNovember1964NASA/IEEE Conference on Short Term Frequency Stability and editedthe February1966Special Issue on Frequency Stability of the Proceedings of the IEEE.The context of that time included the appreciation that self-limiting oscillators andmany systems(FM receivers with limiters,for example)are nonlinear in that theylimit amplitude variations(AM noise);hence the focus on phase noise.The modestfrequency limits of semiconductor devices of that period dictated the common usage ofnonlinear-reactance frequency multipliers,which multiply phase noise to the point whereit dominates the output noise spectrum.These typical circuit conditions were secondnature then to the“short-term stability community”but might not come so readily tomind today.More informationForewords xiii Thefirst step of the program to craft a standard that would define frequency stabilitywas to understand and meld the frequency-and time-domain descriptions of phaseinstability to a degree that was predictive and permitted analysis and optimization.Bythe time the subcommittee edited the Proc.IEEE special issue,the wide exchange ofviewpoints and concepts made it possible to synthesize concise summaries of the workin both domains,of which my own model was one.The committee published its“Characterization of frequency stability”in IEEE Trans.Instrum.Meas.,May1971.This led to the IEEE1139Standards that have served thecommunity well,with advances and revisions continuing since their initial publication.Rubiola’s book,based on his extensive seminar notes,is a capstone tutorial on thetheoretical basis and experimental measurements of oscillators for which phase noiseand frequency stability are primary issues.In hisfirst chapter Rubiola introduces the reader to the fundamental statistical de-scriptions of oscillator instabilities and discusses their role in the standards.Then in thesecond chapter he provides an exposition of the sources of noise in devices and circuits.In an instructive analysis of cascaded stages,he shows that,for modulative or parametricflicker noise,the effect of cascaded stages is cumulative without regard to stage gain.This is in contrast with the well-known treatment of additive noise using the Friisformula to calculate an equivalent input noise power representing noise that may originateanywhere in a cascade of real amplifiers.This example highlights the concept that“themodel is not the actual thing.”He also describes concepts for the reduction offlickernoise in amplifier stages.In his third chapter Rubiola then combines the elements of thefirst two chapters toderive models and techniques useful in characterizing phase noise arising in resonatorfeedback oscillators,adding mathematical formalism to these in the fourth chapter.Inthefifth chapter he extends the reader’s view to the case of delay-line oscillators suchas lasers.In his sixth chapter,Rubiola offers guidance for the instructive“hacking”ofexisting oscillators,using their external phase spectra and other measurables to estimatetheir internal configuration.He details cases in which resonatorfluctuations mask circuitnoise,showing that separately quantifying resonator noise can be fruitful and that devicenoisefigure and resonator Q are not merely arbitraryfitting factors.It’s interesting to consider what lies ahead in thisfield.The successes of today’sconsumer wireless products,cellular telephony,WiFi,satellite TV,and GPS,arise directlyfrom the economies of scale of highly integrated circuits.But at the same time thisintroduces compromises for active-device noise and resonator quality.A measure ofthe market penetration of multi-signal consumer systems such as cellular telephonyand WiFi is that they attract enough users to become interference-limited,often fromsubscribers much nearer than a distant base station.Hence low phase noise remainsessential to preclude an unacceptable decrease of dynamic range,but it must now beachieved within narrower bounds on the available circuit elements.A search for new understanding and techniques has been spurred by this requirementfor low phase noise in oscillators and synthesizers whose primary character is integrationand its accompanying minimal cost.This body of knowledge is advancing througha speculative and developmental phase.Today,numerical nonlinear circuit analysisMore informationxiv Forewordssupports additional design variables,such as the timing of the current pulse in nonlinearoscillators,that have become feasible because of the improved capabilities of bothsemiconductor devices and computers.Thefield is alive and well,with emerging players eager tofind a role on the stage fortheir own scenarios.Professionals and students,whether senior or new to thefield so ablydescribed by Rubiola,will benefit from his theoretical rigor,experimental viewpoint,and presentation.David B.LeesonStanford UniversityFebruary2008More informationPrefaceThe importance of oscillators in science and technology can be outlined by two mile-stones.The pendulum,discovered by Galileo Galilei in the sixteenth century,persistedas“the”time-measurement instrument(in conjunction with the Earth’s rotation period)until the piezoelectric quartz resonator.Then,it was not by chance that thefirst inte-grated circuit,built in September1958by Jack Kilby at the Bell Laboratories,was aradio-frequency oscillator.Time,and equivalently frequency,is the most precisely measured physical quantity.The wrist watch,for example,is probably the only cheap artifact whose accuracy ex-ceeds10−5,while in primary laboratories frequency attains the incredible accuracy ofa few parts in10−15.It is therefore inevitable that virtually all domains of engineeringand physics rely on time-and-frequency metrology and thus need reference oscillators.Oscillators are of major importance in a number of applications such as wireless com-munications,high-speed digital electronics,radars,and space research.An oscillator’srandomfluctuations,referred to as noise,can be decomposed into amplitude noise andphase noise.The latter,far more important,is related to the precision and accuracy oftime-and-frequency measurements,and is of course a limiting factor in applications.The main fact underlying this book is that an oscillator turns the phase noise of itsinternal parts into frequency noise.This is a necessary consequence of the Barkhausencondition for stationary oscillation,which states that the loop gain of a feedback oscillatormust be unity,with zero phase.It follows that the phase noise,which is the integral ofthe frequency noise,diverges in the long run.This phenomenon is often referred to asthe“Leeson model”after a short article published in1966by David B.Leeson[63].Onmy part,I prefer the term Leeson effect in order to emphasize that the phenomenon isfar more general than a simple model.In2001,in Seattle,Leeson received the W.G.Cady award of the IEEE International Frequency Control Symposium“for clear physicalinsight and[a]model of the effects of noise on oscillators.”In spring2004I had the opportunity to give some informal seminars on noise in oscil-lators at the NASA/Caltech Jet Propulsion Laboratory.Since then I have given lecturesand seminars on noise in industrial contexts,at IEEE symposia,and in universities andgovernment laboratories.The purpose of most of these seminars was to provide a tuto-rial,as opposed to a report on advanced science,addressed to a large-variance audiencethat included technicians,engineers,Ph.D.students,and senior scientists.Of course,capturing the attention of such a varied audience was a challenging task.The stimu-lating discussions that followed the seminars convinced me I should write a workingMore informationxvi Prefacedocument1as a preliminary step and then this book.In writing,I have made a seriouseffort to address the same broad audience.This work could not have been written without the help of many people.The gratitudeI owe to my colleagues and friends who contributed to the rise of the ideas containedin this book is disproportionate to its small size:R´e mi Brendel,Giorgio Brida,G.JohnDick,Michele Elia,Patrice F´e ron,Serge Galliou,Vincent Giordano,Charles A.(Chuck)Greenhall,Jacques Groslambert,John L.Hall,Vladimir S.(Vlad)Ilchenko,LaurentLarger,Lutfallah(Lute)Maleki,Andrey B.Matsko,Mark Oxborrow,Stefania R¨o misch,Anatoliy B.Savchenkov,Franc¸ois Vernotte,Nan Yu.Among them,I owe special thanks to the following:Lute Maleki for giving me theopportunity of spending four long periods at the NASA/Caltech Jet Propulsion Labora-tory,where I worked on noise in photonic oscillators,and for numerous discussions andsuggestions;G.John Dick,for giving invaluable ideas and suggestions during numerousand stimulating discussions;R´e mi Brendel,Mark Oxborrow,and Stefania R¨o misch fortheir personal efforts in reviewing large parts of the manuscript in meticulous detail andfor a wealth of suggestions and criticism;Vincent Giordano for supporting my effortsfor more than10years and for frequent and stimulating discussions.I wish to thank some manufacturers and their local representatives for kindness andprompt help:Jean-Pierre Aubry from Oscilloquartz;Vincent Candelier from RAKON(formerly CMAC);Art Faverio and Charif Nasrallah from Miteq;Jesse H.Searles fromPoseidon Scientific Instruments;and Mark Henderson from Oewaves.Thanks to my friend Roberto Bergonzo,for the superb picture on the front cover,entitled“The amethyst stairway.”For more information about this artist,visit the website.Finally,I wish to thank Julie Lancashire and Sabine Koch,of the Cambridge editorialstaff,for their kindness and patience during the long process of writing this book.How to use this bookLet usfirst abstract this book in one paragraph.Chapter1introduces the language ofphase noise and frequency stability.Chapter2analyzes phase noise in amplifiers,includ-ingflicker and other non-white phenomena.Chapter3explains heuristically the physicalmechanism of an oscillator and of its noise.Chapter4focuses on the mathematics thatdescribe an oscillator and its phase noise.For phase noise,the oscillator turns out to bea linear system.These concepts are extended in Chapter5to the delay-line oscillatorand to the laser,which is a special case of the latter.Finally,Chapter6analyzes indepth a number of oscillators,both laboratory prototypes and commercial products.Theanalysis of an oscillator’s phase noise discloses relevant details about the oscillator.There are other books about oscillators,though not numerous.They can be divided intothree categories:books on radio-frequency and microwave oscillators,which generallyfocus on the electronics;books about lasers,which privilege atomic physics and classical1E.Rubiola,The Leeson Effect–Phase Noise in Quasilinear Oscillators,February2005,arXiv:physics/0502143,now superseded by the present text.PrefacexviideeperreadingbasictheoreticaladvancedtheoreticallegendexperimentalistlecturerdeeperreadingFigure1Asymptotic reading paths:on the left,for someone planning lectures on oscillatornoise;on the right,for someone currently involved in practical work on oscillators.optics;books focusing on the relevant mathematical physics.The present text is uniquein that we look at the oscillator as a system consisting of more or less complex interactingblocks.Most topics are innovative,and the overlap with other books about oscillatorsor time-and-frequency metrology is surprisingly small.This may require an additionaleffort on the part of readers already familiar with the subject area.The core of this book rises from my experimentalist soul,which later became con-vinced of the importance of the mathematics.The material was originally thought anddrafted in the following(dis)order(see Fig.1):3Heuristic approach,6Oscillator hack-ing,4Feedback theory,5Delay-line oscillators.Thefinal order of subjects aims at amore understandable presentation.In seminars,I have often presented the material in the3–6–4–5order.Y et,the best reading path depends on the reader.T wo paths are suggestedin Fig.1for two“asymptotic”reader types,i.e.a lecturer and experimentalist.Whenplanning to use this book as a supplementary text for a university course,the lecturer More information。
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摘要：材料表面的细菌粘附常引起食品腐败或植入性感染，有时甚至会引发疾病，而控制细菌 在材料表面的初始粘附能够减少这些安全隐N。作者通过化学接枝的方法，制备了不同表面浸 润性的材料，并与大肠杆菌、铜绿假单胞菌及金黄色葡萄球菌等3种常见致病菌共同培养,系统 地研究了材料表面浸润性对细菌粘附的影响。研究结果表明，随着材料表面疏水性的增加，其抗 细菌粘附能力显著提升。另夕卜，表面带负电材料的抗菌能力更强。这些结果能够帮助理解细菌在 材料表面粘附的内在机理，同时有助于抗菌材料的设计和制备。 关键词：表面接枝；表面浸润性；抑制细菌粘附；生物膜 中图分类号:TS 206.1 文章编号：1673-1689(2019)03-0026-06 DOI: 10.3969/j.issn. 1673-1689.2019.03.004
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等离子体辅助纳米涂层的构建及其成骨性能
文章编号： 1008-9357(2022)01-0054-07DOI: 10.14133/ki.1008-9357.20210330004等离子体辅助纳米涂层的构建及其成骨性能郭西萌， 金莉莉， 李春旺， 何宏燕， 刘昌胜（华东理工大学材料科学与工程学院，材料生物学与动态化学前沿科学中心，教育部医用生物材料工程研究中心，上海 200237）摘 要： 通过氧等离子体处理，在聚对苯二甲酸乙二酯（PET ）表面引入羟基，提高了其表面的亲水性。
利用静电吸附等方式在PET 材料表面先后载入表没食子儿茶素没食子酸酯（EGCG ）、纤维黏连蛋白（Fn ）和骨形态发生蛋白-2 （rhBMP-2），构建了rhBMP-2/EGCG/Fn 有机组装的纳米涂层，改性后的PET 表面表现出优异的细胞相容性，rhBMP-2的高效载入、活性维持、以及缓慢释放，赋予了改性表面高诱骨活性和成骨分化能力。
关键词： 聚对苯二甲酸乙二酯；骨形态发生蛋白；成骨分化；生物相容性；骨间充质干细胞中图分类号： R318.08 文献标志码： AConstruction and Osteogenic Properties of Plasma-Assisted Nano-CoatingGUO Ximeng, JIN Lili, LI Chunwang, HE Hongyan, LIU Changsheng（School of Materials Science and Engineering, Frontiers Science Center for Materiobiology and Dynamic Chemistry,Medical Biomaterials Engineering Research Center of the Ministry of Education, East China University of Science and Technology, Shanghai 200237, China ）Abstract: In recent years, polyethylene terephthalate (PET) based Ligament Advanced Reinforcement System(LARS)artificial ligaments have become popular in anterior cruciate ligament (ACL) reconstruction. However, due to its poor biological activity and high hydrophobicity, its application is limited to clinical uses. In order to improve the biological activity of materials and enhance the tendon-bone healing effect, oxygen plasma was used to introduce hydroxyl groups on the surface of PET. It has been found that the surface physiochemical treatment and immobilization of bioactive molecules have great effects on the bioactivity improvement of the inert surfaces. Therefore, bone morphogenetic proteins (rhBMP-2)with typical indicator and fibronectin (Fn) for enhancing the binding capacity of rhBMP-2 molecules were chosen as modifying molecules. The functional molecules such as epigallocatechin-3-gallate (EGCG) were coated on the PET surface first. There are six ortho phenolic hydroxyl groups in the molecular structure of EGCG. Fn molecules were then easily immobilized on the EGCG-PET surfaces. Since each subunit of Fn had a high-affinity binding site for rhBMP-2, rhBMP-2molecules are biological anchored on the surface through long-chained Fn, which simulates the biomimetic design in the extracellular matrix. Thus, such molecules EGCG, Fn, and rhBMP-2 are sequentially immobilized on the PET surfaces. The nanocoating of rhBMP-2/EGCG/Fn is assembled to further enhance the loading efficiency of rhBMP-2 and control the release收稿日期： 2021-03-30基金项目： 国家自然科学基金创新群体项目（51621002）；国家重点研发计划战略性国际科技创新合作重点专项（SQ2018YF020328）作者简介： 郭西萌（1994—），女，硕士，主要研究方向为骨修复生物材料。
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a r X i v :0803.0941v 2 [c o n d -m a t .s t r -e l ] 26 J u n 2008Fermi surface and van Hove singularities in the itinerant metamagnet Sr 3Ru 2O 7A.Tamai,1,∗M.P.Allan,1J.F.Mercure,1W.Meevasana,2R.Dunkel,2D.H.Lu,2R.S.Perry,3A.P.Mackenzie,1D.J.Singh,4Z.-X.Shen,2and F.Baumberger 11Scottish Universities Physics Alliance,School of Physics and Astronomy,University of St Andrews,North Haugh,St.Andrews,Fife KY169SS,UK2Departments of Applied Physics,Physics,and Stanford Synchrotron Radiation Laboratory,Stanford University,Stanford,California 94305,USA3Scottish Universities Physics Alliance,School of Physics and Centre for Science at Extreme Conditions,The University of Edinburgh,Mayfield Road,Edinburgh,EH93JZ,UK4Materials Science and Technology Division,Oak Ridge National Laboratory,Oak Ridge,TN 37831-6114,USA(Dated:June 26,2008)The low-energy electronic structure of the itinerant metamagnet Sr 3Ru 2O 7is investigated by angle resolved photoemission and density functional calculations.We find well–defined quasiparticle bands with resolution limited line widths and Fermi velocities up to an order of magnitude lower than in single layer Sr 2RuO 4.The complete topography,the cyclotron masses and the orbital character of the Fermi surface are determined,in agreement with bulk sensitive de Haas –van Alphen measurements.An analysis of the d xy band dispersion reveals a complex density of states with van Hove singularities (vHs)near the Fermi level;a situation which is favorable for magnetic instabilities.PACS numbers:71.18.+y,71.20.-b,79.60.-i,75.30.KzQuantum criticality in correlated electron systems con-tinues to attract widespread attention.One reason is that systems near a quantum critical point are highly susceptible to novel ordered phases,the observation and characterization of which promises new insight in the be-havior of strongly interacting systems [1,2].Possibly even more exciting is the prospect that fluctuations asso-ciated with a quantum critical point could dominate the phase diagram of topical materials,including the cuprate superconductors up to high temperatures [3].Evidence for quantum critical points,reached by tuning pressure,chemical composition or magnetic field,has been ob-served in a variety of materials comprising simple metals [4],heavy fermion intermetallics [5]or transition metal oxides such as Sr 3Ru 2O 7,the subject of this study [2,6].Criticality in Sr 3Ru 2O 7is associated with a metamag-netic transition (super–linear rise in magnetization)of the itinerant electron system in applied field.In the ground state Sr 3Ru 2O 7is a paramagnetic Fermi liquid with strongly enhanced quasiparticle masses.Its elec-tronic specific heat value of γ=110mJ/molRuK 2is among the highest in any oxide and the large magnetic susceptibility indicates a substantial Stoner enhancement [7].The Fermi liquid region of the phase diagram extends up to 10–15K in zero field and is continuously sup-pressed towards zero temperature upon approaching the critical field of B ≈8T (for B c )[6].In the vicinity of the putative quantum critical end point non–Fermi–liquid behavior has been observed in various macroscopic quantities including specific heat,resistivity and thermal expansion and has been described on the basis of phe-nomenological models [6,8,9,10].On the other hand,little is known about the micro-scopic origin of the metamagnetism.Theoretical work suggests that the phase diagram of Sr 3Ru 2O 7may be un-derstood from peculiarities in the band structure causing either a local minimum in the density of states (DOS)at the Fermi level ρ(E F )or a sharp increase in DOS over the minute energy scale of the Zeeman splitting (≈1meV for B =10T)[11,12,13].Density functional calcula-tions for Sr 3Ru 2O 7show a number of sharp features in the DOS [14]and have been invoked to support a band structure based model of metamagnetism,although their precision hardly reaches the 1meV scale.Thus,exper-imental information on the evolution of the DOS near the Fermi level is key to advancing the field.A recent spectroscopic STM study detected peaks in the tunnel-ing conductivity around ±4meV,which might be inter-preted as a set of van Hove singularities in the DOS [15].Published photoemission studies on the other hand did not report unusual features on the relevant energy scale [16,17].In this paper,we present a comprehensive high-resolution k–space mapping of the quasiparticle band structure in Sr 3Ru 2O 7by means of angle-resolved pho-toemission.We characterize the d xy DOS in the vicinity of the chemical potential:we identify two peaks in ρ(ǫ)at −4meV and −1meV and discuss their relevance for metamagnetism.Photoemission experiments were performed with a monochromatized He–discharge lamp and a Scienta SES2002analyzer using an energy and angular resolution of 4.5meV /0.3◦full width at half maximum (FWHM).Additional data at various excitation energies were taken at beamline V-4of SSRL using a Scienta R4000analyzer with a combined resolution set to 8.0meV /0.3◦.All data shown in this paper were measured with 21.2eV photons at T =9K and a pressure <5·10−11mbar.FIG.1:Fermi surface of Sr 3Ru 2O 7.(a)shows the experimental data taken in the first quadrant of the larger tetragonal Brillouin zone and symmetrized with respect to the Ru–Ru nearest neighbor direction.X denotes the surface projection of R and M that of a midpoint between two Γpoints (Z or S ).(b)Fermi surface contours extracted from the data shown in panel (a).(c)LDA calculation for the basal plane (k z =0,black)and midplane (k z =1/4,blue).(d)Schematic structure of a single RuO 2plane illustrating the unit-cell doubling due to a 6.8◦rotation of the RuO 6octahedra [18].a t denotes the Ru–Ru nearest neighbor distance and a o the in–plane lattice constant of the orthorhombic unit cell,respectively.High purity single crystals of Sr 3Ru 2O 7were grown in an image furnace [19].The detection of sizable quan-tum oscillations in all samples used for this study indi-cates residual in–plane resistivities <0.5µΩcm.Band structure calculations in the local density approximation (LDA)were performed using the general potential lin-earized augmented planewave method [20]with well con-verged basis sets and zone samplings.Including spin–orbit interaction was found to improve the agreement with experiment.The Fermi surface is based on first principles calculations at 850k –points in the irreducible 1/8wedge of the zone using the experimental crystal structure [18].We start by discussing the Fermi surface of Sr 3Ru 2O 7.A single bilayer of RuO 6octahedra contains 4Ru 4+–ions,each contributing 4conduction electrons distributed over the 3nearly degenerate t 2g levels.Hence,in a firstFIG.2:Band dispersion along ΓM Γ.The Fermi surface crossings are labeled above the momentum distribution curve (MDC)extracted at E F .The inset shows a spectrum at the Γ–point.A peak width of 5.5meV in the raw data indicates an excellent surface quality.approximation one expects up to 12bands crossing the Fermi level.Indeed an earlier electronic structure calcu-lation showed a highly fragmented Fermi surface suggest-ing that its experimental determination could be beyond current capabilities [14].On the other hand,de Haas –van Alphen experiments found only 5distinct frequen-cies corresponding to Fermi surface pockets in the range of 1.1%to 32%of the Brillouin zone area [21,22].Fig.1(a)shows the experimental ARPES Fermi sur-face map.The data have been integrated over ±2meV,resulting in an effective energy resolution (convolution of integration window and spectrometer resolution)of 5.5meV [23].The identification of three Fermi surface pockets centered at Γis straightforward from an analy-sis of individual cuts.The innermost sheet,labeled δ,is nearly circular.Remarkably,its orbital character,as inferred from LDA calculations,is Ru d x 2−y 2,i.e.it be-longs to the e g manifold,which is unoccupied in Sr 2RuO 4and Ca 3Ru 2O 7[24,25,26].The larger square-and cross–shaped hole–like Fermi surfaces with pronounced uniaxial anisotropy derive from the out–of–plane d xz,yz orbitals.Around the M –points,a small lens (β)and a larger lens with back–folded vertices (γ1)can be identified.The shape of these pockets indicates mixing of d xz,yz and d xy orbital character on the γ1sheet and dominant d xz,yz character for the βsheet.The smaller lens is well resolved in the Fermi surface map,while the precise contours of the larger γ1pocket are more difficult to extract.How-ever,its Fermi crossings along the ΓMΓline can clearly be identified from the cut shown in Fig.2.A pronounced shoulder on the left hand side of the γ1peak indicates a small bilayer splitting of this pocket,consistent with the DFT calculations.The intensity maxima in Fig.1(a)connecting the edges of the γ1pockets between adjacent M–points stem from a putative small hole–pocket (γ2)that is barely touching the Fermi surface.We find the top of this band located at −1±1meV (compare Fig.3).TABLE I:Fermi surface volumes and cyclotron masses of Sr3Ru2O7obtained from ARPES and dHvA.The polarity and dominant orbital character of the pockets is indicated in brackets.Errors are estimated from the statistical accuracy of the analysis and the reproducibility of the experiments.The mass ofγ2is estimated from parabolicfits to the dispersion.α1(h+,xz,yz)α2(h+,xz,yz)β(e−,xz,yz)γ1(e−,xy/xz,yz)γ2(h+,xy)δ(e−,x2−y2)dHvA FS–volume A(%BZ)13.0±1.030.1±1.1 1.1±0.2 6.6±0.9– 3.1±0.3 dHvA cyclotron mass m∗(m e) 6.9±0.110.1±0.1 5.6±0.37.7±0.3–8.4±0.7Hence,based on the ARPES data alone we cannot de-cide unambiguously whether it contributes to the Fermisurface.A slight k z dispersion or a minute structural dif-ference between surface and bulk might be sufficient tolift theγ2pocket up to the Fermi level for a considerablefraction of the3D bulk Brillouin zone.The volumes A of all Fermi surface pockets are summa-rized in Table1and compared with recent de Haas–vanAlphen data[27].Cyclotron masses m∗=¯h2FIG.3:Band dispersion around the vHs of the d xy band.(a) Photoemission intensity in the vicinity of the X point along the direction marked in the inset.Peak positions have been determined by afit to the energy distribution curves after nor-malization with the Fermi function.(b)Raw EDCs extracted from the data show in(a).The high intensity above the Fermi level for k near the top of the band hints at the presence of unoccupied states within a few meV of the Fermi level.(c) Contour plot showing the energy position of the lowest ly-ing quasiparticle excitation as a function of(k x,k y).(d)His-togram of near-E F k–states obtained from the band–contours shown in(c).Absolute values are calculated assuming a two-fold degeneracy(or an unresolved bilayer splitting)ofγ1,2. The total density of statesρ(E F)calculated from the mea-sured specific heat is47states/eV/Ru.The horizontal error bar in(d)indicates a±1meV uncertainty in absoluteǫ(k) values estimated from the variation between different mea-surements.transition[11].This motivates a brief and speculative discussion of the effects of an appliedfield on the elec-tronic structure of Sr3Ru2O7.The pocket most likely to be strongly affected isγ2,which could become com-pletely spin polarised in afield of order10tesla.Since it is repeated eight times in the BZ each spin polarised pocket would need only to be modest in area to account for the moment change of≈0.25µB at the metamagnetic transition of Sr3Ru2O7.The hole-like character ofγ2fur-ther means that if it dominated the spin polarisation in a rigid-band picture,one would expect an accompanying decrease in the areas of the hole-like sheetsα1andα2 or an increase in the areas of the electron likeβandγ1 sheets.Intriguingly,a pronounced decrease ofα1andα2 was reported in[21],pointing towards an inter–orbital charge transfer from the d xy to the d xz,yz sheet at the metamagnetic transition of Sr3Ru2O7.Further investi-gation of these issues by detailed de Haas–van Alphen studies and scanning tunnelling spectroscopy in highfield are desirable.In conclusion,we have presented high–resolution ARPES data from Sr3Ru2O7.In combination with new LDA calculations incorporating spin-orbit coupling,the results allow an unambiguous identification of most Fermi surface pockets and of their dominant orbital charac-ter.Moreover,our data provide clear evidence for sharp spikes in the quasiparticle density of states on the natural energy scale of metamagnetism.This work has been supported by the Scottish Funding Council and the UK EPSRC.SSRL is operated by the DOE’s office of Basic Energy Science.Work at ORNL was supported by DOE BES,Division of Materials Sci-ence and Engineering.∗anna.tamai@[1]S.Sachdev,Science288,475(2000).[2]R.Borzi et al.,Science315,214(2007).[3]C.M.Varma,Phys.Rev.B55,14554(1997).[4]A.Yeh,Y.-A.Soh,J.Brooke,G.Aeppli,T.F.Rosen-baum,and S.M.Hayden,Nature419,459(2002).[5]G.R.Stewart,Rev.Mod.Phys.73,797(2001).[6]S.A.Grigera et al.,Science294,329(2001).[7]S.-I.Ikeda,Y.Maeno,S.Nakatsuji,M.Kosaka,andY.Uwatoko,Phys.Rev.B62,R6089(2000).[8]lis,A.J.Schofield,G.G.Lonzarich,and S.A.Grigera,Phys.Rev.Lett.88,217204(2002).[9]P.Gegenwart,F.Weickert,M.Garst,R.S.Perry,andY.Maeno,Phys.Rev.Lett.96,136402(2006).[10]R.S.Perry et al.,Phys.Rev.Lett.86,2661(2001).[11]B.Binz and M.Sigrist,Europhys.Lett.65,816(2004).[12]C.Honerkamp,Phys.Rev.B72,115103(2005).[13]E.P.Wohlfarth and P.Rhodes,Phil.Mag.7,1817(1962).[14]D.J.Singh and I.I.Mazin,Phys.Rev.B63,165101(2001).[15]K.Iwaya et al.,Phys.Rev.Lett.99,057208(2007).[16]A.V.Puchkov,Z.X.Shen,and G.Cao,Phys.Rev.B58,6671(1998).[17]Y.Aiura et al.,Phys.Rev.Lett.93,117005(2004).[18]H.Shaked,J.D.Jorgensen,O.Chmaissem,S.Ikeda,and Y.Maeno,Journal of Solid State Chemistry154, 361(2000).[19]R.S.Perry and Y.Maeno,Journal of Crystal Growth271,134(2004).[20]D.J.Singh and L.Nordstrom,Planewaves,Pseudopo-tentials and the LAPW Method,2nd Edition(Springer, Berlin,2006).[21]R.A.Borzi et al.,Phys.Rev.Lett.92,216403(2004).[22]R.S.Perry et al.,Phys.Rev.Lett.92,166602(2004).[23]The orthorhombic crystal structure of Sr3Ru2O7(spacegroup Bbcb[18])lacks the4–fold symmetry of Sr2RuO4.However,our LDA calculations show that the Ru–Ru nearest-and next–nearest neighbor directions may be treated as approximate symmetry planes in the band structure.In our experiments,we could not resolve a breaking of these symmetries.Hence,we present the data in Fig.1(a)symmetrized alongΓX.[24]A.Damascelli et al.,Phys.Rev.Lett.85,5194(2000).[25]F.Baumberger et al.,Phys.Rev.Lett.96,107601(2006).[26]A.P.Mackenzie et al.,Phys.Rev.Lett.76,3786(1996).[27]The values shown here are from very recent measure-ments(J.F.Mercure et al.,unpublished)with higher pre-cision than those reported in Ref.[21].[28]F.Baumberger et al.,Phys.Rev.Lett.96,246402(2006).[29]F.Reinert,G.Nicolay,S.Schmidt, D.Ehm,and S.H¨u fner,Phys.Rev.B63,115415(2001).[30]Here we assume that matrix elements of all bands in therelevant energy scale arefinite and no bands eluded de-tection.。