Non-BCS pairing in anisotropic strongly correlated electron systems in solids

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PZT的半导体特性

Band structures and band offsets of high K dielectrics on SiJ.Robertson *Engineering Department,Cambridge University,Trumpington Street,Cambridge CB21PZ,UKAbstractVarious high dielectric constant oxides will be used as insulator in ferroelectric memories,dynamic random access memories,and as the gate dielectric material in future complementary metal oxide semiconductor (CMOS)technology.These oxides which have moderately wide bandgaps provide a good test of our understanding of Schottky barrier heights and band offsets at semiconductor interfaces.Metal induced gap states (MIGS)are found to give a good description of these interfaces.The electronic structure and band offsets of these oxides are calculated.It is found that Ta 2O 5and SrTiO 3have small or vanishing conduction band offsets on 2O 3,Y 2O 3,ZrO 2,HfO 2,Al 2O 3and silicates like ZrSiO 4have offsets over 1.4eV for both electrons and holes,making them better gate dielectrics.#2002Elsevier Science B.V .All rights reserved.Keywords:Band structures;Band offsets;Dielectric constant oxides1.IntroductionThe closed shell transition metal (TM)oxides like SrTiO 3have been extensively studied for their ferro-electric properties,phase transitions and soft modes [1].They are now of great technological importance for electronic devices such as dynamic random access memories (DRAMs),ferroelectric non-volatile mem-ories (FeRAMs),and as alternative gate oxides in future complementary metal oxide semiconductor (CMOS)transistors [2±4].This requires them to be considered in terms of their electronic properties,by treating them as wide bandgap semiconductors [5].This paper reviews the band structures of these oxides,and then considers important electronic prop-erties such as their band offsets and Schottky barrier heights (SBHs).It turns out that the oxides have intermediate bandgaps and so they provide a goodtest of our present models of Schottky barriers and band offsets.2.Band structuresThe simplest band structures are those of the cubic ABO 3perovskites such as SrTiO 3or BaTiO 3.The bandgap is direct at G (Fig.1)[6].The valence band consists mainly of the 2p states of the O 2Àions,and the conduction band of the Ti 4 3d (t 2g )states [7].The Sr s and p states lie higher in the conduction band.However,the bonding is 60±70%ionic,and so there is signi®cant mixing of Ti d states in the valence band.The bands of the Pb perovskites differ in that Pb is divalent and it retains its 6s electrons [8].The ®lled Pb s states form an additional valence band at about À7eV as in PbTiO 3(Fig.2)[6,9].There is also some Pb s admixture in the upper valence band.The empty Pb 6p states now lie near the lowest conduction band.When Zr replaces Ti in SrTiO 3(or BaTiO 3),the bandgap increases strongly by 2eV,because itisApplied Surface Science 190(2002)2±10*Tel.: 44-1223-33-2689;fax: 44-1223-33-2662.E-mail address:jr@ (J.Robertson).0169-4332/02/$±see front matter #2002Elsevier Science B.V .All rights reserved.PII:S 0169-4332(01)00832-7controlled by the energy of the Zr d states.In contrast,in PZT,the Pb 6p states form the conduction band minimum,so the gap barely increases from 3.3to 3.7eV [10].It is recognised that the resonant covalence of Ti-d/O-p states is the origin of ferroelectricity in SrTiO 3type perovskites [11].In Pb perovskites,there is additional resonant covalence between Pb s and O p states which increases the ferroelectric polarity.SrBi 2Ta 2O 9is a layered crystal built from perovs-kite blocks separated by Bi 2O 2layers.It turns out that the Bi s and p states form the highest valence band and lowest conduction bands,respectively,while the ferro-electric response originates mainly from the TaO 3perovskite blocks [12].There is therefore an interest-ing separation of the functionality onto the Ta and Bi sub-lattices.Cubic ZrO 2has the ¯uorite structure.It has a simple band structure,as shown in Fig.3.The O p states form the valence band with a maximum at X [13].The conduction band minimum is at G ,and consists of Zr d states.The Zr d x 2Ày 2and d z 2states lie below the d xy states.The Zr s state lies midway between these at G ,but it disperses rapidly upwards.2.1.Models of Schottky barriers and semiconductor heterojunctionsThe band line-up of two semiconductors is deter-mined,like the SBH of a semiconductor on a metal,by charge transfer across the interface and the presence of any dipole layer at the interface.The charge transfer is that between the metal and the interface states of the semiconductor (Fig.4)[14].The charge transfertendsFig.1.Band structure of BaTiO 3calculated by pseudo-potential method [6].J.Robertson /Applied Surface Science 190(2002)2±103to align the Fermi level E F of the metal to the energy level of the interface states.The SBH for electrons f n between a semiconductor S and a metal M is f n S F M ÀF S F S Àw S(1)Here,F M is the work function of the metal,F S the energy of the semiconductor interface states,w S the semiconductor's electron af®nity (EA)and S the Schottky pinning parameter.S is given by [15]S11 e 2N d =ee 0(2)where e is the electronic charge,e 0the permittivity of free space,N the areal density of the interface states and d their decay length in the semiconductor.The dimensionless pinning factor S describes if the barrieris `pinned'or not.S varies between the limits S 1for unpinned Schottky barriers,and S 0for `Bardeen'barriers pinned by a high density of interface states in which the SBH is f n F S Àw S .There are numerous models of the origins of inter-face states,both intrinsic and extrinsic.In the intrinsic model originating from Bardeen and Heine,a semi-in®nite semiconductor in contact with a metal pos-sesses intrinsic states which are now called metal-induced gap states (MIGS)by Tersoff [14].F S is then the charge neutrality level (CNL)of the interface states,de®ned as the energy above which the states are empty for a neutral surface [16±18].On the other hand,the extrinsic models stress that the metal can react with the semiconductor [19].Brillson correlated the heat of reaction with S .This reaction maycreateFig.2.Band structure of PbTiO 3calculated by pseudo-potential method [6].4J.Robertson /Applied Surface Science 190(2002)2±10interface defects such as vacancies,whose gap states can pin the metal Fermi level,as noted by Spicer [20]and Dow [21].These models were supported by theobservation that pinning occurs even for monolayer coverage of metal,before the MIGS could be estab-lished.It is now believed that,overall,the intrinsic model gives a better description of Schottky barriers,because intrinsic states have a larger pinning dipole,N d ,than surface defects.The pinning parameter S has been in¯uential in our empirical understanding of Schottky barriers.Some years ago,Kurtin et al.[22]noted that S seemed to vary sharply with the ionicity of semi-conductor (Fig.5),from near 0for low ionicity semiconductors like Si and GaAs to 1for higher ionicity solids like SiO 2,SrTiO 3and KTaO 3.S is a dimensionless slope of barrier height to metal work function,S@f n @F M(3)Fig.3.Band structure of ZrO 2calculated by pseudo-potential method[6].Fig.4.Schematic diagram of SBHs.J.Robertson /Applied Surface Science 190(2002)2±105However,Louie [23]and Schluter [24]noted that Kurtin [22]had actually correlated the barrier heights to S H :S H@f n @X(4)which is the slope of barrier height to the Pauling electronegativity of the metal,and not the dimension-less S in (4).The work function and electronegativity vary roughly as [25,26]:F M 2:27X M 0:34(5)Thus,S H 2:27S ,and the Schottky limit should be S H 2:27.The data rarely reach this limit and Schluter [24]observed that S had a better correlation with the dielectric constant of the semiconductor e 0.Empiri-cally,Mo Ènch [14,27]found that S varied with e I as S11 0:1 e I À1 2(6)Certain materials are key tests of Schottky barriermodels.Diamond and xenon [14,28]have zero ioni-city but small e I ,and so their large S values show that S depends on e not on ionicity.This is tested by plotting log 1= S À1 against log e I À1 as in Fig.6.The wide gap oxides provide another key test,because they have intermediate e I values.SrTiO 3and KTaO 3were taken as high ionicity solids in the original Kurtin plot,with S H $1.However,this wasbefore data was actually known.When data [29]became available for SrTiO 3,showing S lying between 0.25and 0.4(Fig.6),it was clear that S is much lower.SrTiO 3falls well on the trend in Fig.3.The reason for this is that the SBHs depend on e I .e I is controlled by the states closest to the bandgap [5].In SrTiO 3,these are the moderately ionic Ti±O states of Ti±O bonds,not the highly ionic Sr±O states which lie well away from the gap and provide a much smaller contribution to e I .This can be seen in the partial density of states (DOS)of SrTiO 3in Fig.6.Thus,SrTiO 3and KTaO 3were misplaced in Fig.5as highly ionic solids.A lesser point is that the moderate value of S of SrTiO 3clearly correlates with e I ,and not with the low frequency dielectric constant e 0,which has a very large value for ferroelectrics and would give S %0from (6).SrTiO 3also serves as an evidence against the defect model,in that the barrier lies some way into the gap,not at the conduction band edge where the O vacancy states lie and would cause pinning.In sum-mary,the MIGS model of Schottky barriers holds for a wide range of solids of various ionicity and dielectric constants [5].The band alignment between two semiconductors is controlled by charge transfer and interface dipoles,just as Schottky barriers [30].For no dipoles,the Schottky limit,the conduction band offset isgivenFig.5.Schottky barrier pinning factor S H in the (incorrect)model of Kurtin etal.Fig. 6.Log±log plot of 1= S À1 vs.e I À1for various semiconductors and insulators to verify the MIGS model of Schottky barrier pinning factor S .6J.Robertson /Applied Surface Science 190(2002)2±10by the difference in their electron af®nities,the `elec-tron af®nity rule'.A similar idea was that for no charge transfer,the band line-ups are derived by placing each semiconductor's band on an absolute energy scale such as those of the free atom energy levels [31].Tersoff [16]showed that the band offset between two semiconductors a and b is controlled by interface dipoles as in the Schottky barrier,and so the conduc-tion band offset is given by f n w a ÀF CNL ;a À w b ÀF CNL ;bS F CNL ;a ÀF CNL ;b(7)The offsets are now described by aligning the CNLs of each semiconductor,modi®ed by the S factor.For simple semiconductors like Si,e I is large,and so S is small and the third term was negligible in the original formulation,but it is retained here for wide gap oxides.For strong pinning,the alignment is just given by the alignment of the two CNLs.The CNL energy below the vacuum level is a measure of the mean electronegativity of the semiconductor,in the same way that the work function of a metal is propor-tional to the metal's electronegativity.Thus,Eq.(7)says that the band alignment is the difference in electronegativity screened by the S factor.A wide ranging quantitative comparison found that the CNL models gives a good description of the band offsets [30].The CNL is the branch point of the semiconductor interface states.It is the integral of the Green's func-tion of the band structure,taken over the Brillouin zone [17],G E ZBZ N E H d H EE ÀE H0(8)Cardona and Christensen later provided a quicker method using a sum over special points of the Bril-louin zone [5,32].G E X i 1E ÀE i (9)2.2.Application to oxidesThe band alignments for the various wide gapoxides in contact with metal or silicon are found by calculating their CNLs and S parameters.The S factors are found from (6)using the experimental values of e Iand are shown in Table 1.The CNLs were found by calculating the oxide band structures by the tight-binding method [5,6,8,33].The tight-binding para-meters are found by ®tting to existing band structures [9,10,34],photoemission spectra and optical data [2,35±37].The CNLs for the various oxides are given in Table 1,together with the experimental values of their bandgaps and electron af®nities [2,38].SrTiO 3is an important oxide for future DRAM capacitor dielectrics.SrTiO 3is also the most studied system and the best test of our calculations.Fig.7compares the predicted SBHs of SrTiO 3on various metals with the experimental values [30,39±43].The experimental data are quite scattered but are quite consistent with S !1and our calculated value of 0.28.This shows that SrTiO 3is a key oxide in the tests of Schottky barrier models.The calculated barrier height for SrTiO 3on Pt is 0.9eV ,which is close to the 0.8eV found by photoemission by Copel et al.[43].However we cannot account for the much larger S value found by Shimizu et al.[42].BaTiO 3has similar band offsets to SrTiO 3.PbTi x Zr 1Àx O 3or PZT is an important ferroelectric for non-volatile memories,optical memories and other applications.The predicted barrier height for Pt onTable 1Calculated values for various oxides of their CNL and conduction band (CB)offset with Si aGap (eV)EA (eV)CNL (eV)e I S CB offset (eV)SiO 290.9 2.250.86 3.5b Si 3N 4 5.3 2.1 4.10.51 2.4b Ta 2O 5 4.4 3.3 3.3 4.840.40.3BaTiO 3 3.3 3.9 2.6 6.10.28À0.1BaZrO 3 5.3 2.6 3.740.530.8TiO 2 3.05 3.9 2.27.80.180.05ZrO 2 5.8 2.5 3.6 4.80.41 1.4HfO 26 2.5 3.740.53 1.5Al 2O 38.81c 5.5 3.40.63 2.8Y 2O 362c 2.4 4.40.46 2.3La 2O 36c 2c 2.440.53 2.3ZrSiO 46.5 2.4 3.6 3.80.56 1.5SrBi 2Ta 2O 94.13.53.35.30.4aExperimental values [36,37]of the bandgap,EA [2,38],dielectric constant e I [37]are also given.In Eqs.(2)and (5),F S is the energy of the CNL below the vacuum level,in this table,it is its energy above the valence band.bExperimental values.cEstimated values.J.Robertson /Applied Surface Science 190(2002)2±107PZT (Pb 0.55Zr 0.45O 3)is 1.45eV ,which is close to the 1.5eV measured by Dey et al.[44].The electron barrier of Pt on PZT is larger than that on BST because its CNL lies lower in the gap.This is because of the different band structure of PZT,in which the Pb 6s and 6p states form the band edges and this tends to lower the CNL.The larger value of the hole barrier than the electron barrier means that PZT thin ®lms can have predominantly electron injection,even though bulk PZT tends to be p-type.SrBi 2Ta 2O 9(SBT)is an important ferroelectric for non-volatile memories [2,45].It does not suffer from the loss of switchable polarisation (fatigue)when used with Pt electrodes,which is a problem for PZT.Note that more recent optical data ®nd that the bandgap of SBT is 4.1eV [2].The Schottky barrier of Pt is predicted to be 1.2eV ,which is essentially the same as that found by photoemission [46].There is an important need for high dielectric constant oxides to act as gate oxides instead of silicon dioxide [3,4].This is because the SiO 2layer is now so thin (2nm),that it no longer acts as a good insulator because of direct tunnelling across it.The solution is to replace SiO 2with a thicker layer of a medium k oxide,with the same equivalent capacitance or `equivalence oxide thickness't ox .The oxides must also satisfy certain other conditions,including chemi-cal stability in contact with Si [47].This rules out Ti and Ta which both react with Si to form SiO 2.The other key requirement is that they act as barriers toboth electrons and holes [5,32].This requires that both their valence and conduction band offsets be over 1eV .There is presently considerable effort to identify the most effective oxide,from a choice of ZrO 2,HfO 2,La 2O 3,Y 2O 3,Al 2O 3and the silicates ZrSiO 4and HfSiO 4.The calculated CB band offsets with Si are given in Table 1and summarised in Fig.8.They are compared in Table 2with recent experimental values [48±53],which is seen to be in good agreement.The important feature of Ta 2O 5and SrTiO 3is that both of them have CB offsets on Si under 1eV ,in fact 0in the case of SrTiO 3.This prediction was recently con®rmed by photoemission data of Chambers et al.[48].This means that SrTiO 3or BST cannot be a good gate oxide.The calculated CB offset for Ta 2O 5is only 0.36eV for Ta 2O 5on Si.This is consistent with recent photoemission data of Miyazaki and Hirose [49].Data for Ta 2O 5gate FETS also showed only a small elec-tron barrier [50].The CB offsets for BST and Ta 2O 5and BST are small or negligible because the bandgap is quite small and the band offsets are so asymmetric.To increasetheparison of calculated and observed SBHs of SrTiO 3on variousmetals.Fig.8.Predicted band offsets of various oxides on Si.Table 2Comparison of calculated and experimental values [48±53]of conduction band offsets on SiCalculatedExperiment References Ta 2O 50.350Miyazaki SrTiO 3À0.1<0.1Chambers ZrO 2 1.4 1.4Miyazaki 2.0Houssa Al 2O 32.82.8Ludeke8J.Robertson /Applied Surface Science 190(2002)2±10CB offset,we must either increase the bandgap or lower the CNL.The gap can be increased by raising the TM d levels,by using4d or5d metals instead of3d metals or using group IIIB metals instead of group IV. We should use zirconates,not titanates.The gap of BaZrO3is2eV wider than BaTiO3.Its offset is0.8eV.A better strategy is to lower the CNL.The CNL is lowered if the metal valence is lowered from4to3. Indeed,in Y2O3and La2O3,the CNL is much lower in the bandgap.Y2O3and La2O3are the oxides with largest CB offsets for reasonable dielectric constants. ZrO2has a bandgap of5.8eV,which is slightly wider than BaZrO3,and it also has a lower metal/ oxygen stoichiometry.This gives a larger CB offset for ZrO2(1.4eV)than BaZrO3,and indeed one which is just high enough.HfO2is similar.The calculated CB offset of1.4eV for ZrO2compares with an experi-mental value of1.4eV from photoemission[51]and a value of2eV by internal photoemission[52].This CB offset is large enough for devices.Zirconium silicate ZrSiO4and hafnium silicate HfSiO4are glassy oxides with bandgaps of $6.5eV.ZrSiO4consists of chains of alternate edge-sharing ZrO4and SiO2tetrahedra,with addi-tional Zr±O bonds between the chains,leading to an overall six-fold Zr coordination.We estimate the bandgap of ZrSiO4to be6.5eV.The calculated CB offsets are1.5eV,slightly more than ZrO2.Al2O3has a bandgap of8eV close to SiO2but with a higher k($9).Its calculated CB offset is2.8eV, which compares exactly with that measured by Ludeke et al.[53].Overall,the agreement between the calculated and subsequent experimental values for CB offsets in Table2is surprisingly good.References[1]M.E.Lines,X.Glass,Ferroelectrics,Oxford UniversityPress,Oxford,1990.[2]J.F.Scott,Ferroelectrics Rev.1(1998)1.[3]G.D.Wilk,R.M.Wallace,J.M.Anthony,J.Appl.Phys.89(2001)5243.[4]A.I.Kingon,J.P.Maria,S.K.Streiffer,Nature406(2000)1032.[5]J.Robertson,J.Vac.Sci.Technol.B18(2000)1785.[6]P.W.Peacock,J.Robertson,Unpublished work.[7]L.F.Mattheis,Phys.Rev.B6(1972)4718.[8]J.Robertson,W.L.Warren,B.A.Tuttle,D.Dimos,D.M.Smyth,Appl.Phys.Lett.63(1993)1519.[9]R.D.King-Smith,D.Vanderbilt,Phys.Rev.B49(1994)5828.[10]J.Robertson,W.L.Warren,B.A.Tuttle,J.Appl.Phys.77(1995)3975.[11]R.E.Cohen,Nature358(1992)136.[12]J.Robertson,C.W.Chen,W.L.Warren,C.D.Gutleben,Appl.Phys.Lett.69(1996)1704.[13]R.H.French,S.J.Glass,F.S.Ohuchi,Y.N.Xu,W.Y.Ching,Phys.Rev.B49(1994)5133.[14]W.MoÈnch,Phys.Rev.Lett.58(1987)1260.[15]W.MoÈnch,Surf.Sci.300(1994)928.[16]A.W.Cowley,S.M.Sze,J.Appl.Phys.36(1965)3212.[17]C.Tejedor,F.Flores,E.Louis,J.Phys.C10(1977)2163.[18]J.Tersoff,Phys.Rev.Lett.52(1984)465.[19]J.Tersoff,Phys.Rev.B30(1984)4874;J.Tersoff,Phys.Rev.B32(1985)6989.[20]L.J.Brillson,Surf.Sci.300(1994)909.[21]W.E.Spicer,T.Kendelewicz,N.Newman,K.K.Chin,I.Lindau,Surf.Sci.168(1986)240.[22]R.E.Allen,O.F.Sankey,J.D.Dow,Surf.Sci.168(1986)376.[23]S.Kurtin,T.C.McGill,C.A.Mead,Phys.Rev.Lett.30(1969)1433.[24]S.G.Louie,J.R.Chelikowsky,M.L.Cohen,Phys.Rev.B15(1977)2154.[25]M.Schluter,Phys.Rev.B17(1978)5044;M.Schluter,Thin Solid Films93(1982)3.[26]W.Gordy,W.J.O.Thomas,Phys.Rev.24(1956)439.[27]H.B.Michaelson,J.Appl.Phys.48(1977)4729.[28]W.MoÈnch,Phys.Rev.Lett.58(1986)1260.[29]W.MoÈnch,Europhys.Lett.27(1994)479.[30]R.C.Neville,C.A.Mead,J.Appl.Phys.43(1972)4657.[31]W.A.Harrison,J.Vac.Sci.Technol.14(1977)1016.[32]M.Cardona,N.E.Christensen,Phys.Rev.B35(1987)6182.[33]E.T.Yu,J.O.McCaldin,T.C.McGill,Solid State Phys.46(1992)1.[34]J.Robertson,C.W.Chen,Appl.Phys.Lett.74(1999)1168.[35]G.M.Rignanese,X.Gonze,A.Pasquarello,Phys.Rev.B63(2001)104305.[36]R.H.French,J.Am.Ceram.Soc.73(1990)477.[37]E.D.Palik,Handbook of Optical Properties of Solids,V ol.1±3,Academic Press,New York,1985.[38]W.Schmickler,J.W.Schultze,in:J.M.O'Bockris(Ed.),Modern Aspects of Electrochemistry,V ol.17,Plenum Press, London,1986.[39]G.W.Dietz,W.Antpohler,M.Klee,R.Waser,J.Appl.Phys.78(1995)6113.[40]H.Hasegawa,T.Nishino,J.Appl.Phys.69(1991)1501.[41]K.Abe,S.Komatsu,Jpn.J.Appl.Phys.31(1992)2985.[42]T.Shimizu,N.Gotoh,N.Shinozaki,H.Okushi,App.Surf.Sci.117(1997)400;()T.Shimizu,N.Gotoh,N.Shinozaki,H.Okushi,Mat.Res.Soc.Symp.Proc.(2000).[43]M.Copel,P.R.Duncombe,D.A.Neumayer,T.M.Shaw,R.M.Tromp,Appl.Phys.Lett.70(1997)3227.[44]S.K.Dey,J.J.Lee,P.Alluri,Jpn.J.Appl.Phys.34(1995)3134.[45]C.A.Paz de Araujo,J.D.Cuchiaro,L.D.McMillan,M.C.Scott,J.F.Scott,Nature374(1995)627.[46]C.D.Gutleben,Appl.Phys.Lett.71(1997)3444.[47]H.J.Hubbard,D.G.Schlom,J.Mater.Res.11(1996)2757.J.Robertson/Applied Surface Science190(2002)2±109[48]S.A.Chambers,Y.Liang,Z.Yu,R.Dropad,J.Ramdani,K.Eisenbeiser,Appl.Phys.Lett.77(2000)1662.[49]S.Miyazaki,Appl.Surface Science(2002)``these proceed-ings''.[50]S.Miyazaki,M.Narasaki,M.Ogasawara,M.Hirose,Microelec.Eng.59(2001)373.[51]A.Chatterjee,et al.,IEDM Tech Digest,1998,p.777.[52]M.Houssa,M.Tuominen,M.Nailli,V.Afansev, A.Stesmans,J.Appl.Phys.87(2000)8615.[53]R.Ludeke,M.T.Cuberes,E.Cartier,Appl.Phys.Lett.76(2000)2886;D.J.Maria,J.Appl.Phys.45(1974)5454.10J.Robertson/Applied Surface Science190(2002)2±10。

1介观物理讲义第一讲

杨氏双缝干涉实验
e
ik 1
e
ik 1
e
ik 2
eik 2

电子可以分为两条路走，在 B 点交汇后，若两电子无相位差，则不会有干涉效应。但是加上磁场后，若走两条路的电子在 B 点产生相位差，则会出现干涉效应。产生相位差不用磁场行吗？可以，我们可以使 l1 l2 来实现，这由上边的右图可以看出。但是电极绕环运动造成相位差实现很困难。 A—B 效应说明了粒子的波动性，证明量子力学正确性。
第一章基本准备
第一节能带结构
自由电子的能量是连续的：E=
2k 2 2m
问题：电子在晶格（周期势）中，本征态是怎样的？即电子的波函数和能级是怎样的？
一．晶格特点
（1）晶格的特点：晶格具有平移对称性，基本重复单元称为元胞（2）周期性边界的困难及解决方法：虽然晶格具有周期性，而且决定材料性质的是材料内部的电子，但材料还是有表面。实际的晶体体积总是有限的。因此必须考虑边界条件。在固体问题中，为了既考虑到晶体势场的周期性，又考虑到晶体是有限的，我们经常合理地采用波恩-卡门提出的周期性边界条件：即有限晶体大小作无限排列，并假定波函数具有长度为 L 的周期。采用周期性边界条件以后，具有 N 个晶格点的晶体就相当于首尾衔接起来的圆环。

二．波函数—Bloch 函数
下面求单电子在周期势中的状态 Hamiltonian
p2 （r ），（r） V ( r - ） H= 2m
周期性条件：
(r ) (r ) 是错误的，因为 (r ) 并不是一个宏观物理量。
G
0

骨架非稠合的非富勒烯受体

骨架非稠合的非富勒烯受体占肖卫【期刊名称】《物理化学学报》【年(卷),期】2019(035)004【总页数】2页(P351-352)【作者】占肖卫【作者单位】北京大学工学院材料科学与工程系,北京 100871【正文语种】中文相对于富勒烯类电子受体，新型非富勒烯受体具有吸光能力强，能级和结构可调等优点，对于提升有机太阳电池光电转换效率具有重要意义。

近年，基于稠环结构的电子受体(FREAs)受到了国内外研究者们最多的关注 1,2。

这一类分子具有良好的骨架平面性，高度离域的电子结构和强聚集倾向的末端基团有利于分子间的π-π堆积和电荷转移。

另外，基于FREAs体系的有机太阳电池能量损失也可以低至0.4-0.5 eV 3。

基于以上稠环结构的设计策略，科研人员设计并合成了许多稠环电子受体，所制备的有机太阳电池器件效率突破了 14% 4。

然而，我们注意到FREAs骨架通过化学键联稠合，往往需要涉及多步的化学反应，合成成本偏高。

并且目前各个课题组的研究方向更是在分子结构中并入了更多的芳环或者使用更复杂的稠环结构，其合成的难度还会成倍增大 5,6。

随着电池效率的不断提高，简化分子结构，降低合成成本对实现有机太阳电池的规模应用具有重要的应用价值。

浙江大学陈红征教授研究团队尝试简化FREAs的结构，提出采用非稠合环核作为构筑单元，利用分子内氢键构筑非富勒烯受体，成功制备了效率超过11%的有机太阳电池7,8，但其化学结构中仍包含了复杂的稠环结构。

如何使用巧妙的化学设计来避免复杂的稠环结构的使用，简化合成步骤，并且保留FREAs的优势，值得进一步研究。

最近，该团队进一步设计了一种结构简单的骨架非稠合的电子受体分子(ICTP)，中心骨架仅有一个苯环和两个噻吩环；同时利用该团队之前掌握的碳氢活化技术 9，简单高效地合成了目标产物，并成功将其应用到了有机太阳电池中。

该工作已在物理化学学报上在线发表(doi: 10.3866/PKU.WHXB201805091) 10。

化学常用英语词汇

化学常用英语词汇————————————————————————————————作者：————————————————————————————————日期：?化学常用英语词汇2. Paｒtial Ｐｒｅsｓurｅs 1．The Ｉdｅal－Gas Equａtioｎ理想气体状态方程?分压３．Real Gaｓeｓ: DeviatioｎfroｍIdealＢｅhaviｏr 真实气体:对理想气体行为的偏离４. Ｔhe van derＷaaｌs Equation范德华方程?５.System and Surrｏuｎ6. State aｎd Stａte Fｕｎctiｏns 状态与状态函数dｉｎgs 系统与环境?7．Ｐrocess 过程?８．Ｐhaｓe 相9.Ｔｈe Ｆｉrst Ｌaw of Theｒmoｄｙnamiｃs热力学第一定律10. Ｈeat and Work 热与功?1１. Endothｅrｍic ａnd Exotherｍｉc Prｏｃesseｓ吸热与发热过程?１２. EnｔhａlpieｓoｆＲeacｔioｎs反应热?１３. Hess’s Lａw 盖斯定律?１4.Entｈａlpies of Formatioｎ生成焓１５. ＲeacｔiｏｎRatｅs反应速率?1６. RｅａｃｔiｏｎOｒｄeｒ反应级数18. Acｔｉvation Energy活化能17. Ｒate Coｎｓtanｔs 速率常数?20. Ｒeａctiｏn 1９．TｈｅArｒｈｅｎius Eｑｕation 阿累尼乌斯方程?Mechanismｓ(机制) 反应机理21. Homogｅneoｕs Caｔaｌｙsｉｓ(catalysis英[k?'t?ｌ?s?s］n.催化作用）均相催化剂22．Heｔｅｒogｅnｅous Caｔalｙsｉs 非均相催化剂24. Tｈe EquｉlibriuｍＣoｎstanｔ平衡常数23. Ｅnzymeｓ酶?25．ｔhｅDｉrection oｆReaction 反应方向2６. Le Chatｅlier’s Prｉnciple 列沙特列原理27. Eｆfects of Vｏlumｅ, Pｒesｓure，Tｅmｐerａtuｒe Cｈａｎgｅs and Catal28. Ｓpontaneｏus Pｒocesses ｙｓts体积，压力，温度变化以及催化剂的影响?自发过程(spontanｅouｓ［sp?n?ｔe?nｉ?ｓ] adj.自发的;自然的;天然产生的;无意识的)29. Ｅｎtropy (Sｔaｎｄａrd Entrｏpy) 熵（标准熵）3１. 3０.Ｔhe Ｓecond Lａｗｏf Thermｏdynａmics热力学第二定律?EntropｙChａｎges 熵变?32. StanｄarｄFreｅ－Energy Changeｓ标准自由能变33. Ａcid-Bases酸碱34. ThｅDissｏciation of Wateｒ水离解3５．Tｈe Pｒoｔｏn in Ｗater 水合质子?3６.TheｐHＳcaｌes ｐH 37．Brｏnstｅd-Lowｒy AcidｓandＢases Bronstｅd－Lowry 酸和碱值?39. Conｊｕgａte Aciｄ-Ｂa 38．Ｐrotoｎ-Trａnsfｅr Reactions 质子转移反应?ｓe Ｐaiｒs 共轭酸碱对41. Leｗi ４0. Ｒelatiｖe Stｒenｇth ｏf Acｉds and Ｂaｓes 酸碱的相对强度?42.Hydrolｙsis ｏf ＭetaｌIons 金属离ｓAcids and Baseｓ路易斯酸碱?子的水解?４3.Buffer Soｌutiｏnｓ缓冲溶液?4４．The Ｃoｍmｏn-Ｉｏn Effects 同离子效应４5. Ｂｕffer Ｃapacity 缓冲容量４6. Ｆormａtiｏn of Ｃoｍplex Ions 配离子的形成?4７．Soｌubilｉtｙ溶解度４8. ThｅSｏｌubｉliｔy-Pｒoduｃt Coｎstａnt Ksp溶度积常数50. Sel 49.Ｐｒｅcｉｐiｔａtion and sｅｐaration of Ionｓ离子的沉淀与分离?ｅｃｔive Pｒecipｉtａtion oｆIons 离子的选择沉淀52. Oxidation N 5１．Oｘidaｔｉon－ReductioｎRｅａctions 氧化还原反应?ｕmber氧化数53. Balａncｉng Oｘidatiｏn-ＲｅdｕcｔioｎEquatiｏnｓ氧化还原反应方程的配平56. Vｏltaic Cell 伏54．Ｈａlf-Ｒeａctｉon 半反应?55．Galvani Cell原电池?特电池57．Ｃeｌl EMF 电池电动势59.Oｘidizing 58. ＳtandaｒｄEleｃｔrｏde Poteｎtｉａｌs 标准电极电势?ａnd Reducing Agents氧化剂和还原剂６0.Ｔhe Ｎeｒnst Equａtion能斯特方程61. Elecｔｒolｙsis 电解6２．Ｔｈe WavｅＢeｈavior of Eｌectrons 电子的波动性６３. Boｈr’ｓMoｄｅｌoｆＴｈe Hｙdrｏgｅn Atom氢原子的波尔模型?6４. Line Ｓpｅctra 线光谱65. Ｑｕaｎtum Numbeｒｓ量子数6６. Eｌectron Sｐin 电子自旋67. Atｏmic Orbital原子轨道68. Tｈｅs (p, d, f) Ｏｒｂitaｌs(p,d,ｆ)轨道69. Maｎy-Elecｔron Atomｓ多电子原子71. Ｔhe Ｐaｕli Exｃlusiｏn Pｒiｎcip ７0. Eneｒgies of Orｂitａｌ轨道能量?ｌe 泡林不相容原理?７２. EleｃｔroｎConｆiguratｉoｎｓ电子构型73. ＴhｅＰeriodic Ｔaｂle 周期表75．Group 族?７6. Iｓotoｐeｓ, Ａtｏmic Numｂerｓ, ａnd ７4.Roｗ行?Mass Ｎuｍberｓ同位素,原子数，质量数78.Ｒ７7. Ｐeｒiodic ProｐeｒｔieｓoｆthｅEｌemenｔs 元素的周期律?ａｄiuｓof Atoms原子半径７9．Ionｉzａtion Energｙ电离能80. Electronegａtivｉty 电负性81. EｆfeｃtivｅNｕclear Chaｒge有效核电荷?８2.Eleｃtｒon Ａｆfｉn ｉｔies 亲电性8３. Ｍetals 金属?８4. Ｎｏnmetals 非金属85. Vaｌeｎce Boｎd Ｔhｅorｙ价键理论87. Orｂital Overlap 轨道重叠?88．Muｌti 8６．Ｃovaｌenｃe Bond 共价键?89. HybriｄOrｂｉtａｌ杂化轨道ｐleＢｏnds 重键?90．The ＶSEPR Moｄel 价层电子对互斥理论91.Molecuｌａr Geomeｔries 分子空间构型93. Diatomic Mｏlｅculeｓ双原子分子92．Moleｃular Ｏrｂital分子轨道?94. Bond Lenｇtｈ键长95. Ｂond Ordeｒ键级96. Ｂｏnd Ａｎgles 键角98. Ｂond Poｌarｉｔy 键矩?９9．DipolｅM 97．Bond Enｔhalpｉｅs 键能?1０１.Ｐｏmentｓ偶极矩?１00. ＰolaｒｉtｙMolecuｌes 极性分子?102. Ｃｒyｓtａl Sｔructure 晶体结构olyatomic Moｌecules 多原子分子?104. Ｃｌｏｓe Packｉnｇof Spheres 球密堆积103. Nｏn-Ｃrystal 非晶体??105. Mｅｔaｌｌic Solｉｄs 金属晶体10６. Metａllic Bonｄ金属键1０７.Allｏys合金?１０８. Ｉonic Ｓoｌids离子晶体109. Iｏn-Dｉpoｌe Forces 离子偶极力?１１0. Mｏｌeculａr Forces 分子间力?111.IntermoｌｅcｕｌａｒForcｅs分子间作用力1１2. Ｈydrogen Bｏndiｎg 氢键11３. Ｃovaｌent－Nｅtｗork Soliｄｓ原子晶体１１4. Cｏmpounｄs化合物?1１5. The Ｎｏmｅnclａturｅ, Ｃomｐｏｓiｔionand Struｃｔuｒe oｆComplｅxes 配合物的命名,组成和结构?１16. Chaｒges，Cｏordiｎation Nｕmｂeｒs, ａnd Geomeｔrｉｅｓ电荷数、配位数、及几何构型117. Ｃheｌateｓ螯合物1１8. Iｓomerism异构现象11９.Structｕral Iｓomerism结构异构?1２0.Sｔｅrｅoiｓoｍｅrｉsm 立体异构?121. Magnetism磁性122. Ｅｌectron Configｕｒations in Ｏctａhｅdral Compｌexes 八面体构型配合123. Teｔｒaｈeｄrａl andＳqｕａre-pｌanar Coｍplexes 四物的电子分布?面体和平面四边形配合物?１24.Gｅneｒal Chａｒaｃtｅristiｃs 共性126.Alｋali Metaｌs 碱金属1２５．s－BlocｋEleｍeｎｔs s区元素?12７. Ａlｋalｉne Earth Metaｌs 碱土金属?１２８．Hydrides 氢化物129.Ｏｘideｓ氧化物１３0．Pｅroｘides and Superoxides 过氧化物和超氧化物?１31. Ｈyｄｒｏxidｅs 氢氧化物１3２. Salｔs 盐133. p－Ｂloｃk Eｌｅmentｓp区元素１34. Boｒｏn Group (Ｂoron, Aluminｉum, Gａllium,Iｎdium, Thａｌliuｍ) 硼族（硼，铝,镓,铟，铊)?１35．Borａne 硼烷136. ＣａrbｏｎGroup(Cａrbｏn, Sｉlicｏｎ, Geｒmａnium, Ｔin,Lead）137．Graｐhｉte, CａｒboｎMonoxｉｄe, Ｃa 碳族（碳，硅，锗，锡，铅）?138. Carboｎｉc Aｃｉｄ, CａｒｂoｎＤioxidｅ石墨,一氧化碳,二氧化碳?13. Oｃcurreｎce and rbonaｔes aｎｄＣaｒｂideｓ碳酸，碳酸盐，碳化物?9Ｐrｅparaｔｉon ｏf Ｓilicｏn硅的存在和制备140. Ｓｉlicic Aciｄ,Silicatｅs 硅酸，硅酸盐1４1. Nitroｇen Gｒouｐ(Pｈosphoｒus，Arsｅniｃ, Aｎtimoｎy, aｎd Bisｍuth)氮族(磷，砷,锑，铋)142. Aｍmonia, NｉtriｃAciｄ, PｈosｐhoriｃAcｉd氨，硝酸，磷酸?1４3. Ph ｏｓpｈｏｒaｔes, phoｓphｏｒｕs Ｈａlides磷酸盐,卤化磷144. Oxygen Grｏｕp （Oｘygen,Ｓulｆｕr, Seleｎiｕm, and Tｅｌｌuｒium）氧族元素(氧,硫，硒,碲）?1４5. Ozonｅ, Ｈydrogｅn Ｐeｒｏxiｄe 臭氧，过氧化氢?１４6. Sulfides 硫化物14７．Halogｅｎs （Fluoｒｉne, Chlｏriｎｅ, Bｒomｉne, Iodine)卤素(氟,氯,溴,碘)14９. The NobｌｅＧａseｓ稀有气148．Halｉdes, Cｈloride 卤化物,氯化物?体151. d-Block elｅmeｎts d区元150.Ｎoｂlｅ-Gas Compounds 稀有气体化合物?素?１52. Transition Meｔals 过渡金属153. PotasｓｉuｍDiｃhrｏmatｅ重铬酸钾?１5４.ＰｏtａssiuｍPｅrmａnganａte 高锰酸钾155. Irｏn Copper ZinｃMercury 铁,铜,锌,汞?１5６. f-BlｏcｋElemeｎtｓf区元素?１５nthanidｅs镧系元素15８．Ｒａdioaｃtiｖitｙ放射性159. Nuclear Ｃheｍｉstry 核化学161. ＮuｃlearＦusioｎ核聚变160．NｕclｅａｒFｉssion核裂变?162．anａlｙtｉcaｌcheｍｉsｔry 分析化学１63. qualiｔａｔive anａlysｉs 定性分析?164．quantｉtative analysｉs 定量分析166. instruｍeｎtaｌanalysｉｓ仪器分析16５. ｃhemical aｎalysis 化学分析?1６7. titｒimetｒy 滴定分析1６8. ｇｒａｖｉmetriｃanalyｓis 重量分析法1７０. chｒomａtｏgraｐhic anａｌysｉs色谱分析?１７1６９. rｅgent试剂?1. prodｕct 产物172.elｅctroｃhemical aｎalysis电化学分析173.oｎ－ｌine anaｌysiｓ在线分析175. ｃhａｒactｅriｓtic 表征174．mａcｒｏanalｙsiｓ常量分析?17６．micro analysiｓ微量分析?１77. ｄeforｍａｔion analysis 形态分析178. sｅｍiｍicroａｎalysis半微量分析?179．systematicａｌｅｒｒor180. ｒoutineａnalｙsiｓ常规分析?１81.rａndｏｍerrｏr偶系统误差?182．arｂitｒaｔion analysｉs 仲裁分析?１83. ｇrｏss error过失误然误差?184. normaｌdistribｕtion 正态分布差?185. accｕrａcy 准确度18６. deｖｉatiｏn偏差187. ｐreｃiｓioｎ精密度18８. relativｅstandaｒd devｉation 相对标准偏差（RSD)189.coefｆiｃient ｖariａｔｉon 变异系数(CV）190. ｃoｎfidence lｅvel 置信水平?１9１. confiｄenｃｅinterval 置信区间?19２. ｓigｎificanｔtest 显著性检验1９4. standard solution 标准溶液１9３．sｉgnifiｃant fiｇure有效数字??195. ｔitraｔiｏn滴定１96.stｏichｉometrｉc point 化学计量点198．ｔiｔｒａｔｉon eｒｒｏr 滴定误差?1 197.end poｉｎt 滴定终点?９9．priｍary ｓtanｄaｒd 基准物质2０0. ａmountｏf subｓtance物质的量?201．stａndardizａtion 标定20２02. cｈemical reaｃtｉｏn化学反应?203. ｃｏncｅntraｔｉｏｎ浓度?４.chemｉcaｌeｑuiｌｉｂriｕm 化学平衡?20５. titer 滴定度?２06. gｅner ａl eqｕaｔion ｆoｒ a chemicａl rｅaｃｔｉoｎ化学反应的通式207．protoｎｔheory of aｃid-bａse 酸碱质子理论2０8. aｃiｄ－bａsｅtiｔｒaｔion 酸碱滴定法?２０９．dissoｃｉaｔiｏn2１0. ｃonjugatｅaｃid－ｂａse ｐａiｒ共轭酸碱conｓｔaｎt 解离常数?对?2１１. aceｔｉc acid 乙酸?２12．ｈydronｉｕm ioｎ水合氢离子2１4. ion-prｏｄucｔconｓtａｎt of water水213．eｌectroｌｙte 电解质?的离子积2１６. ｐroton coｎdition 质子平衡215. ionｉzatiｏn 电离?21８. ｂｕffeｒsｏｌｕｔion 缓冲溶液217．ｚerｏlevｅ零水准?219. mｅthyl ｏraｎgｅ甲基橙220.acid－bａse ｉndicator 酸碱指示剂2２１．phenoｌphtｈaleｉn酚酞22２．ｃoｏrdinatiｏn cｏmpoｕｎd 配位化合物?２23. cenｔｅr ioｎ中心离子２２4．cｕmulative staｂilｉty cｏnstaｎt 累积稳定常数2２５.aｌpｈａcoeffiｃient 酸效应系数2２7. ligaｎｄ配位体2２６.ｏveraｌl stabilitｙｃｏnｓtant总稳定常数?228. eｔhyｌeｎeｄiamine teｔrａaｃeｔiｃacｉd 乙二胺四乙酸23０. cｏoｒdinａtioｎａｔｏ2２9. side reaｃtioｎcoeffｉcient 副反应系数?23２. lone ｐaiｒeleｃ231. cｏｏrdinatiｏn nｕmbｅr 配位数?m 配位原子?tron 孤对电子234. mｅｔal inｄicａtor金属指示剂23３.chelate cｏmｐounｄ螯合物?23５. chelａｔiｎg ａgent 螯合剂237．ｄemａsking 解蔽２３6.maskiｎg 掩蔽?238. ｅｌecｔrｏn电子24１. cataｌｙｓt催化剂2３9. catalysis 催化?24０.oｘidａtiｏｎ氧化?24２. ｒｅduｃtioｎ还原２43．caｔalytic reaction催化反应244. reaｃtion ｒate 反应速率?２４5．electｒodｅpotential电极电势247. ｒｅｄox couｐlｅ氧化还?246．aｃｔｉvation eｎergy 反应的活化能?原电对２48. poｔａssｉuｍperｍanganａte 高锰酸钾249. ｉｏdｉmｅtry 碘量法?2５0. poｔasｓium dichromate 重铬酸钾?２51.252. rｅdｏｘindｉcator 氧化还原指示cerimetrｙ铈量法?２53. oxyｇen cｏnsｕming 耗氧量(OC）２54. chｅmicａl ｏxygen dｅmａｎded化学需氧量(COＤ)２55．dｉｓsolｖed oｘygｅｎ溶解氧（DO)25６. precipｉtａtiｏｎ沉淀反应258. ｈeｔｅrogeneous eqｕｉlibrium oｆiｏｎ257.arｇｅntｉmetry银量法?s 多相离子平衡260. postprecｉpitation 继沉淀２59．ａgｉnｇ陈化?2６1.copｒｅcｉpitatioｎ共沉淀264．decａntatｉｏｎ倾泻法26３. fｉtrａtion 过滤?26２. igniｔion灼烧?２65．cｈemical fａctoｒ化学因数2６6.spectrophotｏmetｒｙ分光光度法?２67．colorimetｒｙ比色分析?2269. abｓorptiviｔy 吸光率６8. ｔraｎｓmｉtｔaｎce透光率?2７０．ｃａlibraｔiｏn cuｒve 校正曲线２7１.ｓtaｎｄard curvｅ标准曲线?２７2. mｏnｏcｈｒomatｏｒ单色器２７3．soｕrce光源２7４. wavｅｌeｎgtｈdispeｒsion 色散２７5．ａbｓoｒptiｏnｃell 吸收池27７. bａtｈochｒoｍｉc ｓhｉf红移27６. detector 检测系统?279．hypｏｃhｒomic shｉft 紫278. Ｍｏｌar absoｒptiｖｉty 摩尔吸光系数?移２80. aｃetylene乙炔282.ａcetylatｉng aｇent 乙酰化剂２8１. etｈylene乙烯?285．ｅtｈyl alcoｈ284.adiethylｅther乙醚?283.acｅtiｃacid 乙酸?ol 乙醇287. β-ｄｉcａrboｎtl compound β–二羰基化合286. acｅｔaldehtdｅ乙醛?物289. biｍoleculａr ｎ２８8. ｂiｍoleculａr eｌｉmiｎatｉon 双分子消除反应?ucleophｉlic subｓtｉtution 双分子亲核取代反应291. ｍolecuｌarｏrbital thｅｏ290. open chaiｎcompound 开链族化合物?ｒｙ分子轨道理论29２. chiｒal molｅcｕle 手性分子?２93.tautoｍｅｒism 互变异构现象?2９4.rｅａcｔion mｅchaｎisｍ反应历程２95. chｅmｉcaｌshift 化学位移296. Ｗａldｅｎｉnversiｏ瓦尔登反转n?２97. Enantｉｏｍoｒpｈ对映体?2９8．ａddｉｔion rea cｔion 加成反应?2９9. dｅｘｔro- 右旋302．steｒeo ｉsoｍｅr 301. sｔｅreocｈemiｓtｒy 立体化学?300. levo- 左旋?30３．Lucas rｅａgｅnｔ卢卡斯试剂?３04. ｃoｖalｅnｔbond 立体异构体?共价键?３05. ｃonjugated dｉene 共轭二烯烃306. cｏnｊｕgated doｕｂｌe bｏｎｄ共轭双键307. conjｕｇａｔed sysｔｅm 共轭体系308.ｃonjugａted effect 共轭效应?３09．isｏmer 同分异构体311. organiｃｃheｍｉｓtry 有机化学３10. isｏmeriｓｍ同分异构现象?31２.hｙbriｄｉzａｔｉｏn 杂化313. hyｂrid oｒbital 杂化轨道315. perｏxｉde effeｃｔ过氧化314．heterocycｌiｃcoｍpound 杂环化合物?物效应ｔ316. ｖalｅｎcｅｂond theory价键理论318．elｅctron-attracting grｏｕp 吸电子基317. sｅquence rule 次序规则?319.Ｈuckeｌrｕle 休克尔规则?３20．Ｈinsbｅrg ｔeｓt 兴斯堡试验３21．iｎfrareｄspｅctrum 红外光谱32２.Michaｅｌrｅacton 麦克尔反应?３23．halｏｇenａted hｙｄrocarbon 卤代烃３24．haloｆｏｒm reａｃtion 卤仿反应32６. Ｎewmaｎｐｒojeｃtｉ325. ｓystematｉc ｎomｅnｃlatur 系统命名法e?on 纽曼投影式327. ａromatiｃcoｍpｏund 芳香族化合物?328. aroｍａｔiｃchaｒactｅｒ芳香性r?3２9．Ｃlaisen ｃｏｎｄｅｎsatiｏn reactｉoｎ克莱森酯缩合反应330. Claisｅn rearrangement 克莱森重排3３1. Diels-Aldｅr ｒｅatioｎ狄尔斯-阿尔得反应33２. Cｌemmｅｎｓen reductiｏn 克莱门森还原３3３. Canniｚzaro rｅactioｎ坎尼扎罗反应334. ｐosｉtiｏnal ｉsoｍers 位置异构体336. 33５. uｎｉmolｅcular eliｍiｎation reaｃtiｏｎ单分子消除反应? unimolecｕlar nuｃｌeophilｉcｓｕbsｔｉｔution 单分子亲核取代反应?３37. benzeｎe 苯?３３８.ｆuｎｃtional ｇroｕ官能团p３３9. ｃonｆｉguraｔioｎ构型341．ｃoｎfomatiｏnａｌｉｓome构象异构体?３40. confｏrｍatioｎ构象?３4２．electrophilic adｄitioｎ亲电加成?３43. eleｃtrophｉｌicｒeagent 344. nuｃleｏｐhｉlｉcａdｄｉtion亲核加成?34５. nuｃleophiｌ亲电试剂?ic reａgent亲核试剂34６．ｎuｃleophiｌｉc suｂstitutｉon ｒｅaｃtiｏｎ亲核取代反应?３4７. ａｃtivｅｉｎtｅrｍｅdiatｅ活性中间体?３48．Saytｚeff rulｅ查依采夫规则3４9. cｉs-trans isｏmeｒｉsm 顺反异构350. indｕｃtiveｅffｅct诱导效应t3５１．Ｆehliｎg’s reaｇent 费林试剂?３5２.pｈａse tranｓfｅr caｔａlysis 相转移催化作用353.ａlipｈaｔic compｏund 脂肪族化合物?3５4. eliｍｉnatiｏn reacｔｉon 消除反应?３５5. Grignard reagent 格利雅试剂３5６. nｕclear magｎetｉc ｒｅsonａnce核磁共振?3５７．alkｅnｅ烯烃359. leａvｉng ｇｒoup离去基团?358. aｌlｙl caｔｉｏｎ烯丙基正离子?３６0．ｏptical actｉviｔy 旋光性?3６1. bｏaｔconfomａtion船型构象?３62. ｓｉlveｒmiｒror rｅaｃｔion银镜反应３63．Fischeｒproｊeｃｔｉon 菲舍尔投影式365. Ｆriｅdｅl-Crafｔs rｅacｔiｏ3６4. Kekｕlｅsｔｒucture 凯库勒结构式?n 傅列德尔-克拉夫茨反应366．Ketonｅ酮368. carbｏxylｉc ａcｉｄderivatｉve 羧酸3６7．carboxylｉc acｉｄ羧酸?衍生物369．hｙdrｏboratiｏn 硼氢化反应370. bond oength 键长37１. bｏnd energy 键能374．c 372．ｂoｎd ａｎｇle 键角?３73．ｃaｒboｈyｄratｅ碳水化合物?ａrbocatｉoｎ碳正离子375.cａrbaｎｉon 碳负离子３76. alcohoｌ醇3７7. Gofmann ｒule 霍夫曼规则?３78. Aｌdehyde 醛380.Polｙｍer 聚合物３79. Etｈer 醚?。

SCI_Chem 影响因子

Abbreviated JournalTitle(linked to journal information)Total CitesImpact Factor5-YearImpactFactor Immediacy Index综合1Nature 0028-0836********.59738.1599.2432Science0036-807550848931.02733.587 6.6913P Natl Acad Sci Usa 0027-84245349519.73710.583 1.893化学综合1Chem Rev 0009-266511259641.29845.79514.3352Nat Mater 1476-11224634835.74942.3768.4113Nat Nanotechnol 1748-33872192031.1736.011 5.8764Chem Soc Rev 0306-00124764624.89230.1817.9975Prog Mater Sci 0079-6425592123.19422.3337.2176Nat Chem 1755-4330865221.75723.02 5.5327Accounts Chem Res 0001-48424211220.83324.633 5.2958Nano Today 1748-0132294417.68918.1920.7849Annu Rev Mater Res 1531-7331525916.17914.4950.66710Surf Sci Rep 0167-5729411515.33322.2817.7511Adv Mater 0935-96489195214.82913.86 2.55712Mat Sci Eng R 0927-796X 485013.90218.9740.66713Angew Chem Int Edit 1433-785122989413.73413.56 2.95914Annu Rev Phys Chem 0066-426X 700213.36518.121 4.13815Nano Lett 1530-69848843113.02514.132 2.47116Acs Nano 1936-0851*******.06212.524 1.9417Energ 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20850.01330.806 409 4.50.027060.735 774 3.20.034350.762 15287.90.107180.745 739 5.40.053960.715 227.60.001180.774 105 5.10.007480.647 129 4.90.00780.74475 3.50.002990.639212 3.70.013920.784 201 5.60.009290.599 500 6.30.06138 1.238 >10.00.00042 1.049 290 6.10.019640.625 251 5.60.017330.895 12498.40.075460.68 241 2.20.005560.628 1341 6.70.120620.829 651 6.90.026690.572 224 5.10.010210.672 290 5.30.013220.702 194 1.60.002660.7278>10.00.000620.792 314>10.00.019270.649 32830.001390.381 520 6.30.034550.62153 5.20.004350.904 200 1.30.002460.856 109 3.70.00563143 5.80.013670.825 439 4.20.025470.66 441>10.00.03210.853 17290.80.002020.494 1527.40.009010.741 624 2.40.016810.714 337 6.40.02850.71 173 1.90.002010.614 124 6.30.008010.593 2207.60.010810.602 4708.20.028730.596 221 5.20.00853 1.29 4957.50.036490.714 967.20.003150.52311>10.00.000450.543 184 3.50.006730.588 1064 2.80.017560.666 2437.60.014140.744 257.10.002380.868 105130.022770.574 10130.003550.834 2518.20.017620.63 16669.90.081330.508 1478 4.10.10840.548 14830.008560.8753427.80.015630.587 559.80.002470.6496 1.50.001250.668648.10.002270.561 178 6.20.010850.6 247>10.00.011750.526 202 5.20.013550.701 1484 5.40.069550.546 116 6.40.005740.60572 2.10.00140.58954>10.00.004010.856 351 6.60.011110.57 960 3.90.021660.681 1549.50.006150.597 5790.008180.646 6720.0008353 2.30.00061176 2.60.005320.633 1947.80.016490.569 223 5.60.014960.968 25280.006360.457 1626 5.50.049760.537 1977.10.008730.585 128 5.40.00580.57919>10.00.001080.734 650 3.70.017210.673 9419.10.050830.59113>10.00.00130.598 21090.007690.475 906>10.00.066080.687 350 3.90.005590.396 2247.80.01640.479 1789 5.50.074220.539 419>10.00.014550.491 579 6.80.034280.585 11717.30.084950.73 918.60.003920.471 458.60.00220.655 100 6.20.007370.666 335 5.10.012850.644 964 5.50.038290.59199 5.20.004810.478 302 6.60.012460.48640 2.10.000610.345 392>10.00.021350.719339>10.00.01560.489 5138.90.025150.615 50 4.50.001620.659 1368.50.005580.639 353 5.90.018730.713 495 4.80.011170.321 1147.60.003960.391 156 6.70.022520.706 508 6.50.027410.476 82 5.10.003380.472 410>10.00.020760.421 400>10.00.012770.531 463 4.70.008250.53 728 5.70.012880.253 2367.10.012090.669 180 3.80.004490.45 360>10.00.018270.679 2957.80.035210.653 950 3.40.026580.586 218 5.20.006840.446 2547.50.007820.487。

等容吸附热焓计算

Electronic Supplementary Material (ESI) for ChemComm. This journal is © The Royal Society of Chemistry 2015
(Supplementary information)
Gas Storage and Separation in Water-Stable [CuI5BTT3]4- Anion Framework Comprising Giant Multi-prismatic Nanoscale Cage
10. Figure S6. The PXRD patterns for compound 1 after different test. 11. Figure S7. TG-DSC curves for the as-synthesized sample of 1 and samples after exchanged with methanol and acetone solvents. 12. Figure S8. N2 and H2 sorption isotherms of 1a at 77K, solid, adsorption; hollow, desorption. 13. Figure S9. The plot of the linear region for the BET equation of 1a (P0/P= 0.005−0.05). 14. Table S5. Low-pressure CO2 (273–298 K) or H2 (77 K) adsorption capacities in selected metal-organic frameworks. 15. Table S6. Low-pressure (LP) and high-pressure (HP) gas sorption capacities of 1a towards CO2, H2, N2 and CH4 at different temperatures. 16. Figure S10. Virial fitting for CO2 isotherms of 1a: (a) The CO2 adsorption isotherms for 1a (solid circle, adsorption; hollow circle, desorption); (b) The details of virial equation (solid lines) fitting to the experimental CO2 adsorption data (symbols) for 1a. 17. Figure S11. (a) The CO2 adsorption enthalpy of 1a; (b) CO2 sorption isotherms of 1a of three consecutive cycles. 18. Figure S12. Comparisons of CO2 uptakes before and after water treatment (immersion in liquid water for 1 day) at 273 and 298 K. 19. Figure S13. Low-pressure CO2/N2, CO2/CH4 and CO2/H2 initial slope selectivity studies for 1a at 273 K (a) and 298 K (b). 20. Table S7. Low-pressure CO2/N2, CO2/CH4 and CO2/H2 selectivity results for 1a analyzed by the initial slope ratio. 21. Figure S14. Low-pressure adsorption isotherms of CO2, H2 and N2 at 273 K (a) and 298 K (b). Lines are fits to a dual-site Langmuir-Freundlich (DSLF) or single-site Langmuir (SSL) equation. 23. Table S8. The refined parameters for the DSLF and SSL equations fit for the pure isotherms of CO2, N2 and H2 in 1a at 273 K. 24. Table S9. The refined parameters for the DSLF and SSL equations fit for the pure isotherms of CO2, N2 and H2 in 1a at 298 K.

Bi2Se3未考虑vdw的错误汇总

在没有考虑vdw作用之前，算Bi2Se3材料soc中出现的错误汇总V ASP自旋轨道耦合计算错误汇总静态计算时，报错：VERY BAD NEWS! Internal内部error in subroutine子程序IBZKPT:Reciprocal倒数的lattice and k-lattice belong to different class of lattices. Often results are still useful (48)INCAR参数设置：对策：根据所用集群，修改INCAR中NPAR。

将NPAR=4变成NPAR=1，已解决！错误：sub space matrix类错误报错：静态和能带计算中出现警告：W ARNING: Sub-Space-Matrix is not hermitian共轭in DA V结构优化出现错误：WARNING: Sub-Space-Matrix is not hermitian in DA V 4 -4.681828688433112E-002对策：通过将默认AMIX=0.4，修改成AMIX=0.2（或0.3），问题得以解决。

以下是类似的错误：WARNING: Sub-Space-Matrix is not hermitian in rmm -3.00000000000000RMM: 22 -0.167633596124E+02 -0.57393E+00 -0.44312E-01 1326 0.221E+00BRMIX:very serious problems the old and the new charge density differ old charge density: 28.00003 new 28.06093 0.111E+00错误：WARNING: Sub-Space-Matrix is not hermitian in rmm -42.5000000000000ERROR FEXCP: supplied Exchange-correletion table is too small, maximal index : 4794错误：结构优化Bi2Te3时，log文件：WARNING in EDDIAG: sub space matrix is not hermitian 1 -0.199E+01RMM: 200 0.179366581305E+01 -0.10588E-01 -0.14220E+00 718 0.261E-01BRMIX: very serious problems the old and the new charge density differ old charge density: 56.00230 new 124.70394 66 F= 0.17936658E+01 E0= 0.18295246E+01 d E =0.557217E-02curvature: 0.00 expect dE= 0.000E+00 dE for cont linesearch 0.000E+00ZBRENT: fatal error in bracketingplease rerun with smaller EDIFF, or copy CONTCAR to POSCAR and continue但是，将CONTCAR拷贝成POSCAR，接着算静态没有报错，这样算出来的结果有问题吗？对策1：用这个CONTCAR拷贝成POSCAR重新做一次结构优化，看是否达到优化精度！对策2：用这个CONTCAR拷贝成POSCAR，并且修改EDIFF（目前参数EDIFF=1E-6）,默认为10-4错误：WARNING: Sub-Space-Matrix is not hermitian in DA V 1 -7.626640664998020E-003网上参考解决方案：对策1：减小POTIM: IBRION=0，标准分子动力学模拟。

AHE

Parallel transport of vector v on curved surface
Constrain v in local tangent plane; no rotation about e3
constraint
angle
Parallel transport
e3 x dv = 0
v acquires geometric angle α relative to local e1
ρ xy = R0 H + ρ ′ xy
′ ρ xy = Rs M
A brief History of the Anomalous Hall Effect 1890? Observation of AHE in Ni by Erwin Hall 1935 Pugh showed ρxy’ ~ M 1954 Karplus Luttinger; transport theory on lattice Discovered anomalous velocity v = eE x Ω. Earliest example of Berry-phase physics in solids. 1955 Smit introduced skew-scattering model (semi-classical). Expts confusing 1958-1964 Adams, Blount, Luttinger Elaborations of anomalous velocity in KL theory 1962 Kondo, Marazana Applied skew-scattering model to rare-earth magnets (s-f model) but RH off by many orders of magnitude. 1970’s Berger Side-jump model (extrinsic effect) 1973 Nozieres Lewiner AHE in semiconductor. Recover Yafet result (CESR) 1975-85 Expt. support for skew-scattering in dilute Kondo systems (param. host). Luttinger theory recedes. 1983 Berry phase theorem. Topological theories of Hall effect 19991999-2003 Berry phase derivation of Luttinger velocity (Onoda, Nagaosa, Niu, Jungwirth, MacDonald, Murakami, Zhang, Haldane)

Magnon Bose condensation in symmetry breaking magnetic field

a r X i v :c o n d -m a t /0607711v 2 [c o n d -m a t .s t r -e l ] 1 S e p 2006Magnon Bose condensation in symmetry breaking magnetic ﬁeld S.V.Maleyev,V.P.Plakhty,S.V.Grigoriev,A.I.Okorokov and A.V.Syromyatnikov Petersburg Nuclear Physics Institute,Gatchina,Leningrad District 188300,Russia E-mail:maleyev@.spb Abstract.Magnon Bose condensation (BC)in the symmetry breaking magnetic ﬁeld is a result of unusual form of the Zeeman energy that has terms linear in the spin-wave operators and terms mixing excitations which momenta diﬀer in the wave-vector of the magnetic structure.The following examples are considered:simple easy-plane tetragonal antiferromagnets (AFs),frustrated AF family R 2CuO 4,where R=Pr,Nd etc.,and cubic magnets with the Dzyaloshinskii-Moriya interaction (MnSi etc.).In all cases the BC is important when the magnetic ﬁeld is comparable with the spin-wave gap.The theory is illustrated by existing experimental results.1.Introduction Magnon Bose condensation (BC)in magnetic ﬁeld was intensively studied in spin singlet materials (see for example [1]and references therein).In this case magnons condens in the ﬁeld just above the triplet gap.In this paper we consider magnon BC that appears in the symmetry breaking magnetic ﬁeld.The theoretical discussion is illustrated by experimental observation of this BC in frustrated antiferromagnet (AF)Pr 2CuO 4and cubic helimagnets MnSi and FeGe.To clarify our idea we begin with consideration of conventional AFs.In textbooks two limiting cases are considered.First,the magnetic ﬁeld is directed along the sublattices.In this case the system remains stable up to the critical ﬁeld H C =∆,where ∆is the spin-wave gap.Then the ﬁrst order transition occurs to the state in which the ﬁeld is perpendicular to sublattices (spin-ﬂoptransition).Second,the ﬁeld is perpendicular to initial staggered magnetization.The system remains stable but the spins are canted toward the ﬁeld by the angle determined by sin ϑ=−H/(2SJ 0),where J 0=Jz ;J and z are the exchange interaction and the number of nearest neighbors,respectively.At H +2SJ 0the spin-ﬂip transition occurs to the ferromagnetic state.To the best of our knowledge the ﬁrst consideration of the symmetry breaking ﬁeld was performed theoretically in [2]in connection with experimental study of the magnetic structure of the frustrated AF R 2CuO 4,where R=Pr,Nd,Sm and Eu [3,4].In these papers the non-collinear structure was observed using the neutron scattering in the ﬁeld directed at angle of δ=450to the sublattices.It was found in[2]that in inclinedﬁeld the Zeeman energy has unusual form with terms which are linear in the spin-wave operators and term mixing magnons which momenta diﬀer in the AF vector k0.As a result the BC arises of the spin-waves with momenta equal to zero and±k0.Similar situation exists in cubic helimagnets MnSi etc.[5].If theﬁeld is directed along the helix wave-vector k the plain helix transforms into conical structure and then the ferromagnetic spin state occurs at criticalﬁeld H C.But if H⊥k the magnon condense with momenta zero,±k,±2k etc.This leads to the following observable phenomena:i)a transition to the state with k directed along theﬁeld at H⊥∼H C1=∆√S/2(a l−a+l),l=1,2 and a l(a+l)are Bose operators.As a result the Zeeman energy has unusual formH Z=H a+q+k0a q+iϑN,i.e. these operators has to be considered as classical variables as in the Bogoliubov theory of the BC in dilute Bose gas.Due to theﬁrst term in(2)we must consider the operatorsa±k0and a+∓kas classical variables too.Minimizing the full Hamiltonian with respectto these variables we obtainE=(∆2sin22ϕ)/(16J0)−S2J0ϑ2−(H H⊥)2/[4J0(∆2(ϕ,H)],(3)where theﬁrst term is the energy of the square anisotropy.In cuprates with S=1/2ithas quantum origin and arises due to pseudodipolar in-plane interaction[9].The secondterm is the energy of the spin canting in perpendicularﬁeld.The last term is the BCenergy and∆2(ϕ,H)=∆2cos4ϕ+H2⊥−H2 is the spin-wave gap in theﬁeld[2].This contribution becomes important at H∼∆.The spin conﬁguration is determined byd E/dϕ=0and equilibrium condition d2E/dϕ2≥0.This theory was veriﬁed by neutrons scattering[10,11].In diagonalﬁeld H (1,1,0)the spin conﬁguration in frustrated Pr2CuO4is governed by Eq.(3)and the intensityof the(1/2,1/2,−1)is given by I∼1+sin2ϕ[2].Neglecting the BC term we getsin2ϕ=−(H/H C)2,where H C=∆.As a result at H→H C we obtain I∼H C−H. But very close to H C the BC term becomes important and we have a crossover to I∼(H C−H)1/2.It is clearly seen inﬁgure2.This crossover was observed in[10,11].3.Frustrated AFsIn frustrated R2CuO4AFs there are two copper spins in unit cell belonging to diﬀerent CuO2planes(see inset inﬁgure1).From symmetry considerations these spins do not interact in the exchange approximation.The orthogonal spin structure is a result of the interplane pseudodipolar interaction(PDI)[2,3]and the ground state energy is given by∆2E=on T we obtain H C≃7.8T andγC≃5.30that is in stronger disagreement wit the experiment.The experimentally obtained anglesαandγat T=18K andδ=9.50are shown inﬁgure4[12].The transition to the collinear state withα∼−450andγC∼200 was observed.Again the non-BC theory can not explain the experimental data.For example it givesγC≃2.50.Explanation of all these experimental data using the BC theory will be given elsewhere.4.BC in helimagnetsIn helimagnets MnSi etc.Dzyaloshinskii-Moriya interaction(DMI)stabilizes the helical structure and the helix wave-vector has the form k=SD[ˆa×ˆb]/A,where D is the strength of the DMI,A is the spin-wave stiﬀness at momenta q≫k,ˆa andˆb are unit orthogonal vectors in the plane of the spin rotation.The classical energy depends on theﬁeld component H along the vector k and the cone angle of the spin rotation is given by sinα=−H/H C,where H C=Ak2is the criticalﬁeld of the transition into ferromagnetic state[5].However at H⊥≪H C rotation of the helix axis toward theﬁeld direction and the second harmonic2k of the spin rotation were observed[6-8].Both phenomena are related to the magnon BC in perpendicularﬁeld[5].The linear and mixing terms appear in the Zeeman energy in much the same way as it was discussed above:H Z=(H a−i H b)2the real form of the BC energy is not so simple.It is determined by nonlinear interactions but consideration of this problem is out of the scope of this paper.As a result the perpendicular susceptibility is proportional to1/(∆2−H2⊥/2)and 2k harmonic appears.The last was observed by neutron scattering[6-8].Intensities of corresponding Bragg satellites have the formI±∼[∆2/(∆2−H2⊥/2)]2[1∓(kP)]δ(q∓2k),(7) where P is the neutron polarization.If H⊥→∆√5.ConclusionsWe discuss a few examples of the magnon BC in symmetry breaking magneticﬁeld.BC appears due to unusual terms in Zeeman energy.Obviously this phenomenon is very general and can be observed in other ordered magnetic systems.Eﬀects related to the BC has to be more pronounced in theﬁeld of order of the sin-wave gap.6.AcknowledgmentsThis work is partly supported by RFBR(Grants03-02-17340,06-02-16702and00-15-96814),Russian state programs”Quantum Macrophysics”,”Strongly Correlated electrons in Semiconductors,Metals,Superconductors and Magnetic Materials””Neutron Research of Solids”,Japan-Russian collaboration05-02-19889-JpPhysics-RFBR and Russian Science Support Foundation(A.V.S.).References1Crisan M,Tifrea I,Bodea D and Grosu I2005Phys.Rev.B721644142Petitgrand D,Maleyev S,Bourges P and Ivaniv A1999Phys.Rev.B5910793D.Petitgrand,Moudden A,Galez P and Boutrouille P1990J.Less-Common Metals164-165768 4ChattpodhayaT,Lynn J,Rosov N,Grigereit T,Barilo S and Zigunov D1994Phys.Rev.B49 99445Maleyev S2006Phys.Rev.B731744026Lebech B,Bernard J and Feltfoft1989J.Phys.:Condens.Matter161057Okorokov A,Grigoriev S,Chetverikov Yu,Maleyev S,Georgii R,B¨o ni P,Lamago D,EckerslebeH and Pranzas P2005Physica B3562598Grigoriev S,Maleyev S,Chetverikov Yu,Georgii R,B¨o ni P,Lamago D,Eckerlebe H and Pranzas P2005Phys.Rev B721344029Yildirim T,Harris A,Aharony A and Entin-Wohlman O1995Phys.Rev.B521023910Plakhty V,Maleyev S,Burlet P,Gavrilov S and Smirnov O1998Phys.Lett.A25020111Ivanov A and Petitgrand D2004J.Mag.Mag Materials272-27622012Plakhty V,Maleyev S,Gavrilov S,Bourdarot F,Pouget S and Barilo S2003Europhys.Lett.61 53413Ivanov A,Bourges P and Petitgrand D1999Physica B259-261879FiguresaFigure 1.Spin conﬁguration in the ﬁeld.Full and dashed arrows correspond to zero and nonzero ﬁeld,respectively.Addition spin canting in H ⊥is shown by broken arrows.Inset:spin conﬁguration in neighboring planes of frustrated AF.Figure 2.Log-Log plot of the (1/2,1/2,−1)Bragg intensity in diagonal ﬁeld,h ∼(H C −H ).Figure3.Theﬁrst order transition in theﬁeld directed along b axis.Calculated intensities for the spinﬂop conﬁgurations when spins are perpendicular to theﬁeld (white arrows).Figure4.Field dependence of anglesαandγatδ=9.50.)10a H mT =)50b H mT =)150c H mT=Figure 5.Bragg reﬂections in the ﬁeld along (1,1,0).a)Four strong spots corresponds to ±(1,1,1)and ±(1,1,−1)reﬂections.Weak spots are the double Bragg scattering.b)The 2k satellites appear.c)The helix vector is directed along the ﬁeld.。

Electrical switching of an antiferromagnet

in AFMs (9). Bistability can be realized in classes of AFMs which possess biaxial magnetic anisotropy. The magneto-transport counterpart of magnetic anisotropy is anisotropic magnetoresistance (AMR). In the early 1990’s, the ﬁrst generation of FM MRAM micro-devices used AMR for the electrical read-out of the memory state (10). AMR is an even function of the magnetic moment which, following again N´ eel’s principle, implies its presence in AFMs (11). While AMR in AFMs was experimentally conﬁrmed in several recent studies (12–14), efﬁcient means for manipulating the AFM moments have remained elusive. External magnetic ﬁeld, whose coupling is linear in the magnetic moment, favors parallel alignment of the moments, i.e., acts against the staggered exchange ﬁeld in the AFM. On the other hand, current-induced even magnetic torques of the form dM/dt ∼ M × (M × p), which are used for electrical writing in the most advanced FM spin-transfer-torque MRAMs (1), have been proposed to allow for a large angle reorientation of the AFM moments (15). Here M is the magnetic moment vector and p is the electrically injected carrier spinpolarization. Translated to AFMs, the effective ﬁeld proportional to (MA,B × p) which drives the torque dMA,B /dt ∼ MA,B × (MA,B × p) on individual spin sublattices A and B is staggered, i.e., alternates in sign between the opposite spin sublattices. The staggered property of the ﬁeld is the key for its strong coupling to the N´ eel order. In FM spin-transfer-torque MRAMs, spin polarized carriers are injected into the free FM layer from a ﬁxed FM polarizer by an out-of-plane electrical current driven through the FMFM stack. Reversible 180◦ switching is achieved by reversing the polarity of the out-of-plane current. In analogy with FM spin-transfer-torque MRAMs, the above theory proposed for AFMs (15) assumes injection of the spin polarized carriers into the AFM from a ﬁxed FM polarizer by out-of-plane electrical current driven in a FM-AFM stack. Unlike the FM-FM stack, the effect of the spin current injected from a FM to an AFM is independent of the current 3

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arXiv:cond-mat/0112059v1 [cond-mat.str-el] 4 Dec 2001Non-BCSpairinginanisotropicstronglycorrelatedelectronsystemsinsolids

V.A.Khodel†andJ.W.ClarkMcDonnellCenterfortheSpaceSciencesandDepartmentofPhysics,WashingtonUniversity,St.Louis,MO63130,USA†RussianResearchCenter,KurchatovInstitute,Moscow123182,Russia

AbstractTheproblemofpairinginanisotropicelectronsystemspossessingpatchesoffermioncondensateinthevicinityofthevanHovepointsisanalyzed.Attentionisdirectedtoopportunitiesfortheoccurrenceofnon-BCSpairingcorrelationsbetweenthestatesbelongingtothefermioncondensate.Itisshownthatthephysicalemergenceofsuchpairingcorrelationswoulddrasticallyalterthebehaviorofthesingle-particleGreenfunction,thecanonicalpoleofFermi-liquidtheorybeingreplacedbyabranchpoint.

PACS:71.10.Hf,71.27.+a,74.20.MnThegroundstateofconventionalsuperconductorsatT=0isknowntobeacondensateofCooperpairswithtotalmomentumP=0.InFermi-liquidtheory,thefamiliarBCSstructureofthegroundstateisassociatedwiththelogarithmicdivergenceoftheparticle-particlepropagatoratP=0andisindependentofthedetailsofthepairinginteraction.However,amarkedlydiﬀerentsituationcanensueinstronglycorrelatedsystemsinwhichthenecessarystabilityconditionfortheLandaustateisviolatedandtheLandauquasiparticlemomentumdistributionsuﬀersarearrangement.Undercertainconditionsthisrearrangementleadstoafermioncondensate(FC)–acontinuumofdispersionlesssingle-particle(sp)stateswhoseenergyǫ(p)coincideswiththechemicalpotentialµoveraﬁnite(andingeneraldisconnected)domainp∈Ωinmomentumspace[1-11].Asaresult,thepreferenceforpairingwithP=0comesintoquestionbecauseofthedegeneracyoftheFCspspectrum.Inthiscase,thenatureofpairingdependsontheconﬁgurationassumedbytheFC.Herewestudyatwo-dimensionalsquare-latticesysteminwhichtheFCissituatedindomainsadjacenttothevanHovepoints,whilethespstateswithordinarydispersionareconcentratedarounddiagonalsoftheBrillouinzone[3,11].Tobeginwith,wefocusonthenatureofparticle-particlecorrelationsintheFCsubsystemandignorecontributionsfromthespstateswithnonzerodispersion.TraditionalBCSsingletpairingcorrelatesonlythespstatesbelongingtodiagonallyoppositepatchesoftheFC;thedescriptionthereforeinvolvesthesinglecollectiveoperatorCp=ap,−a−p,+anditsadjointC†p,whichconnectthegroundstatewithstatesofNandN∓2particles.However,inanisotropicelectronsystemsinhabitingcrystallinematerialsmanifestingfermioncondensation,allfourFCpatchesshouldbetreatedonanequalfooting.HenceanadditionalrelevantcollectiveoperatorQp=ap,+a−p+Q,−,entersthepicture,togetherwithitsadjointQ†p.WithQ=(π/l,π/l)wherel

1isthelatticeconstant,thisoperatorcharacterizesthepairingcorrelationsaﬀectingspstateslocatedintheneighboringFCpatches.IfsuchadditionalcorrelationsareinvolvedtogetherwiththeordinaryBCScorrelations,theground-statewavefunctionevidentlylosesthesimpleBCSstructure.Asalientfeatureofthisnonabelianexemplarofthepairingproblemisthepresenceoftwodegeneratecollectivemodesintheparticle-particlechannel.ThecreationofaC-pair(Cooperpair)bytheoperatorC†p,followedbysubsequentannihilationofaQ-pairbytheoperatorQp,givesrisetoanexcitedtwo-particle-two-holestateoftheN-fermionsystem.Asweshalldemonstrate,thisprocessenmeshesawholebandofmany-particle-many-holestatesandchangesthestructureofthesingle-particleGreenfunctiondramatically.Werestrictconsiderationstothesimplest,δ-likeformoftheinteractionintheparticle-particlechannel,withstrengthparameterλ.Also,weassumethatalltheparticle-holecontributionshavealreadybeentakenintoaccountintermsofaneﬀectivesingle-particleHamiltonianhavingspspectrumǫ(p)Accordingly,onlypairingcontributionsshouldbeincorporatedintheequationfortheGreenfunctionGαβ(x,x′)=−i󰀋Tψα(x)ψ†β(x′)󰀊.Thisequation,derivedwiththeaidofequationofmotion[ε−ǫ(p)]ψα(x)−λψ†γ(x)ψγ(x)ψα(x)=0,takestheform

󰀋O|Tap1,γ(t)a−p1,α(t)|C󰀊󰀋C|Ta†p,γ(t)a†−p,β(t+τ)|O󰀊++󰀋O|Tap1,γ(t)a−p1+Q,α(t)|Q󰀊󰀋Q|Ta†p,γ(t)a†−p+Q,β(t+τ)|O󰀊.Forsimplicitywehenceforthomitspinindicesα,β,γ,etc.TheequationfortheGreenfunctionthenreads

G(p,ε)=Go(p,ε)󰀃(1−∆F+1,0(p,ε)−DF+0,1(p,ε)󰀆,(2)whereGo(p,ε)=[ε−ǫ(p)]−1.Inthetimedomain,thequantityF+1,0hastheexpres-sionF+1,0(p,t)=󰀋C|Ta†p(t)a†−p(t+τ)|O󰀊andisinterpretedasthetransitionamplitudebetweenthegroundstateandastatediﬀeringfromitbythepresenceofasingleC-pair.Similarly,F+0,1(p,τ)=󰀋Q|Ta†p(t)a†−p+Q(t+τ)|O󰀊isthetransitionamplitudebe-tweenthegroundstateandastatediﬀeringfromitbyasingleQ-pair.Thediagram-block∆∝󰀋O|Tap1,γ(t)a−p1,α(t)|C󰀊∝F1,0(τ=0)hasthesamemeaningasthegapor-derparameterofBCStheory,whilethenewingredientDhasthecorrespondingstructureD∝󰀋O|Tap1,γ(t)a−p1+Q,α(t)|Q󰀊∝F0,1(τ=0).Employingthecomplementaryequationofmotion[ε+ǫ(p)]ψ†α(x)+λψ†α(x)ψ†γ(x)ψγ(x)=0,onecanderiveequationsforthetransitionamplitudesF+1,0andF+0,1: