Spin blockade in ground state resonance of a quantum dot

a r X i v :c o n d -m a t /0109104v 3 [c o n d -m a t .m e s -h a l l ] 9 A u g 2002

A.K.H¨u ttel,1H.Qin,1A.W.Holleitner,1R.H.Blick,1,?K.Neumaier,2

D.Weinmann,3K.Eberl,4and J.P.Kotthaus 1

Center for NanoScience and Sektion Physik,Ludwig–Maximilians–Universit¨a t,Geschwister–Scholl–Platz 1,80539M¨u nchen,

Germany.

Walther-Meissner-Institut f¨u r Tieftemperaturforschung,Walther-Meissner-Stra?e 8,85748Garching,Germany.

Institut de Physique et Chimie des Mat′e riaux de Strasbourg,UMR 7504(CNRS-ULP),23rue du Loess,67037Strasbourg,

France.

Max-Planck-Institut f¨u r Festk¨o rperforschung,Heisenbergstra?e 1,70569Stuttgart,Germany.

(February 6,2008)

We present measurements on spin blockade in a laterally integrated quantum dot.The dot is tuned into the regime of strong Coulomb blockade,con?ning ～50electrons.At cer-tain electronic states we ?nd an additional mechanism sup-pressing electron transport.This we identify as spin blockade at zero bias,possibly accompanied by a change in orbital mo-mentum in subsequent dot ground states.We support this by probing the bias,magnetic ?eld and temperature dependence of the transport spectrum.Weak violation of the blockade is modelled by detailed calculations of non-linear transport taking into account forbidden https://www.360docs.net/doc/f95662734.html,,85.35.Gv,72.25.Rb

Conventional electronics relies on controlling charge in semiconductor transistors.The ultimate limit of integra-tion is reached when these transistors,termed quantum dots,are operated by exchanging single electrons only.The mechanism governing electron transport through dots is known as Coulomb blockade (CB)[1,2].Apart from this,electrons naturally possess a spin degree of freedom,which recently attracted considerable interest regarding the combination of spintronics and quantum information processing [3].Hence,studies on the inter-play of spin and charge quantum states in quantum dots form an integral contribution for de?ning and controlling electron spin quantum bits.

One of the key techniques applied to study electronic structure in quantum dots is transport spectroscopy:De?ning the dots by locally depleting a two-dimensional electron gas enables this direct monitoring of ground and excited states of the arti?cial atoms [4].In contrast to Kondo physics [5]in the limit of transparent tunneling barriers between the quantum dot and the reservoirs,we are focusing on the regime of opaque barriers and Coulomb blockade.In other words the strong hybridiza-tion with electronic reservoir states found for the dot elec-trons in Kondo physics is suppressed and both electron spin and orbital quantum numbers remain well-de?ned.Inspired by an early experiment of Weis et al.[6]it was suggested by Weinmann et al.[7]that transport through single quantum dots can be blocked due to spin e?ects.Spin selection rules particularly prohibit single electron

tunneling (SET)transitions between N and N +1elec-tron ground states of the dot which di?er in total spin by ?S >1/2.This phenomenon was termed spin block-ade (SB)(type-II),occuring in addition to conventional CB and leading to a suppression of the corresponding conductance peak in linear transport [7].

Here,we demonstrate a spin blockade e?ect in the many-electron (N ～50)limit in a two-dimensional quan-tum dot,in contrast to earlier measurements by Rokhin-son et al.[8]on a small three-dimensional silicon quantum dot with only a few electrons.In particular we present detailed measurements on the bias and magnetic ?eld dependence of the transport spectrum of our laterally gated quantum dot.Weak violation of spin blockade due to spin orbit coupling is found.Modelling the system by numerical calculations taking into account type-II spin blockade and weak spin relaxation,we observe excellent agreement with the transport spectrum.

2002503000.10.01

110

-1

240

260

280

300V sd 4

(b)

?V (mV)

NDC

V 3

V 2V g

1D S

(a)

250nm

σ(μS)4532

(mV)

(c)

?V g

?1 mV 1 mV FIG.1.(a)SEM micrograph of the gate electrodes de?n-ing the quantum dot (top view).Approximate dot area (cir-cle),source (S)and drain (D)contacts are marked schemat-ically.(b)Conductance measurement on the quantum dot

(B =0T;white denotes ?0.1μS (NDC),grey (large areas)0μS,black ≥2.0μS).(c)Conductance trace at V sd =0V;an exponential ?t through the conductance peak maxima has been added (dashed line).Conductance peak three is sup-pressed by spin blockade.

The quantum dot we use is shown in Fig.1:A num-

ber of split gates is de?ned by electron beam lithogra-phy on top of an AlGaAs/GaAs heterostructure.When

applying negative gate voltages V1,V2,V3,and V g,a single nearly circular quantum dot is formed in the two-

dimensional electron system(2DES)120nm below the

surface.At4.2K the carrier density of the2DES is n s= 1.8×1015m?2and the electron mobility is75m2/Vs.

For the measurements presented here a dot with an elec-

tronic diameter of approximately90nm was de?ned.The 2DES was cooled to a bath temperature of23mK and an

electron temperature of T el=95mK in a3He/4He dilu-tion https://www.360docs.net/doc/f95662734.html,ing an excitation voltage of12μV at

18Hz,the noise in the CB regime is lower than50nS.

Electronic radius and mean level spacing both lead to an estimate of N～50electrons on the dot.

In Fig.1(b)the conductance is plotted as a function

of gate voltage V g and source/drain bias V sd.Near V g=?290mV,a capacitance ratio ofα=C g/CΣ=0.059has been obtained from this measurement,leading to a total

dot capacitance of CΣ=83aF.Therefore the Coulomb charging energy E C=e2/2CΣof around1.9meV,giv-ing the electrostatic energy required to add an electron to the quantum dot,is dominant compared to the spa-tial quantization energy?.Nevertheless,a rich spectrum of excited state resonances in all SET regions is revealed. In addition,multiple lines of negative di?erential conduc-tance(NDC)are visible,as predicted in Ref.[7].Hence, we can conlude that in these regions spin polarized ex-cited states lead to a reduction of current via spin block-ade type-I.

As a striking feature,the conductance at peak three

in Fig.1is,for small|V sd|,signi?cantly below the ex-pected value as compared to peaks two and four.Only for|V sd|≥300mV transport via an excited state be-comes possible,and the conductance increases.Such strong suppression of ground state tunneling is caused by spin blockade of type-II.This phenomenon involves ground state transitions only.An electron is blocked from entering the dot,since the transition involves two levels with total spin di?erence?S>1/2.

Fig.1(c)shows the conductance trace at V sd=0in logarithmic scale.As the width of the tunneling barri-ers increases at higher|V g|,the maximum current ap-proaches zero in the case of complete pinch-o?.In a simple quantum-mechanical picture the maximum peak conductance is assumed to decrease exponentially with ?V g.Again,the amplitude of peak three is consider-ably below the most general maximum/minimum bounds (dotted lines in Fig.1(c)).An exponential?t through the peak maxima(dashed line)allows us to estimate a life-time of the spin state causing spin blockade.We assume that the tunneling ratesΓL/R/h of the left and right bar-rier de?ning the dot are equal–which appears reasonable because of the high degree of symmetry shown in the di-amond conductance structure of Fig.1(b).

In our case of weak coupling to the reservoirs,where Γ?k B T??

σmax=

4k B T el

Di?erent explanations for this phenomenon are pos-sible.On one hand,recent measurements by Pallecchi et al.[12]indicate the possibility of greatly enhanced g -factors in 2D quantum dots;values of up to g ～20have been observed in AlGaAs/GaAs quantum wires.As an example,at g ≈5.4line shifts can be approximated solely by the Zeeman shift caused by a spin di?erence ?S =5/2of subsequent electron number ground states (cf.Ref.[13]),thus explaining spin blockade.At nearby,non-blocked resonances,the peak shift is then consistent with a spin change in the dot of ?S =1/2,i.e.the ad-dition of a single electron spin.Theoretical predictions [14]support a g -factor deviation in case of unusually large spin-orbit interaction.

However,orbital states are modi?ed by the magnetic ?eld perpendicular to the 2DES as well.Hence,on the other hand a change in orbital quantum numbers,partic-ularly ground state angular momentum,is an alternative explanation for the peak shift.Since momentum and an-gular momentum of an electron are not preserved when traversing the quantum point contacts [15],a misalign-ment of spatial quantum numbers alone will not lead to a total blocking of transport.Therefore,a change in both L and S between subsequent electron number ground states leads to a scenario explaining the data.

?10?505?101?10

05?10

V sd

1V sd

? V (mV)(a)B=0 mT B=450 mT (b)

B=150 mT 2E G

2E G (c)

FIG.3.(a)to (c):E?ect of an external perpendicular magnetic ?eld on the spin blocked SET resonance three.(a)Detail from Fig.1(b).(b)At B =150mT the gap has partly closed.Conductance is still suppressed for |V sd |<200μV.(c)Blockade phenomena disappear completely at 450mT.Si-multaneously regions of NDC are evolving.(d)Magnetic ?eld dependence of the transport blockade gap as indicated in (a)and the maximum conductance at V sd =0V.At approxi-mately 300mT the gap is quenched.

In addition nonlinear conductance measurements at ?-nite magnetic ?eld perpendicular to the 2DES have been taken.In Fig.3(a)to (c)the transport-blocked SET res-onance is shown at 0mT,150mT,and 450mT.At a ?eld strength of only 300mT the quantum levels in the dot are already shifted su?ciently to reenable ground state transport.This is also demonstrated in Fig.3(d),

which shows the conductance at V sd =0V and the block-ade gap energy E G as function of B .At B =300mT a strong increase in conductance is seen.Here,one quan-tum ground state participating in SET changes because of a level crossing;for higher B ,|?S |=1/2for the N and N +1electron ground state and SET transport takes place.This assumption is directly supported by the data of Fig.2(b),B =300mT being the ?eld strength where the B -dependence of addition energies around peak three adapts to the one around nearby peaks.For high B the overall conductance through the quantum dot is decreas-ing because of a gradual compression of the dot states by the magnetic ?eld [16].

The data indicate strong electronic correlations in the quantum dot involving both spin and orbit of the wavefunction.The expected impact of correlation ef-fects can be estimated by the conventional parameter

r s =1/

√

conservation in tunneling processes and the total spin of the electrons con?ned in the dot to be a good quantum number,the theory yields transport spectra which are qualitatively di?erent from the experimental ones(see Fig.4(a)).This comparison of the theory and the mea-surements indicates that spin blockade is weakly violated, possibly due to spin-orbit coupling.Such a state mix-ing mechanism in the quantum dot leads to a violation of both spin and angular momentum conservation.The couplings might di?er considerably in our case from pre-vious observations[8];possible reasons include the mate-rial system(AlGaAs/GaAs instead of Si),the potential shape of the dot,and their e?ect on the details of the spin-orbit Hamiltonian.

We take this e?ect into account by including a phe-nomenological spin-independent transition rate between many-body states in our model,allowing for electron tun-neling processes from and into the dot in which the spin selection rules are https://www.360docs.net/doc/f95662734.html,ing the small value of1% of the spin-allowed transition rates,and assuming quan-tum levels as displayed in Fig.4(b),excellent agreement of theory and experiment is found in Fig.4(c)and(d). The magnetic?eld was introduced as a Zeeman-like shift of the levels,leading to a level crossing in the N-electron spectrum at B/gμB≈0.17.This explains that the spin blockade is lifted at stronger magnetic?eld,in agreement with the experimental observations.

In conclusion,we have demonstrated transport block-ade in a quantum dot containing approximately50elec-trons,caused by spin selection rules:electronic correla-tions lead to a discontinuity in both ground state spin and spatial quantum numbers for subsequent electron counts. As a result,ground state transport blockade caused by spin selection rules is found.

We observe the properties predicted for such a system: Spin blockade can be lifted by raising the temperature, or applying a source/drain voltage.Shifting the quan-tum levels via a magnetic?eld leads to a change in both spatial and spin quantum numbers,lifting spin blockade as well.Two alternative mechanisms for the observed level shift are proposed,?rstly,a large Zeeman shift via g-factor enhancement,secondly,a combined change of spin and orbital quantum numbers.

In the measurement,spin blockade is weakly violated.

A likely candidate for this conduction process is given by the spin-orbit interaction induced spin state mixing in the quantum dot,being consistent with both proposed mechanisms of level shifting.Taking a corresponding weak violation of selection rules into account,numeri-cal calculations of a straightforward spin blockade model lead to an excellent agreement of theory and experiment, and the properties of the nonlinear transport spectrum at zero and large

B are accurately reproduced.

We like to thank L.Rokhinson for detailed dis-cussions.We acknowledge?nancial support by the Deutsche Forschungsgemeinschaft(Bl/487-2-2,SFB-348)and the Bundesministerium f¨u r Forschung und Technolo-gie(project01BM/914).Many thanks to the Studien-stiftung des deutschen Volkes and the Stiftung Maximi-lianeum(AKH),the Volkswagenstiftung(HQ),and the European Union(DW,RTN program)for their support.?Corresponding author-e-mail:

robert.blick@physik.uni-muenchen.de