C. Brüne et al- Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures

8/3/2019 C. Brne et al- Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures

1/7

ARTICLESPUBLISHED ONLINE: 2 MAY 2010 | DOI: 10.1038/NPHYS1655

Evidence for the ballistic intrinsic spin Hall effect

in HgTe nanostructures

C. Brne1, A. Roth1, E. G. Novik1, M. Knig1, H. Buhmann1*, E. M. Hankiewicz2, W. Hanke2, J. Sinova3

and L. W. Molenkamp1

In the spin Hall effect, a current passed through a spinorbit coupled electron gas induces a spin accumulation of inverse signon either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, andthey may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying theeffect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliablesignatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques.Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE)in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobilityHgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal

due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spinorbit splitting is reduced,the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimentalobservations by quantum transport calculations.

Control, manipulation and detection of spin polarized carriersare the focal goals of spintronics1. The creation of newtechnologies based on spin current manipulation requires

new methods andmaterials for generating and controlling the spin-basedproperties of active devices. Although progress has beenmadein spin injection from a ferromagnetic metal into a semiconductorthrough tunnel barriers, its detection efficiency is still problematic.Applications of ferromagnetic semiconductors are challenged bytheir ferromagnetic transition temperatures, which remain below

room temperature.A clear avenueto circumvent several of these keyproblems is the direct use of electric fields to manipulate electronspins through spinorbit coupling based effects in paramagneticsystems. Of this class of effects one of the premier candidates atpresent is the spin Hall effect (SHE; refs 27) in which a transversespin accumulation is created when an electric current is passedthrough a material with strong spinorbit coupling, coming eitherfrom the band structure (ISHE) or from the scattering of electronson heavy impurities (extrinsic spin Hall effect, ESHE). Although theSHE has been very actively studied theoretically over the past few

years5, few experimental results have been reported because of thedifficulty of detecting the effect. Early experiments demonstratingthe effect used sensitive optical techniques810. Electrical detectionof the SHE, although much more desirable from the device point

of view, is even more challenging and has been demonstrated onlyin metallic nanostructures1115. The detected signals are weak, toa large extent because samples in mostly weak spinorbit coupledsystems are in the diffusive transport regime. Whereas most ofthe above experiments appear to result from the ESHE, refs 9and 15 have attributed their observations the ISHE, involving theactual band structure spinorbit coupling effects. A larger effectcan be expected in samples where the transport is ballistic and theeffect unequivocally stems then from the ISHE (refs 16,17). Such

1Physikalisches Institut (EP3), Universitt Wrzburg, 97074 Wrzburg, Germany, 2Institut fr Theoretische Physik und Astrophysik, Universitt Wrzburg,

97074 Wrzburg, Germany, 3Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA.

*e-mail: [email protected].

an experiment is the topic of this paper: we provide experimentalevidence for electrical detection of the ballistic ISHE in high-mobility HgTe-based nanostructures.

Samples

HgTe is a zero-gap semiconductor which forms a type-III QWwith Hg0.3Cd0.7Te barriers that have an inverted band structurewhen the well width is larger than 6.3 nm (ref. 18) and a normalband structure for narrower widths. The two-dimensional electron

gas (2DEG) in these structures exhibits a high carrier mobilityand a large, gate-controllable, Rashba-type spinorbit splitting19,20.The three samples studied in this paper were chosen to representvarious regimes of Rashba splitting: we study two QWs with aninverted band structure (8.0 nm wide), in which the spinorbitis very large as a result of the extensive mixing of the valenceand conduction bands21, these are samples Q2197 and Q2198.In the former, the structure contains donor-doped barrier layerson both sides of the QW, resulting in a smaller electric fieldacross the well at zero gate voltage, and thus a smaller Rashbasplitting than in Q2198, where the QW is asymmetrically doped.Additionally, we study a narrow (5.7 nm wide, asymmetricallydoped) sample, Q2398, which has a normal band structure, leadingto a much reduced spinorbit splitting, especially in the conduction

band. At zero gate voltage, we find mean carrier mobilitiesof = 2.5,1.2 and 1.3 105 cm2 V1 s1, and carrier densitiesns = 1.7,2.0 and 5.5 10

11 cm2 for samples Q2197, Q2198 andQ2398, respectively.

To electrically detect the ISHE, we have fabricated H-shapedmesa structures (see Fig. 1) using electron beam lithography anddry-etching techniques, following a design proposed previously bysome of us in ref. 16. A Au/Ti electrode is deposited on top of a110 -nm-thick SiO/SiN gate insulator layer that covers the entire

NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephysics 1
http://www.nature.com/doifinder/10.1038/nphys1655mailto:[email protected]://www.nature.com/naturephysicshttp://www.nature.com/naturephysicsmailto:[email protected]://www.nature.com/doifinder/10.1038/nphys1655


2/7

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS1655

4

2

1

5

Q2197 Q2198

a b

200 nm

200 nm

6 1

3 2 4 3

5 6

Figure 1 | H-structure samples. a,b, Sample layout and electron beam micrograph of samples (a) Q2197 and (b) Q2198.

sample. Ohmic contacts are fabricated by thermal In-bonding. Twoadditional leads have been added to the H-structures to allowfurther characterization measurements. These leads are attached toa vertical leg either far away from (for example, sample Q2197,Fig. 1a) or in close proximity to the horizontal leg of the H-bar (forexample, sample Q2198, Fig. 1b). The H-structures consist of legs1m long and 200nm wide, with the connecting part being 200 nmwide and 200 nm long. The estimated mean free path in thesesystems is l 2.5m, which establishes that the samples studied are

well within the quasi-ballistic regime.

Transport experiments on H-bar structures

The idea behind the transport measurements is as follows 16. Whenan electric current flows in one of the legs of the H-bar structure(say between contacts 1 and 2 in Fig. 1a), a transverse spin currentdue to the intrinsic spin Hall effect is induced in the connectingpart. Subsequently, this spin current produces, owing to the inversespin Hall effect22, a non-local voltage difference in the oppositeleg of the H-bar structure (in our example, between contacts3 and 6 in Fig. 1a) which can be measured by a voltmeter3,16.Sweeping the gate voltage in the sample now allows us to vary thestrength of the Rashba spinorbit splitting by a variation of boththe electrical field across the QW, as well as the Fermi level in the

QW; this evidently results in a strong modulation of the non-localvoltage, which can be analysed by comparison with theory. TheH-shape of the structure strongly suppresses any residual voltagebetween contacts 3 and 6 resulting from spreading of the potentialdifference applied between contacts 1 and 2. As an upper limitof the stray signal, we have computed the spreading voltage bysolving Poissons equation for the parameters of each sample (notethat this implies assuming diffusive transport, as quasi-ballistictransport spreading effects are much smaller). Below, we plotthis residual voltage alongside the experimental non-local voltageto emphasize that the observed effect is solely due to the SHE.Experimentally, all measurements were performed using standarda.c. lock-in techniques under a voltage bias (we apply 100 V acrossthesample anda reference resistor of similar resistance), at a sampletemperature of 1.8 K.

Figure 2a shows the gate-voltage dependence of the samplecurrent (red traces) and the longitudinal resistance (black traces)of samples Q2197 and Q2198 (Rij,kl denotes a resistance calculatedfrom the voltage measured between ohmic contacts k and l whilepassing a current between contacts i and j). To assist in thecomparison, we shift the gate voltage axis such that renormalizedgate voltage (Vg

= 0 V) corresponds to the situation where thebulk Fermi level is in the centre of the energy gap (the actualvoltages where Vg

= 0V are Vg 1.0 (0.7)V for Q2197

(Q2198), respectively). Figure 2b shows the carrier density as afunction of the renormalized gate voltage. This data was obtainedthrough Hall-measurements on large Hall-bars fabricated fromthe same wafer and demonstrates that we can vary the carrierconcentration sufficiently to tune the sample from strongly n-type(n 8 1011 cm2), through the gap, down to a p-type regime atVg

= 1 V (p 3 1011 cm2). For Vg between 0.5 V and 0.5 V

the samples are insulating.We recently showed18 that the inverted band structure in HgTe

quantum wells wider than 6.3 nm gives rise to the occurrence of thequantum spin Hall effect(QSHE),a newtypeof quantum Hall effectthat occurs at zero magnetic field, when the bulk of the sample is inthe insulating regime. In samples that are smaller than the inelasticscattering length, the electrical conductance is then quantized at

2e

2

/h. Both the current and the resistance data on Q2197 andQ2198 (see Fig. 2a) indeed show a resistance of the same orderof magnitude as the conductance quantum when the gate voltagetunes the sample into the insulating regime (0.5 V


3/7

NATURE PHYSICS DOI: 10.1038/NPHYS1655 ARTICLES

R36,2

1(k)

18

16

14

12

10

8

6

4

2

0

Q2197 Q2198

Vg* (V) Vg* (V)

1 0

Vg* (V)

1

p-cond. p-cond.

p-cond. p-cond.

n-cond.

n-cond. n-cond.

Insul. Insul.

Insul. Insul.

10

8

6

4

2

0

I(nA)

I(nA)

n

1011(

cm2)

8

6

4

2

0

2

40 1 2 3

Vg* (V)

1

n

1011(

cm2)

35

30

25

20

15

10

5

0

12

10

8

6

4

2

8

6

4

2

0

2

4

0 1 2 3

1 0 1 2

V

V

a

b

n-cond.I

I

R36,4

5(k)

Figure 2 | Localresistance data andcarrier density of samples Q2197 andQ2198. a, Resistance data (in black) in measurement configurations on one leg

of the H-bar show signatures of the QSHE; the red curves give the current through the samples. b, Dependence of the carrier density on the applied

gate-voltage. The contact configurations used here are indicated in the insets.

it tends to swamp the ISHE signaldespite the fact it showsits maximum at a different gate voltage. The experiments shownin Fig. 3 represent two different approaches to suppress thenon-local QSHE signal. One approach is to make the devices

sufficiently small so as to provoke backscattering of the QSHE edgechannels. Zhou et al. recently showed theoretically24 that QSHEbackscattering occurs when the wave functions for opposite spinchannels overlap, and estimate that this happens for a device widthof roughly 200250 nm. This is the reason that we report hereon very narrow (lateral) devices as well as (see below) a narrowquantum well device. The second method to suppress the QSHEis to choose a non-local configuration that implies edge channeltransport over distances (much) longer than the inelastic length(which typically is a few micrometre18). This is why we havefabricated the additional leads in the Q2198 H-bar: in the QSHEregime, the extra leads to the mesa force the edge channels to takea detour of some 10 m to ohmic contacts 3 and 6 (indicated bycrosses in theinsets ofFig. 3b) before entering the detector contacts.

An extra benefit is that the extra ohmic contacts cause equilibrationof theQSHE edge channels. Note that theISHE signalis notaffectedby either of these mechanismsin fact, the close proximity ofcontacts 1 and2 to thehorizontalleg of theH-bar increasesthe ISHEsignal in the measurement configurations ofFig. 3b, in agreementwith the simulations.

Figure 3a,b shows the non-local resistance in a configurationsuitable for picking up the ISHE signal as a function of appliedgate voltage for samples Q2197 and Q2198 respectively. The upperand lower panels show the results for an interchange of current andvoltage contacts. One observes that for both samples the non-localsignal strongly increases with gate voltage in the p-regime. Thenon-local resistance is of the order of several 100 for sampleQ2197 and greater than 1 k for sample Q2198. This is the signalwe attribute to the ISHE: on making the gate voltage more negative,

we scan the Fermi level of the devices deeper and deeper into thevalence band, leading to a strong increase in spinorbit splitting 21.The electrical signal of the H-bar is roughly quadratic16 in thestrength of the spinorbit coupling. The relevant number here

is the difference in the populations of the two spinorbit splitsubbands, which evidently increases sharply from zero when theFermi level leaves the gap. This explains the behaviour observed forthe p-regime. In the n-regime, the subband population asymmetryin the HgTe well is an order of magnitude smaller than in thep-regime and one hardly expects to observe a strong ISHE signal.Indeed, the experimental signal for positive gate voltages is small,does not show an appreciable dependence on gate voltage andcannot with confidence be attributed to the ISHE. Thus thephenomenology of our observations agrees well with what weexpect for the ISHE. Moreover, for sample Q2197, any non-localcontribution of the QSHE edge channels is totally suppressedand, therefore, we attribute the observed signal to the ISHE. Thefinite non-local resistance around Vg

= 0 for sample Q2198 is an

indication that in this experiment we have some residual non-localQSHE signal, possibly owing to the slightly larger width of thehorizontal bar. However, the significant increase of the non-localresistance signal in the p-type metallic regime can only be inducedby the ISHE. For both samples, the strong non-local signal in thep-regime remains almost unchanged even if the current and voltagecontacts are exchanged. The tracesthus obey the Onsager symmetryrelations for linear response, which demonstrates the robustnessof the experiment. We have incorporated in Fig. 3 (blue traces)the calculated residual voltages owing to current spreading at theapplied bias voltage, to illustrate clearly that the observed signal issolely because of the ISHE. Note that these traces, calculated fordiffusive transport, represent an upper limit for the actual spreadingsignal, as the transport in the devices is in fact quasi-ballistic, whichstrongly reduces the spreading effects.

http://www.nature.com/doifinder/10.1038/nphys1655http://www.nature.com/naturephysicshttp://www.nature.com/naturephysicshttp://www.nature.com/doifinder/10.1038/nphys1655


4/7


R36,2

1()

R45,2

1(k)

Q2197 Q2198

p-cond.

p-cond.

p-cond.

p-cond.

n-cond.

n-cond.

n-cond.

n-cond.Insul.

Insul. Insul.

Insul.

500

400

300

200

100

0

R21,3

6(

)

R21,4

5

(k)

1.5 1.0 0.5

Vg* (V)

Vg* (V) Vg* (V)

1.5 1.0 0.5

Vg* (V)

a b

2.0

1.5

1.0

0.5

0

500

400

300

200

100

1.5 1.0 0.5 0 0.5 1.0 2.01.5

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

VV

V

V

I

I I

I

1.5 1.0 0.5 0 0.5 1.0 2.01.5

0 0.5 1.0 2.01.5 0 0.5 1.0 2.01.5

Figure 3 | Non-local resistance data for samples Q2197 and Q2198. Non-local resistance signal for (a) Q2197 and (b) Q2198 . The inset indicates the

measurement configuration for current injection (arrows) and voltage probes (V). The crosses indicate additional ohmic contacts. The blue solid curves

indicates the residual voltage owing to current spreading.

Non-inverted control sample

As a control, we have performed similar experiments on sampleQ2398, which has a narrower (5.7 nm) QW and a non-inverted

band structure (its layout is similar to that of Q2197). Becauseof the much reduced Rashba spinorbit splitting in this sample,one expects a much smaller non-local ISHE signal than for theexperiments on Q2197 and Q2198. Furthermore, the QSHE doesnot occur in wells with a normal band structure, so that in Q2398any contributions from QSHE edge channels can be excluded.Figure 4a and b show the results of these experiments. Figure 4ais comparable to Fig. 2 in that the top panel displays the deviceresistance and the bottom panel gives the dependence of the carrierconcentration on the gate-voltage. Note that the resistance of thesample in the insulating regime is now much larger than for theinverted samples in Fig. 2. This is because the insulating regimein Q2398, owing to the absence of the QSHE edge channels, istruly insulating. In the non-local resistance data ofFig. 4b, we again

observe a non-local voltage when the well is in the p-regime, butnow reduced to a few hundred ohms, considerably smaller than insamples Q2198 and Q2197. We will show below that this signal isin line with theoretical expectations. In the insulating region and inthe n-regime the signal is virtually zero, which allows a calibrationof our estimate of the diffusive spreading signal (blue curve).Although in these experiments the spreading signal is no longernegligible in the p-regime, the different gate-voltage dependence ofthe spreading signal and the actual data leaves no doubt that theobserved signal is due to the ISHE.

Modelling by tight-binding calculations

For further confirmation of this interpretation of our experimentalresults, we now proceed with a numerical modelling of theexperiments. Transport in the ballistic regime can be modelled

theoretically within the well-established LandauerBttiker (LB)formalism. We first extract the effective masses and spinorbitparameters from a series of 8 8kp band structure calculations21,

where the influence of the top gate voltage is included in aself-consistent manner. We evaluate these parameters in thevicinity of the Fermi energy, because at low temperatures thequantum transport can be described by propagating modes atthe Fermi energy. Figure 5a and b show the calculated invertedband structures for two representative carrier densities n = 4.42 1011 cm2 and p = 3.26 1011 cm2. In inverted HgTe/HgCdTequantum wells, the conduction band (conventionally labelled H1;ref. 21) has, in the vicinity ofk = 0, a heavy-hole character whereasthe valence band (E1) is electron-like. However, hybridization ofthe energy states starts to play a role for k = 0 and the spinorbitsplitting of both heavy hole- and electron-like bands must beconsidered in the form of a combination of linear and cubic terms.This is clearly relevant in samples Q2197 and Q2198, because

we find that the Fermi level passes through the H1 band aroundk = 0.15nm1 in the n-regime and through the E1 band aroundk = 0.35nm1 in the p-regime (see Fig. 5). We find that thefollowing Hamiltonian matches all the important features emergingfrom theband structurecalculations close to theFermi level:

H=p2

2m+1

h(xpy ypx) +

i2

2h3(p3+ p

3+) + Hdis

where m = 0.305 me for the p-regime and m = 0.03 me for n-type

samples. 1 > 0 and 2 < 0 are the spinorbit coupling parameters,and in the p-regime |2/1| = 2.9,|2/1| = 2.5 and 1.1 for samplesQ2197, Q2198, and Q2398, respectively, whereas in the n-regimewe have |2/1| = 3.8,|2/1| = 4.5, and 10.1 (again referring tosamples Q2197, Q2198, and Q2398). Hdis is the disorder potential.

4 NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephysics


5/7


R36,4

5(k)

R36,1

2()

R12,3

6()

p-cond. p-cond.

p-cond.p-cond.

n-cond. n-cond.

n-cond.n-cond.

Insul. Insul.

Insul.Insul.

Vg* (V)

Vg* (V)

400

450

300

250

350

200

150

100

50

01 0 1 2 3

Vg* (V)

n

1011(

cm2)

6

5

4

3

2

1

0

1

21 0 1 2 3

4

3

2

1

0

I(nA)

300

250

200

150

100

50

0

200

150

100

50

02 1 0 1 2 3 4

Vg* (V)

2 1 0 1 2 3 4

V

V

V

I

I

I

a b

Figure 4 | Experiments on the non-inverted control sample Q2398. The sample layout and contact configuration is similar to Q2197, displayed in Fig. 1a.

a, Local resistance and gate-dependent carrier density. b, Non-local resistance signals. Again, the insets indicate the measurement configurations, and the

blue solid curves plot the residual voltage due to current spreading.

E

(meV)

75

50

25

0

25

50

75

E

(meV)

75

50

25

0

25

50

75

k (nm1)

0 0.1 0.2 0.3 0.4 0.5 0.6

k (nm1)

0 0.1 0.2 0.3 0.4 0.5 0.6

n = 4.42 1011 cm2

p = 3.26 1011 cm2H1

H1

E1E1

H2 H2

EF

EF

a b

Figure 5 | Band structure calculation for sample Q2198. 8 8 k p band structure calculation for (a) n-type carrier density n= 4.42 1011 cm2 and (b)

p-type carrier density p= 3.26 1011 cm2. Thedasheddotted line indicates the Fermi level. The band structure calculations forsample Q2197 look similar.

The size of the structures used for the theoretical model is chosen inaccordance with the actual dimensions of the experimental devices.In theexperiments, thegate voltage causes changes in thespinorbitsplitting as well as in thecarrier density and, as a consequence,in theFermi energy. We include this effect in the simulations by changingthe carrier density with gate voltage according to the experimentaldata ofFigs 2b and 4a. The Fermi energies depend on the strengthof the spinorbit interaction and the carrier densities. To performreal-space LB calculations we rewrite the continuum effective massHamiltonian in a tight-binding form (shown in detail in the onlineappendix), using the model structure shown in Fig. 6d. In thetight-binding calculations, the disorder is calculated by randomly

selecting the on-site energies in the range [W/2,W/2], whereW = h/, and is the transport scattering time calculated fromthe effective masses and the experimental mobility values. Fromthe experimental mobility data, we find corresponding disorderstrengths W between 0.155 and 0.3 meV. For such values of W,ten averages over disorder configurations are sufficient to obtainconvergent results. The weak dependence of the observed effecton disorder in these materials is not surprising, given that thedisorder induced by short range scattering gives rise to vanishingvertex corrections25.

We work in the linear response regime and the voltages ondifferent probes are found within the LB formalism using boundary

http://www.nature.com/doifinder/10.1038/nphys1655http://www.nature.com/naturephysicshttp://www.nature.com/naturephysicshttp://www.nature.com/naturephysicshttp://www.nature.com/naturephysicshttp://www.nature.com/doifinder/10.1038/nphys1655


6/7


R12,4

3

()

R12,4

3

()

Vg* (V)

400

300

200

100

0

R12,4

3

()

1.5 1.0 0.5 0 0.5 1.0 1.5

Vg* (V)

Vg* (V)

a

c d

b

1,200

1,000

800

600

400

200

0

p-cond.

p-cond. Insul.

Insul.

n-cond. p-cond. Insul. n-cond.

n-cond.200

150

100

50

0

2 1 0 1 2 3

4

1 2

3

1.5 1.0 0.5 0 0.5 1.0 1.5

Figure 6 | Theoretical resistance signal for samples Q2197, Q2198 and Q2398. ac, Theoretical predictions of the resistance signal induced by the ISHE

as a function of gate voltage for samples ( a) Q2197 (b) Q2198 and (c) Q2398. For all samples, experimental values of the mobility and carrier densities

were input to the calculations. The effective mass and strengths of spinorbit coupling were extracted from the band structure calculations (see text for

details). d, Shows the tight-binding network used in the modelling.

conditions where a charge current of 10 nA, for the setup ofstructure Q2197, is driven between contacts 1 and 2, whereasbetween contacts 3 and 4 the electric current is zero. In thisconfiguration the non-local resistance signal is R12,43 = V43/I12.Details of the calculations can be found in the SupplementaryInformation and in ref. 16.

Figure 6ac show the theoretical predictions for the non-local resistance signal as a function of gate voltage for samplesQ2197, Q2198 and Q2398, respectively. These can be directlycompared with the experimental plots of Figs 3 and 4. Clearly,the theoretical results not only show a very similar behaviour tothe experimental resistance signal, but even have semi-quantitativeagreement. Furthermore, again in agreement with the experiment,the theoretically predicted signals are at least an order of magnitude

stronger for the p- than for the n-regime, as a result of the muchstronger difference in population of the valence band spinorbitsubbands. As in the experiment, we also find in the calculationsthat Q2198 exhibits a larger signal than Q2197. Analysis of thesimulation results shows that this effect stems from the veryclose proximity of voltage leads 1 and 2 in sample Q2198 tothe horizontal part of the H-bar. Furthermore, we calculate thatboth Q2197 and Q2198 yield larger signals than sample Q2398,where the spinorbit interaction is smaller. The oscillating characterof both experimental and theoretical non-local resistance datastems from the fact that the ratio of the Fermi energy to thespinorbit splitting changes over the range of the gate voltage. Weconclude that the numerical calculations are in good agreementwith the experimental results and confirm that the observed effectis indeed the ballistic ISHE.

Received 8 May 2009; accepted 17 March 2010; published online2 May 2010

References1. Awschalom, D. D. & Flatt, M. E. Challenges for semiconductor spintronics.

Nature Phys. 3, 153159 (2007).2. Dyakonov, M. I. & Perel, V. I. Current-induced spin orientation of electrons in

semiconductors. Phys. Lett. A 35, 459460 (1971).3. Hirsch, J. E. Spin Hall effect. Phys. Rev. Lett. 83, 18341837 (1999).4. Hankiewicz, E. M. & Vignale, G. Coulomb corrections to the extrinsic

spin-Hall effect of a two-dimensional electron gas. Phys. Rev. B 73,115339 (2006).

5. Engel, H-A., Rashba, E. I. & Halperin, B. I. Handbook of Magnetism andAdvanced Magnetic Materials (John Wiley, 2007).

6. Murakami, S., Nagaosa, N. & Zhang, S-C. Dissipationless quantum spincurrent at room temperature. Science 301, 13481351 (2003).

7. Sinova, J. et al. Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92,126603 (2004).

8. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation ofthe spin Hall effect in semiconductors. Science 306, 19101913 (2004).

9. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimentalobservation of the spin-Hall effect in a two-dimensional spinorbit coupledsemiconductor system. Phys. Rev. Lett. 94, 047204 (2005).

10. Sih, V. et al. Spatial imaging of the spin Hall effect and current-inducedpolarization in two-dimensional electron gases. Nature Phys. 1, 3135 (2005).

11. Valenzuela, S. O. & Tinkham, M. Direct electronic measurement of the spinHall effect. Nature 442, 176179 (2006).

12. Saitoh, E., Ueda, M., Miyajima, H. & Tatara, G. Conversion of spin current intocharge current at room temperature: Inverse spin-Hall effect. Appl. Phys. Lett.88, 182509 (2006).

13. Kimura, T.,Otani, Y.,Sato, T.,Takahashi,S. & Maekawa, S. Room-temperaturereversible spin Hall effect. Phys. Rev. Lett. 98, 156601 (2007).

14. Seki, T. et al. Giant spin Hall effect in perpendicularly spin-polarized FePt/Audevices. Nature Matter. 7, 125129 (2008).

6 NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephysics


7/7


15. Weng, K., Chandrasekhar, N., Miniatura, C. & Englert, B-G. in ElectronTransport in Nanosystems (eds Bonca, J. & Kruchinin, S.) 4958(Springer, 2008).

16. Hankiewicz,E. M., Molenkamp,L. W., Jungwirth, T. & Sinova, J. Manifestationof the spin Hall effect through charge-transport in the mesoscopic regime.Phys. Rev. B 70, 241301 (2004).

17. Nikoli, B. K., Souma, S., Zrbo, L. & Sinova, J. Nonequilibrium spin Hallaccumulation in ballistic semiconductor nanostructures. Phys. Rev. Lett. 95,046601 (2005).

18. Knig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells.Science 318, 766770 (2007).

19. Gui, Y. et al. Giant spinorbit splitting in a HgTe quantum well. Phys. Rev. B70, 115328 (2004).

20. Hinz, J. et al. Gate control of the giant Rashba effect in HgTe quantum wells.Semicond. Sci. Technol. 21, 501506 (2006).

21. Novik, E. et al. Band structure of semimagnetic HgMnTe quantum wells.Phys. Rev. B 72, 35321 (2005).

22. Hankiewicz, E. M. et al. Charge Hall effect driven by spin-dependent chemicalpotential gradients and Onsager relations in mesoscopic systems. Phys. Rev. B72, 155305 (2005).

23. Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325,294297 (2009).

24. Zhou, B., Lu, H-Z., Chu, R-L., Shen, S-Q. & Niu, Q. Finite size effectson helical edge states in a quantum spin-Hall system. Phys. Rev. Lett. 101,246807 (2008).

25. Yang, W., Chang, K. & Zhang, S-C. Intrinsic spin Hall effect induced byquantum phase transition in HgCdTe quantum wells. Phys. Rev. Lett. 100,056602 (2008).

AcknowledgementsWe thank J. Schneider and N. Eikenberg for assistance in the experiments, and C. Gould,

S-C. Zhang and X-L. Qi for stimulating discussions. We gratefully acknowledge the

financial support by the GermanIsraeli Foundation (I-881-138.7/2005), DFG under

grants AS 327/2-1 and HA5893/1-1, ONR under grant ONR-N000140610122, NSF

under grant DMR-0547875, and SWAN-NRI. We thank the Leibniz Rechenzentrum

Mnich for providing computer resources. J.S. is a Cottrell Scholar of the ResearchFoundation.

Author contributionsDevice fabrication: C.B., A.R., M.K.; experiments and data analysis: C.B., A.R., M.K.,

H.B., L.W.M.; theory: E.G.N., E.M.H., W.H., J.S.; writing: C.B., H.B., E.M.H., J.S.,

L.W.M.; project planning: H.B., L.W.M.

Additional informationThe authors declare no competing financial interests. Supplementary information

accompanies this paper on www.nature.com/naturephysics. Reprints and permissions

information is available online at http://npg.nature.com/reprintsandpermissions.

Correspondence and requests for materials should be addressed to H.B.

http://www.nature.com/doifinder/10.1038/nphys1655http://www.nature.com/naturephysicshttp://npg.nature.com/reprintsandpermissionshttp://www.nature.com/naturephysicshttp://www.nature.com/naturephysicshttp://npg.nature.com/reprintsandpermissionshttp://www.nature.com/naturephysicshttp://www.nature.com/doifinder/10.1038/nphys1655

C. Brüne et al- Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures

Documents

Transcript of C. Brüne et al- Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures