2D Topological insulator in HgTe quantum wells Z.D. Kvon

1. 2D Topological insulator in HgTe quantum wells Z.D. Kvon Institute of Semiconductor Physics, Novosibirsk, Russia 1. Introduction. HgTe quantum wells. 2. 2D topological insulator in HgTe quantum wells. 3. Edge current transport. Ballistics and diffusion. 4. Terahertz photoconductivity. 5. New topological insulator in HgTe QW.

2. Co-authors: • E.B.Olshanetsky • O.A.Shegai • D.A.Kozlov • G.M.Gusev • (Universidade de S˜ao Paulo, Brazil) • K. Dantscher • C. Zot • S.D.Ganichev • (Regensburg University) • N.N. Mikhailov • S.A. Dvoretsky Measurements MBE growth

3. Direct band structure Inverted band structure J=l+s; EC; s (l=0) J=1/2; j=±1/2 EC; p (l=1) J=3/2;j = ±1/2 g  -0.35 eV EV; p (l=1) J=3/2;j = ±3/2 g≈1.5eV J=3/2; j=±3/2; j=±1/2 EV; s (l=0) J=1/2 J=1/2; j=±1/2; EV; p (l=1) J=1/2 Semiconductors with direct andinverted band structure EV; p (l=1) Ve ~ Z2(e2/h) CdTe HgTe

4. Energy spectrum in HgTe quantum well (M.I.Dyakonov and A.V.Khaetskii, JETP, 55, 917 (1982),Y.Lin-Liu, L.Sham, PRB, 32, 5561 (1985); L.G.Gerchikov and A.V.Subashiev, PSS(b), 160, 443(1990), B.Bernevig et al, Science,314, 1757 (2006), E.G.Novik et al. PRB, 83, 193304(2011)), O.E.Raichev, PRB, 85, 045310 (2012)) dw,nm

5. 2D топологический изоляторв HgTe квантовых ямах (dw = 7-9 nm) H1 j = ±3/2 0 W Gap = (10 – 50) meV E1 j = ±1/2 0 W with the gap

6. Energy spectrum (O.E Raichev, Phys. Rev.B 85, 045310 (2012)) Density of states

7. |1>|2> <1|2> = 0if spin dependent interaction is absent Topological protection means no back-scattering!Spin is uniquely connected with momentum due to time resersal symmetry (TRS) s p p s

8. Experimental consequences for 2D TI: two probes conductance • The upper 1D single-mode wire In a ballistic case G = Gu + Gl = I/(μleft –μright) = e2/h + e2/h = 2e2/h insulator L In a diffusive case (max{lu, ll} << L) G = Gu + Gl = [(lu + ll)/L]e2/h = The lower 1D single-mode wire

9. Experiment (Wurzburg group): ballistic case

10. HgTe quantum well field effect transistor

11. Temperature dependence

12. Nonlocal transport Rnl ≈ 2·10-3ρxx для L/W = 2 и Rnl ≈ 10-10ρxxдля L/W = 7

13. Typical experiment

14. Transition 2D TI – 2D Dirac metal induced by in-plain magnetic field Four-terminal local RI=1,4;V=2,3 (black) and nonlocal RI=6,2;V=5,3 (red dashes) resistances as a function ofthe gate voltage at T = 4.2 K and B = 0.

15. Linear positive magnetoresistance caused by the breaking of the TRS in a normal magnetic field According to the theory (J. Maciejko, X-L. Qi, and S-C. Zhang, Phys. Rev. B 82,155310 (2010) : Δσ(B)/σ = - α|B|; αstrongly depends on disorder strength Γ Our experiments are in agreement with the case of a small disorder Γ < Eg

16. Edge current state in 2DTI as single-mode long disorder wire Theoretical picture (Mirlin, Gornyi and Polyakov, PRB, 75, 085421 (2007) Experiment with V-grooves single-mode wires E.Levy et al, PRB, 85, 045315 (2012) T(K)

17. Low temperature behavior of HgTe based 2D TI The resistance Rone of the samplesof Thesample as afunction of the temperature at chargeneutralitypoint (Vg – VCNP) =0measured by various voltage probes inthe temperature interval (4-0.3) K, I=10-9 A. The top panelshows schematicsview of the sample. Conclusion: no one-dimensional localization.

18. Glasman et al model Result: G < 2e2/h only at T>0. So one should observe no localization and significant temperature dependence. It contradicts the experiment in which there is no significant R(T) dependence.

19. Terahertz photoconductivity experiment

20. 2D TI terahertz photoconductivity origin

21. 2D topological insulator with complicate bulk energy spectrum: 14 nm HgTe QW W Γ ~ (∆dW/dW)3

22. Experiment 250μm 100μm 70μm

23. Temperature dependence of local and nonlocal resistance at CNP