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. Semiconductors with direct and inverted band structure E V ; p (l=1) E C ; s (l=0) J=1/2; j=±1/2 J=3/2; j=±3/2; j=±1/2 J=1/2; j=±1/2; Direct band structure J=l+s;  g ≈1.5eV E C ; p (l=1) J=3/2;j = ±1/2 E V ; p (l=1) J=3/2;j = ±3/2 E V ; s (l=0) J=1/2 E V ; p (l=1) J=1/2 Inverted band structure  g  - 0.35 eV CdTeHgTe V e ~ Z 2 (e 2 /h)

4. Energy spectrum in HgTe quantum well d w, nm (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))

5. 2D топологический изолятор в HgTe квантовых ямах (d w = 7-9 nm) H1H1 E1E1 Gap = (10 – 50) meV 0W 0 W with the gap j = ±3/2 j = ±1/2

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

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

8. Experimental consequences for 2D TI: two probes conductance The upper 1D single-mode wire The lower 1D single-mode wire In a ballistic case G = G u + G l = I/(μ left – μ right ) = e 2 /h + e 2 /h = 2e 2 /h In a diffusive case (max{l u, l l } << L) G = G u + G l = [(l u + l l )/L]e 2 /h = insulator L

9. Experiment (Wurzburg group): ballistic case

10. HgTe quantum well field effect transistor

11. Temperature dependence

12. Nonlocal transport R nl ≈ 2·10 -3 ρ xx для L/W = 2 и R nl ≈ 10 -10 ρ xx для L/W = 7

13. Typical experiment

14. Transition 2D TI – 2D Dirac metal induced by in-plain magnetic field Four-terminal local R I=1,4;V=2,3 (black) and nonlocal R I=6,2;V=5,3 (red dashes) resistances as a function of the 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|; α strongly depends on disorder strength Γ Our experiments are in agreement with the case of a small disorder Γ < E g

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 R one of the samples of The sample as a function of the temperature at charge neutrality point (Vg – V CNP ) = 0 measured by various voltage probes in the temperature interval (4-0.3) K, I=10 -9 A. The top panel shows schematics view of the sample. Conclusion: no one-dimensional localization.

18. Glasman et al model Result: G 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 ~ (∆d W /d W ) 3

22. Experiment 70μm 250μm100μm

23. Temperature dependence of local and nonlocal resistance at CNP