1. OF EDGE ELECTRONS IN A STRIP OF 2D TOPOLOGICAL INSULATOR
BACKSCATTERING
OF EDGE ELECTRONS IN A STRIP OF 2D TOPOLOGICAL INSULATOR
L.Magarill, M. Entin
Institute of Semiconductor Physics SB RAS,
Novosibirsk, Russia

2. Edge states in a strip of 2D topological insulatorz y x v S
HgTe S v

3. Outline 1.Edge states in 2D topological insulator 2. Motivation
3. Construction of edge states in a strip
4. Edge state Hamiltonian
5. Scattering between edges in classical model
6. Specific kinds of scattering mechanisms:
impurities, phonons, edge irragularities
7. Forward phonon scattering as a dephasing mechanism
8. Low temperature: localization of edge states in a strip
9. Bulk 2D conductivity

4. ? Motivation In a topological insulator current flows along 1D edges
Hence
At the same time the theory of localization stated that if length of 1D system ?

5. Valence-band Hamiltonian of 2D HgTe
k- is in-plane momentum
A,B,D are band parameters
2M is a 2D gap

6. Edge states
2D states
Edge states

7. Two edges z y x v L
HgTe L v
Gap

8. Edge-state Hamiltonian
System with impurities

9. Impurity scattering: kinetic equation
Electric field
Backscattering rate
Impurity potential x v

10. Conductance of finite strip
Long system
Ballistic case

11. Edge imperfectness scattering

12. Phonon scattering; elastic approximation

13. Localization

14. Single impurity

15. Multiple impurities x v

16. Transition coefficient
Conductance
Localization length

17. Localization length

18. Resistance

19. Phase coherence time Forward scattering Kinetic regime
Localization regime

20. Bulk conductivity of 2D topological insulator
Edge states in Dirac model

21. Random S D S D

22. Resistivity

23. Conclusions
Interedge scattering between edge states determines the conductivity of
2D topological insulator strip.
Interedge scattering exponentially decay with the strip width.
Intraedge inelastic scattering determines the phase decoherence and
kinetic equation applicability.
At low temperature the localization of edge states in a strip occurs.
Random fluctuations of the gap sign determine the network of internal edge states.
Hoppings between these edges yield 2D conductivity.

24. Thank you for attention

25. Nonlocal resistance