OF EDGE ELECTRONS IN A STRIP OF 2D TOPOLOGICAL INSULATOR

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Presentation transcript:

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

Edge states in a strip of 2D topological insulator z y x v S HgTe S v

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

? 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 ?

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

Edge states 2D states Edge states

Two edges z y x v L HgTe L v Gap

Edge-state Hamiltonian System with impurities

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

Conductance of finite strip Long system Ballistic case

Edge imperfectness scattering

Phonon scattering; elastic approximation

Localization

Single impurity

Multiple impurities x v

Transition coefficient Conductance Localization length

Localization length

Resistance

Phase coherence time Forward scattering Kinetic regime Localization regime

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

Random S D S D

Resistivity

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.

Thank you for attention

Nonlocal resistance