BACKSCATTERING

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BACKSCATTERING OF EDGE ELECTRONS IN A STRIP OF
2D TOPOLOGICAL INSULATOR L.Magarill, M.
Entin Institute of Semiconductor Physics SB
RAS, Novosibirsk, Russia
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Edge states in a strip of 2D topological insulator
z
y
x
S
v
HgTe
S
v
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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
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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
?
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Valence-band Hamiltonian of 2D HgTe
k- is in-plane momentum A,B,D are band
parameters 2M is a 2D gap
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Edge states
2D states
Edge states

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Two edges
z
y
x
v
L
HgTe
v
L
Gap
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Edge-state Hamiltonian
System with impurities
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Impurity scattering kinetic equation
Electric field
Backscattering rate
Impurity potential
x
v
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Conductance of finite strip
Long system
Ballistic case
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Edge imperfectness scattering
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Phonon scattering elastic approximation
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Localization
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Single impurity
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Multiple impurities
x
v
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Transition coefficient
Conductance
Localization length
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Localization length
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Resistance
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Phase coherence time
Forward scattering
Kinetic regime
Localization regime
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Bulk conductivity of 2D topological insulator
Edge states in Dirac model
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Random
S
D
D
S
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Resistivity
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• 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.

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Thank you for attention
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Nonlocal resistance