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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 – PowerPoint PPT presentation

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Title: BACKSCATTERING


1
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 insulator
z
y
x
S
v
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
v
L
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
D
S
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
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