Assa Auerbach, Ilya Finkler, Bert Halperin and Amir Yacoby - PowerPoint PPT Presentation

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Assa Auerbach, Ilya Finkler, Bert Halperin and Amir Yacoby

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Dark magneto resistance: Shubnikov-de-Haas oscillations. at large B ... Magneto Transport theory. j(E) is determined by microscopics at lengthscales lc ... – PowerPoint PPT presentation

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Title: Assa Auerbach, Ilya Finkler, Bert Halperin and Amir Yacoby


1
Self Organization in Non Equilibrium The
Quantum Hall Zero Conductance State
  • Assa Auerbach, Ilya Finkler, Bert Halperin and
    Amir Yacoby

Phys. Rev. Lett. 94, 196801 (2005)
  • Organizing Principle Lyapunov Functional
  • Zero Conductance Domains Phase.
  • Introducing Long Range Disorder .
  • Experimental effects of disorder potentials.

2
ZRS
3
Microscopic Theory negative conductivity
4
Magneto Transport theory
5
The Lyapunov functional
1. Extrema of G are Kirchoff Steady States.
2. G is a spontaneously decreasing function of
time! (like a Free Energy).
6
The Global Lyapunov Minimum(Ground Steady-State)
7
The Zero Conductance state (no long range
disorder)
Free motion of domain wall under external bias
Zero Conductance
8
Domains in two dimensions Clean system
What are the effects of a long range potential
disorder?
9
Coupling a slowly varying internal field
10
White noise disorder (Imry-Ma argument)
11
One dimensional disorder
12
stability constraints on domain walls with
disorder
13
The separable Egg Carton potential
14
correlated disorder f(x)g(y)
15
2D disorder (non separable)
Field E cannot fully align with disorder field
Ed Frustration
16
Charge and dissipative currents
1. Domain walls are pinned.2. Frustration
drives circulating dissipative currents. 3.
I(V) is discontinuous, walls jump between
steady states. gt glassiness.
17
conclusions
  • For constant Hall conductivity, there is a
    Lyapunov functional which organizes the
    stability of steady states
  • The Zero Conductance State survives weak 2D white
    noise disorder.
  • The disorder fields produces a photo voltage
    and circulating dissipative currents.
  • 1D and correlated or strong 2D disorder pins
    domain walls and produce finite resistivity.
  • 5. Soon A fuller microscopic theory for
    j(E) the magnitude of induced fields,
  • detailed phase diagram and frequency dependent
    magnetoresistance.
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