Title: Assa Auerbach, Ilya Finkler, Bert Halperin and Amir Yacoby
1Self 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.
2ZRS
3Microscopic Theory negative conductivity
4Magneto Transport theory
5The Lyapunov functional
1. Extrema of G are Kirchoff Steady States.
2. G is a spontaneously decreasing function of
time! (like a Free Energy).
6The Global Lyapunov Minimum(Ground Steady-State)
7The Zero Conductance state (no long range
disorder)
Free motion of domain wall under external bias
Zero Conductance
8Domains in two dimensions Clean system
What are the effects of a long range potential
disorder?
9Coupling a slowly varying internal field
10White noise disorder (Imry-Ma argument)
11One dimensional disorder
12stability constraints on domain walls with
disorder
13The separable Egg Carton potential
14correlated disorder f(x)g(y)
152D disorder (non separable)
Field E cannot fully align with disorder field
Ed Frustration
16Charge 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.
17conclusions
- 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.