Transcript Phys. Rev. Lett. 94, 196801 (2005)

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)
1.
2.
3.
4.
Organizing Principle: Lyapunov Functional
Zero Conductance Domains Phase.
Introducing Long Range Disorder .
Experimental effects of disorder potentials.
ZRS
Hall resistance (classical)
Dark magneto resistance:
Shubnikov-de-Haas oscillations
at large B
Microwave photo resistance.
oscillations with period:
ZRS
Microscopic Theory: negative conductivity
Ando+Uemura.
No radiation, weak magnetic field: (SCBA)
Durst et. al. (Yale).
Displacement Photoconductivity (DP)
---> negative conductivity
Dimitriev, Mirlin, Polyakov, Aleiner, Vavilov
Distribution Function (DF) photoconductivity.
Magneto Transport theory
If:  H  const
Hall current drops out!
j(E) is determined by microscopics at lengthscales < lc
Since
there exists a scalar functional
The Lyapunov functional
If
exists, then
1. Extrema of G are Kirchoff Steady States.
2. G is a spontaneously decreasing function of time!
(like a ‘Free Energy’).
Electrostatics:
The Global Lyapunov Minimum:
(Ground Steady-State)
B
A
B
A
The Zero Conductance state
(no long range disorder)
Negative conductivity is unstable toward creation of finite field domains
corbino
Free motion of domain wall under external bias: Zero Conductance
Domains in two dimensions: Clean system
Lyapunov function
photoinduced electric potential
unstable regime
domain walls bisect field
directions
What are the effects of a long range potential disorder?
Coupling a slowly varying internal field
Microscopics: the different role of electric and electrochemical fields
in the current equation:
photocurrent
electrochemical field
More Generally: a weak internal field modifies g:
The induced field would align with the disorder, but it is frustrated by
the stability constraint
White noise disorder (Imry-Ma argument)
In D=2 white noise disorder is irrelevant to the
Zero Conductance State.
Mesoscopic current fluctuations
One dimensional disorder
1.
2.
Resistance is finite:
Disorder induces a photovoltaic effect:
stability constraints on domain walls with disorder
1.
The field magnitude at domain walls is marginally stable .
2. E is a gradient: domain walls locally constrained by
3.
Currents at domain walls are
4. Domains enclose zero ``2D charge’’ of the disorder
potential
The separable `Egg Carton’ potential
Charge density
correlated disorder f(x)+g(y)
2D disorder (non separable)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Field E cannot fully align
with disorder field Ed:
Frustration
radiation
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Charge and dissipative currents
dissipative currents
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
1. Domain walls are pinned.
2. Frustration drives circulating dissipative currents.
3. I(V) is discontinuous, walls jump between steady states.
==> glassiness.
conclusions
1.
For constant Hall conductivity, there is a Lyapunov functional which organizes
the stability of steady states
2.
The Zero Conductance State survives weak 2D white noise disorder.
3.
The disorder fields produces a photo voltage and circulating dissipative
currents.
4.
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.