56 research outputs found
Random Network Models and Quantum Phase Transitions in Two Dimensions
An overview of the random network model invented by Chalker and Coddington,
and its generalizations, is provided. After a short introduction into the
physics of the Integer Quantum Hall Effect, which historically has been the
motivation for introducing the network model, the percolation model for
electrons in spatial dimension 2 in a strong perpendicular magnetic field and a
spatially correlated random potential is described. Based on this, the network
model is established, using the concepts of percolating probability amplitude
and tunneling. Its localization properties and its behavior at the critical
point are discussed including a short survey on the statistics of energy levels
and wave function amplitudes. Magneto-transport is reviewed with emphasis on
some new results on conductance distributions. Generalizations are performed by
establishing equivalent Hamiltonians. In particular, the significance of
mappings to the Dirac model and the two dimensional Ising model are discussed.
A description of renormalization group treatments is given. The classification
of two dimensional random systems according to their symmetries is outlined.
This provides access to the complete set of quantum phase transitions like the
thermal Hall transition and the spin quantum Hall transition in two dimension.
The supersymmetric effective field theory for the critical properties of
network models is formulated. The network model is extended to higher
dimensions including remarks on the chiral metal phase at the surface of a
multi-layer quantum Hall system.Comment: 176 pages, final version, references correcte
Exploring Level Statistics from Quantum Chaos to Localization with the Autocorrelation Function of Spectral Determinants
The autocorrelation function of spectral determinants (ASD) is used to
characterize the discrete spectrum of a phase coherent quasi- 1- dimensional,
disordered wire as a function of its length L in a finite, weak magnetic field.
An analytical function is obtained depending only on the dimensionless
conductance g= xi/L where xi is the localization length, the scaled frequency
x= omega/Delta, where Delta is the average level spacing of the wire, and the
global symmetry of the system. A metal- insulator crossover is observed,
showing that information on localization is contained in the disorder averaged
ASD.Comment: 4 pages, 3 figure
Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered Wires
The crossover in energy level statistics of a quasi-1-dimensional disordered
wire as a function of its length L is used, in order to derive its averaged
localization length, without magnetic field, in a magnetic field and for
moderate spin orbit scattering strength. An analytical function of the magnetic
field for the local level spacing is obtained, and found to be in excellent
agreement with the magnetic field dependent activation energy, recently
measured in low-mobility quasi-one-dimensional wires\cite{khavin}. This formula
can be used to extract directly and accurately the localization length from
magnetoresistance experiments. In general, the local level spacing is shown to
be proportional to the excitation gap of a virtual particle, moving on a
compact symmetric space.Comment: 4 pages, 2 Eqs. added, Eperimental Data included in Fig.
Localization Length in Anderson Insulator with Kondo Impurities
The localization length, , in a 2--dimensional Anderson insulator
depends on the electron spin scattering rate by magnetic impurities,
. For antiferromagnetic sign of the exchange, %constant, the time
is {\em itself a function of }, due to the Kondo correlations. We
demonstrate that the unitary regime of localization is impossible when the
concentration of magnetic impurities, , is smaller than a critical
value, . For , the dependence of on the
dimensionless conductance, , is {\em reentrant}, crossing over to unitary,
and back to orthogonal behavior upon increasing . Sensitivity of Kondo
correlations to a weak {\em parallel} magnetic field results in a giant
parallel magnetoresistance.Comment: 5 pages, 1 figur
Disorder-quenched Kondo effect in mesosocopic electronic systems
Nonmagnetic disorder is shown to quench the screening of magnetic moments in
metals, the Kondo effect. The probability that a magnetic moment remains free
down to zero temperature is found to increase with disorder strength.
Experimental consequences for disordered metals are studied. In particular, it
is shown that the presence of magnetic impurities with a small Kondo
temperature enhances the electron's dephasing rate at low temperatures in
comparison to the clean metal case. It is furthermore proven that the width of
the distribution of Kondo temperatures remains finite in the thermodynamic
(infinite volume) limit due to wave function correlations within an energy
interval of order , where is the elastic scattering time. When
time-reversal symmetry is broken either by applying a magnetic field or by
increasing the concentration of magnetic impurities, the distribution of Kondo
temperatures becomes narrower.Comment: 17 pages, 7 figures, new results on Kondo effect in quasi-1D wires
added, 6 Refs. adde
Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder
Quantum transport properties in quantum Hall wires in the presence of
spatially correlated random potential are investigated numerically. It is found
that the potential correlation reduces the localization length associated with
the edge state, in contrast to the naive expectation that the potential
correlation increases it. The effect appears as the sizable shift of quantized
conductance plateaus in long wires, where the plateau transitions occur at
energies much higher than the Landau band centers. The scale of the shift is of
the order of the strength of the random potential and is insensitive to the
strength of magnetic fields. Experimental implications are also discussed.Comment: 5 pages, 4 figure
Free Magnetic Moments in Disordered Metals
The screening of magnetic moments in metals, the Kondo effect, is found to be
quenched with a finite probability in the presence of nonmagnetic disorder.
Numerical results for a disordered electron system show that the distribution
of Kondo temperatures deviates strongly from the result expected from random
matrix theory. A pronounced second peak emerges for small Kondo temperatures,
showing that the probability that magnetic moments remain unscreened at low
temperatures increases with disorder. Analytical calculations, taking into
account correlations between eigenfunction intensities yield a finite width for
the distribution in the thermodynamic limit. Experimental consequences for
disordered mesoscopic metals are discussed.Comment: RevTex 4.0, 4.3 pages, 4 EPS figures; typos fixed, reference added,
final published versio
Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires
The quantum phase diagram of disordered wires in a strong magnetic field is
studied as a function of wire width and energy. The two-terminal conductance
shows zero-temperature discontinuous transitions between exactly integer
plateau values and zero. In the vicinity of this transition, the chiral
metal-insulator transition (CMIT), states are identified that are
superpositions of edge states with opposite chirality. The bulk contribution of
such states is found to decrease with increasing wire width. Based on exact
diagonalization results for the eigenstates and their participation ratios, we
conclude that these states are characteristic for the CMIT, have the appearance
of nonchiral edges states, and are thereby distinguishable from other states in
the quantum Hall wire, namely, extended edge states, two-dimensionally (2D)
localized, quasi-1D localized, and 2D critical states.Comment: replaced with revised versio
- …