92 research outputs found
Network Models in Class C on Arbitrary Graphs
We consider network models of quantum localisation in which a particle with a
two-component wave function propagates through the nodes and along the edges of
an arbitrary directed graph, subject to a random SU(2) rotation on each edge it
traverses. The propagation through each node is specified by an arbitrary but
fixed S-matrix. Such networks model localisation problems in class C of the
classification of Altland and Zirnbauer, and, on suitable graphs, they model
the spin quantum Hall transition. We extend the analyses of Gruzberg, Ludwig
and Read and of Beamond, Cardy and Chalker to show that, on an arbitrary graph,
the mean density of states and the mean conductance may be calculated in terms
of observables of a classical history-dependent random walk on the same graph.
The transition weights for this process are explicitly related to the elements
of the S-matrices. They are correctly normalised but, on graphs with nodes of
degree greater than 4, not necessarily non-negative (and therefore
interpretable as probabilities) unless a sufficient number of them happen to
vanish. Our methods use a supersymmetric path integral formulation of the
problem which is completely finite and rigorous.Comment: 17 pages, 3 figure
Critical fixed points in class D superconductors
We study in detail a critical line on the phase diagram of the Cho-Fisher
network model separating three different phases: metallic and two distinct
localized phases with different quantized thermal Hall conductances. This
system describes non-interacting quasiparticles in disordered superconductors
that have neither time-reversal nor spin-rotational invariance. We find that in
addition to a tricritical fixed point on that critical line there exist
an additional repulsive fixed point (where the vortex disorder
concentration ), which splits RG flow into opposite directions: toward
a clean Ising model at W=0 and toward .Comment: 3 pages, one figur
Universal critical exponent in class D superconductors
We study a physical system consisting of non-interacting quasiparticles in
disordered superconductors that have neither time-reversal nor spin-rotation
invariance. This system belongs to class D within the recent classification
scheme of random matrix ensembles (RME) and its phase diagram contains three
different phases: metallic and two distinct localized phases with different
quantized thermal Hall conductances. We find that critical exponents describing
different transitions (insulator-to-insulator and insulator-to-metal) are
identical within the error of numerical calculations and also find that
critical disorder of the insulator-to-metal transition is energy independent.Comment: 3.5 pages 4 figure
Decoherence induced by magnetic impurities in quantum Hall system
Scattering by magnetic impurities is known to destroy coherence of electron
motion in metals and semiconductors. We investigate the decoherence introduced
in a single act of electron scattering by a magnetic impurity in a quantum Hall
system. To this end we introduce a fictitious nonunitary scattering matrix
for electrons that reproduces the exactly calculated scattering
probabilities. The strength of decoherence is identified by the deviation of
eigenvalues of the product from unity. Using
the fictitious scattering matrix, we estimate the width of the metallic region
at the quantum Hall effect inter-plateau transition and its dependence on the
exchange coupling strength and the degree of polarization of magnetic
impurities.Comment: 13 pages, 4 figure
Hyperfine interaction induced critical exponents in the quantum Hall effect
We study localization-delocalization transition in quantum Hall systems with
a random field of nuclear spins acting on two-dimensional (2d) electron spins
via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network
model, which corresponds to the projection onto the lowest Landau level. The
inhomogeneous nuclear polarization acts on the electrons as an additional
confining potential, and, therefore, introduces additional parameter (the
probability to find a polarized nucleus in the vicinity of a saddle point of
random potential) responsible for the change from quantum to classical
behavior. In this manner we obtain two critical exponents corresponding to
quantum and classical percolation. We also study how the 2d extended state
develops into the one-dimensional (1d) critical state.Comment: 9 pages, 3 figure
Quantum Hall effects in layered disordered superconductors
Layered singlet paired superconductors with disorder and broken time reversal
symmetry are studied. The phase diagram demonstrates charge-spin separation in
transport. In terms of the average intergrain transmission and the interlayer
tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2
separated by a spin metal phase. We identify a spin metal-insulator
localization exponent as well as a spin conductivity exponent of ~0.9. In
presence of a Zeeman term an additional phase with spin Hall coefficient of 1
appears.Comment: 4 pages, 4 figure
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