V. Kagalovsky

Thermal metal in network models of a disordered two-dimensional superconductor

We study the symmetry class for localization which arises from models of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry and show the appearance of the metallic phase.

QUANTUM HALL PLATEAU TRANSITIONS IN DISORDERED SUPERCONDUCTORS

We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realised in a dirty, gapless superconductor in which time reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions.

Landau-level mixing and spin degeneracy in the quantum Hall effect

We study the dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing in a random intrachannel potential; the channels represent either two Landau levels or two spin states. We consider channel mixing as a function of the energy separation of the two extended states and show that its effect changes from repulsion to attraction as the energy separation increases. For two Landau levels this leads to level floating at low magnetic fields, while for Zeeman-split spin states we predict level attraction at high magnetic fields, accounting for electron spin resonance data. We also study random mixing of two degenerate channels, while the intrachannel potential is periodic (nonrandom). We find a single extended state with a localization exponent \ensuremath{\nu}\ensuremath{\approx}1.1 for real scattering at nodes; the general case also has a single extended state, though the localized nature of nearby states sets in at unusually large scales.

Temperature Scaling of Conductance between Quantum Hall Plateaus

We show that tunnelling in the quantum Hall regime acquires the form of thermal activation above a crossover temperature T1. The width of the conductance peak σxx between Hall plateaus scales then with temperature as Tκ with κ = 3/7 at T T1. We find that T1 decreases for longer-range potentials or for higher magnetic fields, hence at a given temperature range the apparent κ should decrease for samples with shorter-range scattering or in a given sample at higher Landau levels. These results are consistent with data showing 0.3 κ 0.8 for different Landau levels and for the remarkable difference between InxGa1-xAs/InP and GaAs/AlxGa1-xAs heterostructures.

Random matrix theory and metal–insulator transition in disordered superconductors

Abstract Level statistics for symmetry class D of random matrix ensembles is investigated. It arises in models of non-interacting quasiparticles in disordered superconductors without time-reversal and spin-rotation invariance. In the metallic regime, the nearest-neighbor spacing distribution (NNSD) reproduces exactly the Wigner surmise for GUE as one should expect in the presence of magnetic field, whereas in the localized regime, level repulsion is supressed. NNSD therefore reflects some basic symmetries of the system while ignoring particle–hole symmetries.

Monte Carlo study of particle renormalizations in the presence of dissipative environments

We study the Aharonov-Bohm oscillations of a charged particle on a ring of radius R coupled to a dirty metal environment. With Monte-Carlo methods we evaluate the curvature of these oscillations which has the form 1/M*R^2, where M* is an effective mass. We find that at low temperatures T the curvature approaches at large R>l an R independent M*>M, where l is the mean free path in the metal. This behavior is also consistent with perturbation theory in the particle - metal coupling parameter. At finite temperature T we identify dephasing lengths that scale as T^{-1} at R>l and as T^{-1/4} at R<<l.

Quantum Hall effects in layered disordered superconductors.

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied, demonstrating a phase diagram with charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunneling we find quantum Hall phases with spin Hall coefficients of sigma(spin)(xy)=0,2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of approximately 0.96. In the presence of a Zeeman term an additional sigma(spin)(xy)=1 phase appears.

VARIOUS FACETS OF CHALKER–CODDINGTON NETWORK MODEL

We briefly discuss various applications of the Chalker–Coddington network model, starting with the original one, proposed to describe inter-plateaux transition in the integer quantum Hall effect (IQHE). Next, we present generalization appropriate for the IQHE allowing to include spin, and conclude with recent applications to dirty superconductors. We then describe how numerical calculations on an open network produce data for the localization length behavior in the metal-insulator transition, whereas calculations on the closed system allow elucidation of various levels statistics. We also discuss how numerical algorithm for systems with additional symmetries is modified in order to improve the accuracy. Finally, results for the nearest-neighbor spacing distribution in dirty superconductors are presented.

Spin quantum Hall transition in disordered superconductors

Abstract We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realized in a dirty, gapless superconductor in which time-reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions.

Coalescence of extended states in large quantum dots

Abstract We study quantum Hall systems in which two states become degenerate at some strong magnetic field B 0 . It is shown that random mixing between these states produces two extended states with energy separation vanishing as | B − B 0 | φ ( φ >1), which we denote as level coalescence. In a relatively wide range near B 0 the localization exponent is ν ≈1.1 (though strictly ν ≈1.1 only at B 0 ) while outside this regime the usual quantum Hall value is found ν ≈2.5. We propose that this phenomenon accounts for the observed bunching phenomenon in the addition spectrum of large quantum dots (QD).