Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect

Abstract

We investigate numerically the quasiparticle density of states $\varrho (E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a logarithmic divergence in $\varrho (E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho (E)$ is finite at E=0. At the plateau transition between these phases, $\varrho (E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho (E)\sim |E|\ln (1/|E|)$ derived from calculations for Dirac fermions with random mass.

8 pages, 8 figures, published version

References in corpus (22)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Random Matrix Theories in Quantum Physics: Common Concepts
• Scaling Theory of the Integer Quantum Hall Effect
• Statistics of energy levels and eigenfunctions in disordered systems
• Riemannian symmetric superspaces and their origin in random matrix theory
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• The two-dimensional random-bond Ising model, free fermions and the network model
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Quantum Hall plateau transitions in disordered superconductors
• Thermal metal in network models of a disordered two-dimensional superconductor
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• Particle-hole symmetric localization in two dimensions
• Criticality in the two-dimensional random-bond Ising model
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Quasiparticle density of states in dirty high-T_c superconductors
• Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential
• Superconducting ``metals'' and ``insulators''
• Griffiths phase in the thermal quantum Hall effect
• Quasiparticle Localization Transition in Dirty Superconductors

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