Numerical study of spin quantum Hall transitions in superconductors with broken time-reversal symmetry

TL;DR

This study numerically investigates spin quantum Hall transitions in disordered p-wave superconductors with broken time-reversal symmetry, revealing critical energies and transition behaviors similar to integer quantum Hall effects.

Contribution

It provides new numerical evidence on the critical behavior and energy merging phenomena of spin quantum Hall transitions in disordered superconductors with broken time-reversal symmetry.

Findings

Critical energies exist only at discrete points in the thermodynamic limit.

The spin-quantum Hall transition shares critical behavior with the integer quantum Hall transition.

Disorder causes critical energies to merge and vanish, akin to lattice models for quantum Hall transitions.

Abstract

We present results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin components is conserved. The transport properties of the system are studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by calculating the Chern and Thouless numbers of the quasiparticle states. We find that in the presence of disorder, (spin-)current carrying states exist only at discrete critical energies in the thermodynamic limit, and the spin-quantum Hall transition driven by an external Zeeman field has the same critical behavior as the usual integer quantum Hall transition of non-interacting electrons. These critical energies merge and disappear as disorder strength increases, in a manner similar to those in lattice models for integer quantum Hall transition.