Multifractal Study of Quasiparticle Localization in Disordered Superconductors

TL;DR

This paper investigates the transition from thermal metal to insulator in disordered superconductors, using multifractal analysis and transfer matrix methods to determine critical disorder parameters.

Contribution

It introduces a combined approach of transfer matrix and multifractal finite size scaling to accurately characterize the quasiparticle localization transition in disordered superconductors.

Findings

Critical disorder strength and correlation exponent determined

Agreement between transfer matrix and multifractal scaling results

Enhanced understanding of quasiparticle localization in disordered systems

Abstract

The thermal metal to thermal insulator transition due to random disorder is studied in the context of the symmetries of the Bogoliubov de Gennes Hamiltonian. We focus on a three dimensional system with gapless s-wave pairing that possesses time reversal and spin rotational symmetry. The quasiparticle excitations (bogolons) undergo a metal insulator transition as the disorder increases. We determine the critical disorder strength and correlation exponent first by the transfer matrix method (TMM). We then apply a multifractal finite sized scaling (MFSS) of the bogolon wavefunction obtained from large scale diagonalization of the Hamiltonian and obtain the critical disorder strength and exponent, in agreement with those found by TMM.