Magnetoresistance of an Anderson insulator of bosons

TL;DR

This paper investigates how magnetic fields affect the localization of bosonic excitations in two-dimensional Anderson insulators, revealing a specific scaling law and linking quantum interference to classical directed polymer models.

Contribution

It introduces a novel analysis of bosonic Anderson insulators under magnetic fields, establishing a scaling law for localization length and connecting quantum interference to directed polymer models.

Findings

Localization length decreases with magnetic field as B^{4/5}

Quantum interference maps onto directed polymers in random media

Implications for superconductor-insulator transitions and cold atom experiments

Abstract

We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunnelling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length \xi(B) is found to change as \xi^{-1}(B)-\xi^{-1}(0)\sim B^{4/5}. The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the non-trivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.