Vortex Pinning and Non-Hermitian Quantum Mechanics

TL;DR

This paper explores how non-Hermitian quantum mechanics models flux line depinning in superconductors, revealing a delocalization transition driven by an imaginary vector potential and analyzing associated physical phenomena.

Contribution

It introduces a non-Hermitian quantum model for flux line depinning, linking complex eigenvalues to vortex behavior, and characterizes the transition and related physical effects.

Findings

Delocalization transition occurs with increasing imaginary vector potential.

Complex eigenvalues correspond to vortex depinning and flux line behavior.

Penetration length and magnetization exhibit singular behavior near transition.

Abstract

A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of flux lines from extended defects in type-II superconductors subject to a tilted external magnetic field. The physical meaning of the complex eigenvalues and currents of the non-Hermitian system is elucidated in terms of properties of tilted vortex lines. The singular behavior of the penetration length describing stretched exponential screening of a perpendicular magnetic field (transverse Meissner effect), the surface transverse magnetization, and the trapping length are determined near the flux-line depinning point.