Vortex Pinning and the Non-Hermitian Mott Transition

TL;DR

This paper explores a non-Hermitian boson Hubbard model analogy for vortex lines in superconductors, revealing a transition from insulator to superfluid phases influenced by transverse magnetic fields.

Contribution

It introduces a non-Hermitian extension of the boson Hubbard model to describe vortex line behavior under tilted magnetic fields, identifying a novel phase transition.

Findings

Insulating phase is stable at small transverse fields due to exponential screening.

A superfluid phase of tilted vortices emerges at larger transverse fields.

Transition universality class matches vortex entry into the Meissner phase.

Abstract

The boson Hubbard model has been extensively studied as a model of the zero temperature superfluid/insulator transition in Helium-4 on periodic substrates. It can also serve as a model for vortex lines in superconductors with a magnetic field parallel to a periodic array of columnar pins, due to a formal analogy between the vortex lines and the statistical mechanics of quantum bosons. When the magnetic field has a component perpendicular to the pins, this analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find that for small transverse fields, the insulating phase is preserved, and the transverse field is exponentially screened away from the boundaries of the superconductor. At larger transverse fields, a ``superfluid'' phase of tilted, entangled vortices appears. The universality class of the transition is found to be that of vortex lines entering the Meissner phase at H_{c1}, with the additional feature that the direction of the tilted vortices at the transition bears a non-trivial relationship to the direction of the applied magnetic field. The properties of the Mott Insulator and flux liquid phases with tilt are also discussed.