Landau, Abrikosov, Hofstadter: Magnetic Flux Penetration in a Lattice Superconductor

TL;DR

This paper models magnetic flux penetration in lattice superconductors using Ginzburg-Landau equations, revealing complex phenomena and novel effects related to Hofstadter's work, with implications for large-scale simulations.

Contribution

It formulates Ginzburg-Landau equations as a lattice gauge theory and compares solutions with classical models, uncovering new effects near the continuum limit.

Findings

Identification of Hofstadter-related effects in flux penetration

Comparison of lattice gauge theory solutions with classical models

Cautionary insights for large-scale simulations

Abstract

Magnetic flux penetration in superconductors involves a rich variety of subtle phenomena, much of which is still poorly understood. Here these complexities are studied by formulating the Ginzburg-Landau equations as a lattice gauge theory. Their solutions are compared and contrasted with the (heuristic) Landau model of type I superconductivity, and the (perturbative) Abrikosov model for type II superconductors. Novelties arise as the continuum limit is approached, related to an effect discovered by Hofstadter. Various cautionary remarks pertinent to large-scale simulations are made.