Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

TL;DR

This study maps the vortex phase diagram in disordered two-dimensional superconductors using large-scale Bogoliubov-de Gennes simulations, revealing various vortex lattice structures and the role of disorder in phase coherence.

Contribution

It provides the first large-scale simulation-based phase diagram of vortex states in disordered superconductors, highlighting new vortex lattice geometries and the impact of disorder on phase coherence.

Findings

Weak disorder preserves a distorted Abrikosov lattice.

Increasing flux induces a rectangular vortex lattice.

Disorder enhances critical magnetic flux, maintaining phase coherence.

Abstract

We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to $100\times100$ where the magnetic flux is introduced by the Peierls's substitution. The substantial larger size than in previous approaches ($\leq 36\times 36$) has allowed us to identify a rich phase diagram as a function of the magnetic flux and the disorder strength. For sufficiently weak disorder, and not too strong magnetic flux, we observe a slightly distorted Abrikosov triangular vortex lattice. An increase in the magnetic flux leads to an unexpected rectangular vortex lattice. A further increase in disorder, or flux gradually destroy the lattice symmetry though strong vortex repulsion persists. An even stronger disorder leads to deformed single vortices with an inhomogeneous core. As number of vortices increases, vortices overlap becomes more frequent. Finally, we show that global phase coherence is a feature of all these phases and that disorder enhances substantially the critical magnetic flux with respect to the clean limit with a maximum on the metallic side of the insulating transition.