Two-dimensional Coulomb glass as a model for vortex pinning in superconducting films

TL;DR

This paper models vortex pinning in highly disordered superconducting films using a two-dimensional Coulomb glass framework, revealing a non-ergodic glass state with strong collective pinning and a wide distribution of pinning energies.

Contribution

It introduces a novel glass model for vortex pinning in disordered superconductors near the quantum phase transition, applying replica theory to analyze non-ergodic vortex states.

Findings

Vortex system exhibits a non-ergodic glass state.

Distribution of local pinning energies has a wide gap.

Strong collective pinning dominates in disordered superconductors.

Abstract

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase -- such as $\mathrm{In O}_x$, $\mathrm{Nb N}$, $\mathrm{Ti N}$, $\mathrm{Mo Ge}$, nano-granular aluminium, and others -- is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with large kinetic inductance per square $L_K$. Distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap, i.e. the probability to find a weakly pinned vortex is extremely low.