Charging in the vortex lattice of type-II superconductors

TL;DR

This study investigates how vortex-core charge in type-II superconductors varies with magnetic field, revealing the dominance of pair-potential gradient effects at low fields and Lorentz force effects at higher fields, with significant charge accumulation estimated for cuprates.

Contribution

The paper introduces a comprehensive numerical analysis incorporating pair-potential gradient terms alongside Lorentz force effects to understand vortex-core charging in superconductors.

Findings

Charge redistribution varies with magnetic field strength.

Pair-potential gradient effects dominate at weak fields.

Lorentz force effects lead to a peak in core charge around half the upper critical field.

Abstract

We study the magnetic-field dependence of the vortex-core charge in the Abrikosov lattice of an $s$-wave superconductor based on the augmented quasiclassical equations, where we incorporate the pair-potential gradient (PPG) terms characteristic of charging in superconductors besides the well-known Lorentz force. Our numerical results at $T=0.2 T_{\rm c}$ and $0.5 T_{\rm c}$ reveal that periodic charge redistribution is superimposed on the magnetic flux-line lattice with different spatial patterns at different fields. The PPG terms are dominant at weak fields over the Lorentz force for accumulating charge in the vortex cores, whereas the Lorentz force prevails at higher fields to give rise to a peak structure in the core charge around $H\sim \frac{1}{2}H_{{\rm c}2}$. We estimate the peak value of the core charge at $T=0.2 T_{\rm c}$ using parameters appropriate for cuprates to obtain a large value of $Q \sim 10^{-2} |e|$ in the core region of radius $0.2 \xi_0$ in the $ab$ plane and length $1 \ {\rm nm}$ along the $c$ axis.