# Charging due to Pair-Potential Gradient in Vortex of Type-II Superconductors

## TL;DR

This paper investigates a new charging mechanism in type-II superconductor vortices caused by the pair-potential gradient, which dominates over the Lorentz force in core charging.

## Contribution

It introduces the pair-potential gradient mechanism into superconductivity models and demonstrates its dominant role in vortex core charging.

## Key findings

- PPG mechanism causes charge 10-100 times larger than Lorentz force.
- Core charge depends on temperature, spatial position, and magnetic penetration depth.
- PPG and Lorentz mechanisms work additively at the vortex core.

## Abstract

Besides the magnetic Lorentz force familiar from the Hall effect in metals and semiconductors, there exists a mechanism for charging peculiar to superconductors that is caused by the pair-potential gradient (PPG). We incorporate it in the augmented quasiclassical equations of superconductivity with the Lorentz force to study charging of an isolated vortex in an equilibrium s-wave type-II superconductor. It is found that the PPG mechanism gives rise to charging concentrated within the core whose magnitude at the core center can be 10 to 100 times larger than that caused by the Lorentz force. Our detailed calculations on the spatial, temperature, and magnetic-penetration-depth dependences of the vortex-core charge reveal that the PPG mechanism contributes dominantly to the core charging of the isolated vortex over a wide parameter range. The two mechanisms are also found to work additively at the core center for the present model with an isotropic Fermi surface.