Charging in a Superconducting Vortex Due to the Three Force Terms in Augmented Eilenberger Equations

TL;DR

This paper derives augmented Eilenberger equations including the Lorentz, PPG, and SDOS pressure forces to better understand vortex charging in superconductors, revealing the SDOS pressure's significant role near the transition temperature.

Contribution

The paper introduces the SDOS pressure into augmented Eilenberger equations, enhancing the microscopic understanding of vortex charging mechanisms in superconductors.

Findings

SDOS pressure significantly affects vortex charging near transition temperature.

Vortex-core charging due to SDOS pressure exceeds other forces.

Inclusion of SDOS pressure improves modeling accuracy of superconductor vortices.

Abstract

We derive augmented Eilenberger equations that incorporate the following missing force terms: (i) the Lorentz force, (ii) the pair-potential gradient (PPG) force, and (iii) the pressure difference arising from the slope in the density of states (DOS). Recently, augmented Eilenberger equations with the Lorentz and PPG forces have been derived microscopically by studying the Hall and charging effects in superconductors, but the pressure due to the slope in the DOS has not yet been considered in augmented Eilenberger equations, despite phenomenological indications that it is a charging mechanism in a vortex of type-II superconductors. This newly added pressure is called "the SDOS pressure". We calculate the charging in an isolated vortex of an s-wave superconductor with a spherical Fermi surface using the augmented Eilenberger equations incorporating the Lorentz force, PPG force, and SDOS pressure. When we compare the charge densities due to the three force terms in the augmented Eilenberger equations, the vortex-core charging due to the SDOS pressure is larger than that due to the other forces near the superconducting transition temperature. Thus, when we calculate the charging in an isolated vortex of a superconductor with a finite slope in the DOS, we should consider not only the Lorentz and PPG forces but also the SDOS pressure.