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We derive augmented Eilenberger equations that incorporate the followingmissing force terms: (i) the Lorentz force, (ii) the pair-potential gradient(PPG) force, and (iii) the pressure difference arising from the slope in thedensity of states (DOS). Recently, augmented Eilenberger equations with theLorentz and PPG forces have been derived microscopically by studying the Halland charging effects in superconductors, but the pressure due to the slope inthe DOS has not yet been considered in augmented Eilenberger equations, despitephenomenological indications that it is a charging mechanism in a vortex oftype-II superconductors. This newly added pressure is called "the SDOSpressure". We calculate the charging in an isolated vortex of an s-wavesuperconductor with a spherical Fermi surface using the augmented Eilenbergerequations incorporating the Lorentz force, PPG force, and SDOS pressure. Whenwe compare the charge densities due to the three force terms in the augmentedEilenberger equations, the vortex-core charging due to the SDOS pressure islarger than that due to the other forces near the superconducting transitiontemperature. Thus, when we calculate the charging in an isolated vortex of asuperconductor with a finite slope in the DOS, we should consider not only theLorentz and PPG forces but also the SDOS pressure.

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