Charging in the Abrikosov lattice of type-II superconductors

We study the temperature and magnetic field dependence of the vortex-core charge in the Abrikosov lattice of an $s$-wave superconductor based on the augmented quasiclassical equations with the Lorentz force and the pair-potential gradient (PPG) force. It is shown that the charging is dominated by the PPG force at weak magnetic fields and by the Lorentz force at strong magnetic fields, since the charge due to the PPG force, which is large at weak magnetic fields, decreases monotonically as the magnetic field increases, and that due to the Lorentz force has a large peak for the average of the flux density $\bar{B}$ near $B_{{\rm c}2}/2$, where $B_{{\rm c}2}$ is the upper critical field. Moreover, we estimate the magnitude of the vortex-core charge using the parameters used for cuprate superconductors, and found good agreement between our theoretical predictions and the NMR/NQR measurements by Kumagai {\it et al}. We show that the vortex-core charge peaks near $T=0$ and $\bar{B}=B_{{\rm c}2}/2$, which makes it the most suitable region for a measurement of the charge.