Anomalous and magnetic Hall effect of the Abrikosov vortex in type-II superconductors

Vortices in type-II superconductors have not only a flux quantum but also charge. This vortex-core charging has attracted the interest of many researchers and numerous theoretical studies have been performed. However, its origin is not yet fully understood.

We derive the quasiclassical equations of superconductivity with the Lorentz force, the pair-potential gradient (PPG) force, and the pressure difference due to the slope in the density of states [1]. Using them, we calculate the temperature and magnetic field dependence of the vortex-core charge to study this mechanism and the best parameters for measuring it. We show that the contribution of the PPG force is dominant in a very wide parameter range. Moreover, low temperature and about half the upper critical field are suitable for measuring the charge. We also discuss the zero-field surface charge in nodal superconductors [2] to compare with the vortex-core charge. We can explain that the vortex-core charging due to the PPG force is caused by the anomalous Hall effect of circulating supercurrents since it is large even at zero field such as an isolated vortex and the high-κ limit and dominantly comes from the phase of the pair potential.

[1] H Ueki et al., JPSJ. 87, 044704 (2018).
[2] ES Joshua et al., JPSJ. 89, 104702 (2020).