Vortex Hall effect in the BCS-BEC crossover: Theory

Superconductivity due to the Cooper pairs, which is described by the Bardeen-Cooper-Schrieffer (BCS) theory, is connected to the Bose-Einstein condensation (BEC) of tightly bound pairs through the BCS-BEC crossover. Recently, the BCS-BEC crossover has been realized in the layered ionic-gating device by controlling carrier doping [1]. In this study, motivated by the recent experiments, we theoretically considered the vortex Hall effect in the BCS-BEC crossover region. Using the phenomenological time-dependent Ginzburg-Landau model [2,3], we found the enhancement of the typical Hall angle toward the crossover region. Further, calculating the temperature dependence of the longitudinal and transverse conductivities due to the vortex liquid, we obtained a possible sign reversal of the Hall effect. In the presentation, we will also discuss the relation to the experimental data explained in the previous talk.

[1] Y. Nakagawa et al., Science 372, 190 (2021).

[2] C. A. R. Sá de Melo, M. Randeria, and J. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993).

[3] S. Ullah and A. Dorsey, Phys. Rev. B 44, 262 (1991).