Unconventional Hall Effect in Gapless Superconductors: Transverse Supercurrent Converted from Normal Current

A normal metallic system proximitized by a superconductor can exhibit a gapless superconducting state characterized by segmented Fermi surfaces, as confirmed experimentally. In such a state, quasiparticle states remain gapless along one direction, while a superconducting gap opens in the perpendicular direction. This anisotropy enables a novel Hall effect in gapless superconductors, termed the superconducting Hall effect (ScHE), where a longitudinal normal current carried by quasiparticles is converted into a dissipationless transverse supercurrent. Employing both the thermodynamic approach for bulk systems and quantum transport theory for a four-probe setup, we demonstrate the existence of this effect and reveal its intrinsic origin as the quasiparticle Berry curvature. The predicted ScHE can be experimentally verified via the standard angular-dependent Hall measurements performed on gapless superconductors.