Inhomogeneity-driven multiform Spontaneous Hall Effect in conventional and unconventional superconductors

The spontaneous Hall effect (SHE), a finite voltage occurring transversal to the electrical current in zero-magnetic field, has been observed in both conventional and unconventional superconductors, appearing as a peak near the superconducting transition temperature. The origin of SHE is strongly debated, with proposed explanations ranging from intrinsic and extrinsic mechanisms such as spontaneous symmetry breaking and time-reversal symmetry breaking (BTRS), Abrikosov vortex motion, or extrinsic factors like material inhomogeneities, such as non-uniform critical temperature (T_c) distributions or structural asymmetries. This work is an experimental study of the SHE in various superconducting materials. We focused on conventional, low-T_c, sharp transition Nb and unconventional, intermediate-Tc, smeared transition Fe(Se,Te). Our findings show distinct SHE peaks around the superconducting transition, with variations in height, sign and shape, indicating a possible common mechanism independent of the specific material. We propose that spatial inhomogeneities in the critical temperature, caused by local chemical composition variations, disorder, or other forms of electronic spatial inhomogeneities could explain the appearance of the SHE. This hypothesis is supported by comprehensive finite elements simulations of randomly distributed Tc's by varying T_c-distribution, spatial scale of disorder and amplitude of the superconducting transition. The comparison between experimental results and simulations suggests a unified origin for the SHE in different superconductors, whereas different phenomenology can be explained in terms of amplitude of the transition temperature with respect to Tc-distribution.