Unconventional Scaling of Electric Hall Effect in Magnetic Weyl Semimetals

Abstract

Electric Hall Effect (EHE), a unique phenomenon in two-dimensional (2D) magnetic systems, refers to the generation of Hall current by an out-of-plane electric field $\Ez$. Here, we demonstrate that for 2D magnetic Weyl semimetals that host doubly degenerate nodal points, the EHE features multiple unconventional scaling laws. At zero temperature, the EHE exhibits a topological $E_F^{-1}$ Fermi-energy scaling. Remarkably, the prefactor of the scaling is determined by the global topological charge of the point without any dependence on the local parameters of the system, leading to a universal and significant enhancement of Hall response in any species of Weyl points as the Fermi energy approaches the Weyl point. This significant response enables a weak electric field to be directly converted into a measurable Hall signal. Surprisingly, this enhanced Hall response is not diminished by temperature, but evolves into an unconventional logarithmically corrected scaling at finite temperature $σ_{xy}\propto\Ez\ln(1/|\Ez|)$ for weak $\Ez$, still yielding a divergent electric-field susceptibility. Thus, our work not only unveils intriguing scaling laws resulting from the interaction between magnetism and topology, but also suggests a novel scaling-enhanced and temperature-robust mechanism that may enable weak electric-field sensing through a practical and all-electric route.