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Exploring new Hall effect is always a fascinating research topic. The ordinary Hall effect and the quantum Hall effect, initially discovered in two-dimensional (2D) non-magnetic systems, are the phenomena that a transverse current is generated when a system carrying an electron current is placed in a magnetic field perpendicular to the currents. In this work, we propose the electric counterparts of these two Hall effects, termed as electric Hall effect (EHE) and quantum electric Hall effect (QEHE). The EHE and QEHE emerge in 2D magnetic systems, where the transverse current is generated by applying an electric gate-field instead of a magnetic field. We present a symmetry requirement for intrinsic EHE and QEHE. With a weak gate-field, we establish an analytical expression of the intrinsic EHE coefficient. We show that it is determined by intrinsic band geometric quantities: Berry curvature and its polarizability which consists of both intraband and interband layer polarization. Via first-principles calculations, we investigate the EHE in the monolayer Ca (FeN) ₂, where significant EHE coefficient is observed around band crossings. Furthermore, we demonstrate that the QEHE can appear in the semiconductor monolayer BaMn₂S₃, of which the Hall conductivity exhibits steps that take on the quantized values 0 and 1 in the unit of e²/h by varying the gate-field within the experimentally achievable range. Due to the great tunability of the electric gate-field, the EHE and QEHE proposed here can be easily controlled and should have more potential applications.
Cui et al. (Fri,) studied this question.