Electric Hall Effect and Quantum Electric Hall Effect

TL;DR

This paper introduces electric and quantum electric Hall effects in 2D magnetic systems, driven by electric gate-fields, with theoretical analysis and first-principles calculations demonstrating their properties and potential for tunable applications.

Contribution

The work proposes the electric and quantum electric Hall effects, deriving their symmetry conditions, analytical coefficients, and demonstrating their occurrence in specific 2D materials through first-principles calculations.

Findings

Significant EHE coefficient observed in monolayer Ca(FeN)$_2$ near band crossings.

QEHE exhibits quantized Hall conductivity steps of 0 and ±1 in $ m BaMn_2S_3$.

EHE and QEHE are controllable via electric gate-fields, enabling potential applications.

Abstract

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 $\rm BaMn_2S_3$, of which the Hall conductivity exhibits steps that take on the quantized values $0$ and $\pm1$ in the unit of $e^2/h$ 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.