Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry

TL;DR

This paper numerically studies the second-order nonlinear Hall effect in a four-terminal system with time-reversal symmetry, highlighting the roles of Coulomb interactions, symmetry, and phase relaxation in generating nonlinear Hall responses.

Contribution

It introduces a comprehensive numerical framework including Coulomb potential and phase relaxation to analyze nonlinear Hall effects in four-terminal systems with specific symmetries.

Findings

Nonlinear Hall effect observed only in the y direction for Mx symmetry.

Internal Coulomb potential contributes to additional nonlinear Hall response.

Phase relaxation induces a dephasing-related nonlinear Hall effect.

Abstract

We numerically investigate the second-order nonlinear Hall transport properties of a four-terminal system with time-reversal symmetry and broken inversion symmetry. Within the nonequilibrium Green's function formalism, the second-order nonlinear conductances are derived, where the internal Coulomb potential in response to external voltages is explicitly included to guarantee the gauge invariance. For the system with single mirror symmetry Mx, nonlinear Hall properties are only observable in the y direction and contributed solely from the second-order nonlinear effect. From the symmetry point of view, the observed nonlinear Hall transport phenomena have one-to-one correspondence with the Berry curvature dipole induced nonlinear Hall effect semiclassically obtained for the same Hamiltonian. In addition to the nonlinear Hall effect originated from symmetries of the system, it is found that the internal Coulomb potential has the same symmetry of the four-terminal system, which gives rise to an extra nonlinear Hall response. Moreover, the phase relaxation mechanism modeled by virtual probes leads to the dephasing-induced nonlinear Hall effect.