Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry

TL;DR

This paper develops a quantum nonlinear transport theory for the third-order Hall effect in four-terminal devices with time-reversal symmetry, revealing quantum signatures like enhancement due to interference and disorder effects, extending understanding beyond bulk experiments.

Contribution

It introduces a quantum formalism for third-order nonlinear Hall response in multi-terminal devices, independent of system symmetry, and identifies quantum interference and disorder effects as key signatures.

Findings

Quantum enhancement of third-order Hall current with sharp peaks

Disorder-induced enhancement of the third-order Hall effect

Quantum signatures are independent of system symmetry

Abstract

The third-order nonlinear Hall effect induced by Berry-connection polarizability tensor has been observed in Weyl semimetals T$_d$-MoTe$_2$ as well as T$_d$-TaIrTe$_4$. The experiments were performed on bulk samples, and the results were interpreted with the semiclassical Boltzmann approach. Beyond the bulk limit, we develop a quantum nonlinear transport theory to investigate the third-order Hall response of a four-terminal setup with time-reversal symmetry in quantum regime. The quantum nonlinear theory is verified on a model system of monolayer MoTe$_2$, and numerical results on the angle-resolved Hall currents are qualitatively consistent with the experiment. More importantly, quantum signatures of the third-order Hall effect are revealed, which are independent of the system symmetry. The first quantum signature is quantum enhancement of the third-order Hall current, which is characterized by sharp current peaks whose magnitudes are three orders larger than the first-order Hall current. Such quantum enhancement originates from quantum interference in coherent transport, and it can be easily destroyed by dephasing effect. The second quantum signature is disorder-induced enhancement of the third-order Hall current for weak disorders. Our findings reveal quantum characteristics of the third-order Hall effect, and we propose feasible ways to enhance it in nanoscale systems. The quantum third-order theory developed in this work provides a general formalism for describing nonlinear coherent transport properties in multi-terminal devices, regardless of the system symmetry.