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

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• Nonreciprocal Ballistic Transport in Asymmetric Bands
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• Quantum nonlinear ac transport theory at low frequency
• Classification of spin Hall effect in two-dimensional systems
• Tunable linear and nonlinear anomalous Hall transport in two-dimensional CrPS${}_4$
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
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