Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers

TL;DR

This paper introduces a new nonlinear dynamical Hall effect in layered materials with chiral symmetry, driven by combined in-plane and out-of-plane ac fields, revealing a novel interlayer Berry connection polarizability and potential for unique quantum responses.

Contribution

It proposes a new nonlinear Hall effect in twisted bilayers based on interlayer Berry connection polarizability, expanding understanding of quantum metric responses in layered materials.

Findings

Sizable nonlinear Hall effects observed in twisted bilayer transition metal dichalcogenides.

The phase difference of orthogonal fields controls the Hall current's direction and magnitude.

Effect demonstrated over a broad range of twist angles.

Abstract

We propose a novel nonlinear dynamical Hall effect characteristic of layered materials with chiral symmetry, which is driven by the joint action of in-plane and time variation of out-of-plane ac fields $\boldsymbol{j}_{\text{H}}\sim\boldsymbol{\dot{E}_{\perp}}\times\boldsymbol{E}_{\parallel}$. A new band geometric quantity -- interlayer Berry connection polarizability, which probes a mixed quantum metric characteristic of layer hybridized electrons by twisted interlayer coupling, underlies this effect. When the two orthogonal fields have common frequency, their phase difference controls the on/off, direction and magnitude of the rectified Hall current. We show sizable effects in twisted homobilayer transition metal dichalcogenides and twisted bilayer graphene over broad range of twist angles. Our work opens the door to discovering mixed quantum metric responses unique to van der Waals stacking and concomitant applications under the nonlinear spotlight.