# Tunable valley Hall effect in gate-defined graphene superlattices

## TL;DR

This paper theoretically explores how gate-defined graphene superlattices with broken inversion symmetry can enable tunable valley Hall effects, showing potential for controllable valley-dependent electronic transport.

## Contribution

It introduces a model for valley Hall effects in graphene superlattices and demonstrates tunability and robustness of valley currents through Berry curvature analysis.

## Key findings

- Valley Hall conductivity can be tuned by superlattice potential.
- Valley currents are robust against dielectric irregularities.
- The superlattice structure resembles a gapped Dirac model.

## Abstract

We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding procedure. In this manner we obtain the valley Hall conductivities from the Berry curvature distribution in the superlattice Brillouin zone, and demonstrate the tunability of this conductivity by the superlattice potential. Finally, we calculate the valley Hall angle relating the transverse valley current and longitudinal charge current and demonstrate the robustness of the valley currents against irregularities in the patterned dielectric.