# Electrostatic Superlattices on Scaled Graphene Lattices

## TL;DR

This paper develops a scalable tight-binding model to simulate quantum transport in graphene superlattices, successfully matching experimental results for gate-controlled superlattices and exploring Dirac cone emergence.

## Contribution

The study introduces a large-scale tight-binding approach for graphene superlattices, accurately modeling transport phenomena and revealing new Dirac cones at strong superlattice modulations.

## Key findings

- Good agreement with experiments at low magnetic fields for moiré superlattices
- Identification of multiple extra Dirac cones at high superlattice modulation
- Simulation accuracy for gate-controlled superlattices without higher-order terms

## Abstract

A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moir\'e patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moir\'e superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple model Hamiltonian that does not comprise higher-order terms of effective vector potential and Dirac mass terms. In the case of gate-controllable superlattices, no higher-order terms are involved, and the simulations are expected to be numerically exact. Revisiting a recent experiment on graphene subject to a gated square superlattice with periodicity of 35 nm, our simulations show excellent agreement, revealing the emergence of multiple extra Dirac cones at stronger superlattice modulation.