Double moir\'e with a twist: super-moir\'e in encapsulated graphene

TL;DR

This paper investigates the complex electronic effects in encapsulated graphene caused by super-moiré patterns resulting from slight misalignments, revealing how these patterns influence the material's electronic spectrum and properties.

Contribution

It introduces a geometrical approach to analyze super-moiré patterns in graphene and distinguishes effects from lattice relaxation and interference, explaining recent experimental observations.

Findings

Band gaps at Dirac points in the spectrum due to super-moiré effects.

Identification of super-moiré features in density of states and conductivity.

Enhanced gaps expected with interaction effects.

Abstract

A periodic spatial modulation, as created by a moir\'e pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moir\'e patterns, resulting in a so-called super-moir\'e (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the non-relaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures.