Substrate-induced topological minibands in graphene

TL;DR

This paper analytically explores how substrate-induced superlattice potentials in graphene can create topological minibands, including unique Dirac cones and high valley Chern numbers, guiding future substrate engineering for topological electronic properties.

Contribution

It provides an analytical framework for understanding and designing topological minibands in graphene via substrate-induced superlattice potentials, including symmetry analysis and band crossing characterization.

Findings

Identification of a 1.5 Dirac cone from a three-band crossing.

Mapping of parameter space for topological minibands and gap closures.

Discovery of complex band crossings with valley Chern numbers greater than one.

Abstract

The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise from superlattice potentials as induced by a substrate such as hexagonal boron-nitride. Making use of the general form of a weak substrate potential as dictated by symmetry, we analytically derive the low-energy minibands of the superstructure, including a characteristic 1.5 Dirac cone deriving from a three-band crossing at the Brillouin zone edge. Assuming a large supercell, we focus on a single Dirac cone (or valley) and find all possible arrangements of the low-energy electron and hole bands in a complete six-dimensional parameter space. We identify the various symmetry planes in parameter space inducing gap closures and find the sectors hosting topological minibands, including also complex band crossings that generate a valley Chern number atypically larger than one. Our map provides a starting point for the systematic design of topological bands by substrate engineering.