Substrate-induced topological minibands in graphene
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.
- Publication:
-
Physical Review B
- Pub Date:
- September 2018
- DOI:
- 10.1103/PhysRevB.98.125408
- arXiv:
- arXiv:1805.10670
- Bibcode:
- 2018PhRvB..98l5408W
- Keywords:
-
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Condensed Matter - Materials Science;
- Condensed Matter - Quantum Gases;
- Physics - Optics
- E-Print:
- 13 pages, 7 figures, 1 appendix. (Published version)