Band structures of bilayer graphene superlattices

TL;DR

This paper develops a low-energy model for bilayer graphene superlattices, revealing how periodic modulations induce Dirac fermions, tunable velocities, and potential gaps, with implications for transport properties.

Contribution

It introduces a minimal effective Hamiltonian capturing the effects of superlattices on bilayer graphene's band structure, including Dirac points and gap formation.

Findings

Periodic modulations generate anisotropic massless Dirac fermions.

Electric field superlattices map onto coupled chain models with topological edge modes.

Certain symmetries prevent gap opening at quadratic band touching points.

Abstract

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of 'topological' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.