Confinement in bilayer graphene via intra- and inter-layer interactions

Abstract

Abstract We consider confinement of Dirac fermions in AB-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems where the stationary equation is reducible into two stationary equations with 2 × 2 Dirac-type Hamiltonians and auxiliary interactions. We show that the localized states are given in terms of solutions of an effective Schrödinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogeneous (pseudo-)magnetic field, on-site interactions or inter-layer coupling. In explicit examples, we provide analytical solutions for the states localized by local fluctuations or periodicity defects of the interactions.