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

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 $2\times 2$ Dirac-type Hamiltonians and auxiliary interactions. We show that it is possible to find localized states by solving an effective Schrödinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogneous (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.

References in corpus (13)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• The electronic properties of bilayer graphene
• Topological confinement in bilayer graphene
• Zero-energy states in corrugated bilayer graphene
• Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• On zero energy states in graphene
• Construction of zero energy states in graphene through the supersymmetry formalism
• Graphene p-n junctions with nonuniform Rashba spin-orbit coupling
• Bilayer graphene in magnetic fields generated by supersymmetry
• Valley current generation using biased bilayer graphene dots
• Strain dependent conductivity in biased bilayer graphene
• Reduction scheme for coupled Dirac systems