Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Abstract

Starting from the effective Hamiltonian arising from the tight-binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second-order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second-order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create non-singular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated with quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.