Bilayer graphene in periodic and quasiperiodic magnetic superlattices

TL;DR

This paper investigates the low-energy excitations in bilayer graphene subjected to periodic and quasiperiodic magnetic superlattices, using supersymmetry transformations to engineer potentials with bound states for quantum metamaterials.

Contribution

It introduces a method to create nonsingular Schrödinger potentials with defects and embedded bound states in quasiperiodic magnetic superlattices using second order supersymmetry transformations.

Findings

Bound states can be engineered in quasiperiodic magnetic superlattices.

Supersymmetry transformations enable control over potential defects.

Potential applications in quantum metamaterials.

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 Schr\"odinger Hamiltonians intertwined by a second order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create nonsingular Schr\"odinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated to 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.