Stable defect states in the continuous spectrum of bilayer graphene with magnetic field

TL;DR

This paper demonstrates that stable defect states can exist within the continuous spectrum of bilayer graphene under a magnetic field by designing defects that are resilient to spectral variations caused by the Hofstadter butterfly pattern.

Contribution

It introduces a defect design in bilayer graphene that maintains stable bound states despite magnetic field-induced spectral fluctuations.

Findings

Bound defect states remain stable under varying magnetic fields.

Defect design shields bound states from the Hofstadter butterfly effects.

Stable defect states are compatible with interlayer coupling in bilayer graphene.

Abstract

In a tight-binding model of AA-stacked bilayer graphene, it is demonstrated that a bound defect state within the region of continuous spectrum can exist stably with respect to variations in the strength of a perpendicular magnetic field. This is accomplished by creating a defect that is compatible with the interlayer coupling, thereby shielding the bound state from the effects of the continuous spectrum, which varies erratically in a pattern known as the Hofstadter butterfly.