Magic radius of AA bilayer graphene quantum dot

TL;DR

This paper investigates the electronic properties of AA bilayer graphene quantum dots, identifying specific 'magic' radii where electron states exhibit layer parity degeneracy, and draws an analogy to twisted bilayer graphene at magic angles.

Contribution

It introduces the concept of 'magic' radii in AA bilayer graphene quantum dots and explores their relation to twisted bilayer graphene's magic angles, offering new insights into electronic structure.

Findings

Identification of discrete 'magic' radii with degenerate electron states

Layer parity of the highest occupied level changes at magic radii

Analogy established between AA quantum dots and twisted bilayer graphene

Abstract

We study analytically and numerically electronic properties of a circular quantum dot made from AA bilayer graphene. We observe a discrete set of dot radii for which the low-energy electron states are degenerate with respect to the layer parity. By analogy with the ``magic angles" in the twisted bilayer graphene we refer to these radii as ``magic". Such a feature is unique for the AA structures and is related to a specific layer-symmetry of the AA graphene bilayer: the parity of the highest occupied level changes from layer-symmetric to layer-antisymmetric when the radius of the AA dot is equal to its magic value. We explore an analogy in the electronic structure between twisted bilayer graphene at the magic twist angle and the AA quantum dot with magic radius. We argue that this analogy can be helpful for theoretical description of the electronic properties of the twisted bilayer graphene.