Patterns of the Aharonov-Bohm oscillations in graphene nanorings

TL;DR

This study uses tight-binding calculations to explore the Aharonov-Bohm effect in various graphene nanorings, revealing universal oscillation periods and complex patterns influenced by shape and electron count.

Contribution

It demonstrates the universality of AB oscillation periods in graphene rings and uncovers new odd-even and shape-dependent oscillation patterns.

Findings

Universal integer and half-integer AB oscillation periods.

Presence of odd-even sawtooth patterns related to electron number.

Complex oscillation patterns depending on ring shape and size.

Abstract

Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary conditions. Unlike the previous literature, we demonstrate the universality of integer (hc/e) and half-integer (hc/2e) values for the period of the AB oscillations as a function of the magnetic flux, in consonance with the case of mesoscopic metal rings. Odd-even (in the number of Dirac electrons, N) sawtooth-type patterns relating to the halving of the period have also been found; they are more numerous for a monolayer hexagonal ring, compared to the cases of a trigonal and a bilayer hexagonal ring. Additional more complicated patterns are also present, depending on the shape of the graphene ring. Overall, the AB patterns repeat themselves as a function of N with periods proportional to the number of the sides of the rings.