Partial spectral flow and the Aharonov-Bohm effect in graphene

TL;DR

This paper investigates the Aharonov-Bohm effect in graphene, revealing that magnetic flux induces energy level crossings and electron-hole pair creation, using a novel partial spectral flow concept.

Contribution

It introduces the concept of partial spectral flow to analyze energy level crossings and electron-hole pair creation in graphene under magnetic flux.

Findings

Energy levels cross the Fermi level due to magnetic flux

Number of electron-hole pairs equals the number of flux quanta

Partial spectral flow generalizes spectral flow in condensed matter physics

Abstract

We study the Aharonov-Bohm effect in an openended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the vicinity of the graphene sheet and its flux through the tube is adiabatically switched on. It is shown that, in the process, the energy levels of the tight-binding Hamiltonian of pi-electrons unavoidably cross the Fermi level, which results in the creation of electron-hole pairs. The number of pairs is proven to be equal to the number of magnetic flux quanta of the external field. The proof is based on the new notion of partial spectral flow, which generalizes the ordinary spectral flow already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics.