Graphene-like massless Dirac fermions in Harper systems

TL;DR

This paper demonstrates that Harper systems can host Dirac points at the spectrum center under specific magnetic flux conditions, revealing a graphene-like behavior in these quantum systems.

Contribution

It shows the emergence of Dirac points in Harper systems at certain flux fractions, linking spectral features to the Hofstadter nesting property and experimental magnetic field effects.

Findings

Dirac points occur at spectrum center for even denominator flux fractions

Dirac points result from touching of two subbands in Harper systems

Supports the Hofstadter nesting conjecture and Peierls-Onsager ansatz

Abstract

It is shown that systems described by Harper's equation exhibit a Dirac point at the center of the spectrum whenever the field parameter is a fraction of even denominator. The Dirac point is formed by the touching of two subbands, and the physics around such point is characterized by the relative field only, as if the latter were null at the reference value. Such behavior is consistent with the nesting property conjectured by Hofstadter, and its experimental verification would give support to such hypothesis as well as the Peierls-Onsager ansatz used to arrive at Harper's equation when crystalline electrons move in a uniform external magnetic field