A semi-Dirac point in the Hofstadter spectrum

TL;DR

This paper investigates how a uniaxial staggered potential can merge Dirac points in a square lattice's Hofstadter spectrum, leading to a topological transition to a semi-Dirac phase with hybrid dispersion, relevant for cold atom experiments.

Contribution

It introduces a mechanism for merging Dirac points into a semi-Dirac point in the Hofstadter spectrum using a staggered potential, revealing a topological transition.

Findings

Dirac points merge into a semi-Dirac point under specific conditions

Spectrum becomes linear in one direction and quadratic in the other at transition

Potential observation in cold atom optical lattice experiments

Abstract

The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair of Dirac points may merge into a single one, with a topological transition towards a gapped phase. At the transition, the spectrum is linear in one direction and quadratic in the other one (a spectrum recently named "hybrid" or "semi-Dirac"). This transition is studied in the framework of a general Hamiltonian describing the merging of Dirac points. The possibility of creating gauge fields for cold atoms in optical lattices may offer the first opportunity to observe this merging of Dirac points and the hybrid dispersion relation.