A semi-Dirac point in the Hofstadter spectrum

Details A semi-Dirac point in the Hofstadter spectrum A semi-Dirac point in the Hofstadter spectrum

2010-01-22

arxiv.org/abs/1001.3952v1

Phys. Rev. B 82, 035438 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 7 figures

Scientific paper

10.1103/PhysRevB.82.035438

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.

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