A semi-Dirac point in the Hofstadter spectrum

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.

8 pages, 7 figures

References in corpus (23)

• The electronic properties of graphene
• A tight-binding approach to uniaxial strain in graphene
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Rapidly Rotating Atomic Gases
• Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Merging of Dirac points in a two-dimensional crystal
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Gauge fields for ultracold atoms in optical superlattices
• A new magnetic field dependence of Landau levels on a graphene like structure
• Quantum phase transitions from topology in momentum space
• Zero modes of tight binding electrons on the honeycomb lattice
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Prefect Klein tunneling in anisotropic graphene-like photonic lattices
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Massless Dirac Fermions in a Square Optical Lattice
• Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field
• Low temperature quasiparticle transport in a d-wave superconductor with coexisting charge order

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• Tunable transmittance in anisotropic 2D materials
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• Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Pseudo-magnetic fields in square lattices
• Microscopic lattice model for quartic semi-Dirac fermions in two dimensions
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Energy quantization at the "three-quarter Dirac point" in a magnetic field
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• Deep-lying semi-Dirac fermions in hexagonal close-packed cadmium
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Probing imbalanced Weyl nodes in two-dimensional anisotropic Weyl semimetal via optical conductivity
• Exact Mappings in Condensed Matter Physics
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals
• Winding vectors of topological defects: Multiband Chern numbers