Instabilities of a birefringent semi-metal

Abstract

Birefringent fermions arise as massless fermionic low energy excitations of a particular tight binding model for spinless fermions on a square lattice which have two "speeds of light" [M. P. Kennett, $etal.$, Phys. Rev. A $83$, 053636 (2011)]. We use mean field theory to study phases that can arise when there are nearest neighbour and next-nearest neighbour repulsive interactions in this model and demonstrate robustness of the birefringent semi-metal phase in the presence of weak interactions and identify transitions to staggered density and quantum anomalous Hall ordered phases. We consider the effect of coupling birefringent fermions to a magnetic field, and find analytic expressions for the corresponding Landau levels and demonstrate that their integer Quantum Hall effect displays additional plateaux beyond those observed for regular Dirac fermions, such as in graphene. We briefly discuss a tight-binding construction that leads to three dimensional birefringent fermions.

arXiv comment8 pages, 7 figures

References in corpus (33)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Dirac semimetal in three dimensions
• Unconventional Integer Quantum Hall effect in graphene
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Topological Mott Insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• Flat bands, Dirac cones and atom dynamics in an optical lattice
• Lattice generalization of the Dirac equation to general spin and the role of the flat band
• Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Tight-binding couplings in microwave artificial graphene
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Orbital currents in extended Hubbard models of high-T${}_c$ cuprates
• Phases of correlated spinless fermions on the honeycomb lattice
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Diverging dc conductivity due to a flat band in disordered pseudospin-1 Dirac-Weyl fermions
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Fractionalization in a square-lattice model with time-reversal symmetry
• Flat bands with non-trivial topology in three dimensions
• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Birefringent break up of Dirac fermions in a square optical lattice
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Tunable multiple layered Dirac cones in optical lattices
• Manipulation of the Dirac cones and the anomaly in the graphene related quantum Hall effect
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene

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• Robust Marginal Fermi Liquid In Birefringent Semimetals
• Charge Density Waves on a Half-Filled Decorated Honeycomb Lattice
• Quantum phase transitions of multi-species Dirac fermions
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Emergence of asymmetric fermionic order in interacting birefringent fermions
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• Three-dimensional honeycomb carbon: Junction line distortion and novel emergent fermions