Coupling, merging, and splitting Dirac points by electron-electron interaction

Abstract

The manipulation and movement of Dirac points in the Brillouin zone by the electron-electron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of the gap or splitting of the Dirac points, depending on the inter- or intrasublattice nature of the merging and the sign of the interaction. The topology of the spectrum can therefore be efficiently changed by simply tuning the interaction between particles, as opposed to the usual careful band structure engineering. This is illustrated around the merging transition of one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like Hamiltonian that describes the quadratic band-crossing in three dimensions is also proposed, and its stability under interactions is addressed.

6 pages, 3 figures, published version

References in corpus (20)

• The electronic properties of graphene
• Topological nodal semimetals
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Electronic states and Landau levels in graphene stacks
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
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• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Bloch-Zener oscillations across a merging transition of Dirac points
• Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
• Topological Weyl Semi-metal from a Lattice Model
• Electronic multicriticality in bilayer graphene
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• Massless Dirac Fermions in a Square Optical Lattice
• Chiral anomaly and strength of the electron-electron interaction in graphene
• Interaction induced mergence of Dirac points in Non-Abelian optical lattices
• Majorana mass, time reversal symmetry, and the dimension of space

Cited by in corpus (16)

• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Pseudospin Vortex Ring with a Nodal Line in Three Dimensions
• Nematic, topological and Berry phases when a flat and a parabolic band touch
• Quantum phase transitions in Dirac fermion systems
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Semi-Dirac Fermions in a Topological Metal
• Non-monotonic response and light-cone freezing in gapless-to-(partially) gapped quantum quenches of fermionic systems
• Interplay of Coulomb interaction and disorder in a two-dimensional semi-Dirac fermion system
• Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition
• Quantum Monte Carlo simulation of topological phase transitions
• Microscopic lattice model for quartic semi-Dirac fermions in two dimensions
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Dirac points merging and wandering in a model Chern insulator
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Anomaly non-renormalization in interacting Weyl semimetals