Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions
arXiv:1907.11810 · doi:10.1103/PhysRevB.100.155101
Abstract
Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions towards charge, spin-density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell RG. We generalize to a large number of fermion flavors to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including corrections. The latter depend on the specific form of the bosonic infrared propagator in 2+1 dimensions, which needs to be included to regularize divergencies. The corrections are surprisingly small, suggesting that the expansion is well controlled in the physical dimension. The order-parameter correlations inherit the electronic anisotropy of the semi-Dirac fermions, leading to correlation lengths that diverge along the spatial directions with distinct exponents, even at the mean-field level. We conjecture that the proximity to the critical point may stabilize novel modulated order phases.
arXiv comment10, pages, 4 figures, 1 table
References in corpus (29)
- The electronic properties of graphene
- Topological Insulators
- Topological insulators and superconductors
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Strain-induced gap modification in black phosphorus
- Electron-Electron Interactions in Graphene: Current Status and Perspectives
- Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
- Interactions and phase transitions on graphene's honeycomb lattice
- Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor -(BEDT-TTF)I Salt
- Merging of Dirac points in a two-dimensional crystal
- Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
- Many-body instability of Coulomb interacting bilayer graphene: RG approach
- Half-metallic semiDirac point generated by quantum confinement in TiO/VO nanostructures
- A new magnetic field dependence of Landau levels on a graphene like structure
- Tight-binding modeling and low-energy behavior of the semi-Dirac point
- Relativistic Mott criticality in graphene
- Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
- Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
- Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
- Emergence of a Chern-insulating state from a semi-Dirac dispersion
- Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
- Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
- Out-of-bounds hydrodynamics in anisotropic Dirac fluids
- Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
- Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
- Superconducting States for Semi-Dirac Fermions at Zero and Finite Magnetic Fields
- Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
- Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
- Hidden Charge Order of Interacting Dirac Fermions on the Honeycomb Lattice
Cited by in corpus (23)
- Semi-Dirac Fermions in a Topological Metal
- Semi-Dirac and Weyl Fermions in Transition Metal Oxides
- Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition
- Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact exponents
- Shear viscosity as a probe of nodal topology
- Coulomb interactions in systems of generalized semi-Dirac fermions
- Quantum Criticality of Excitonic Insulating Transition in Nodal Line Semimetal ZrSiS
- Novel criticality of Dirac fermions from lattice symmetry breaking
- Novel criticality of Dirac fermions in the presence of emergent gauge fields
- Possible instabilities in quadratic and cubic nodal line fermion systems with correlated interactions
- Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids
- Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
- Quantum Hall effective action for anisotropic Dirac semi-metal
- Quantum critical scaling of gapped phases in nodal-line semimetals
- Fermion dispersion renormalization in a two-dimensional semi-Dirac semimetal
- Correlated interaction effects in three-dimensional semi-Dirac semimetal
- Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals
- Bipolaron formed through electron-hole excitation
- Axionic quantum criticality of generalized Weyl semimetals
- Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
- Landau levels of a Dirac electron in graphene from non-uniform magnetic fields
- Interacting type-II semi-Dirac quasiparticles
- Stability of the Néel quantum critical point in the presence of Dirac fermions