Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching

Abstract

We consider two-dimensional Fermi systems with quadratic band touching and $C_3$ symmetry, as realizable in Bernal-stacked honeycomb bilayers. Within a renormalization-group analysis, we demonstrate the existence of a quantum critical point at a finite value of the density-density interactions, separating a semimetallic disordered phase at weak coupling from a gapped ordered phase at strong coupling. The latter may be characterized by, for instance, antiferromagnetic, quantum anomalous Hall, or charge density wave order. In the semimetallic phase, each point of quadratic band touching splits into four Dirac cones as a consequence of the nontrivial interaction-induced self-energy correction, which we compute to the two-loop order. We show that the quantum critical point is in the $(2+1)$-dimensional Gross-Neveu universality class characterized by emergent Lorentz invariance and a dynamic critical exponent $z=1$. At finite temperatures, $T>0$, we hence conjecture a crossover between $z=2$ at intermediate $T$ and $z=1$ at low $T$, and we construct the resulting nontrivial phase diagram as function of coupling strength and temperature.

arXiv comment17 pages, 6 figures. (v2) Additional remarks included, minor typos corrected; final version as published in PRB as Editors' Suggestion

References in corpus (58)

• The electronic properties of graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• The electronic properties of bilayer graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Electronic properties of graphene-based bilayer systems
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene
• Broken symmetry states and divergent resistance in suspended bilayer graphene
• Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
• Theory of interacting electrons on the honeycomb lattice
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
• 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
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Topological semimetal in a fermionic optical lattice
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Electron-electron interactions in graphene bilayers
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Spontaneously gapped ground state in suspended bilayer graphene
• Quantum phase transitions in d-wave superconductors
• Four - Fermi Theories in Fewer Than Four Dimensions
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Competing orders and quantum criticality in doped antiferromagnets
• Asymptotic safety: a simple example
• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• 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
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Bootstrapping 3D Fermions with Global Symmetries
• Electronic multicriticality in bilayer graphene
• Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Instabilities of interacting electrons on the honeycomb bilayer
• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Antiferromagnetism in the Hubbard Model on the Bernal-stacked Honeycomb Bilayer
• Critical behavior of Dirac fermions from perturbative renormalization
• UV fixed-point structure of the three-dimensional Thirring model
• Four loop renormalization of the Gross-Neveu model
• Transport Gap in Suspended Bilayer Graphene at Zero Magnetic Field
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• On the evaluation of sunset-type Feynman diagrams
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Instabilities of quadratic band crossing points
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Effect of Coulomb interaction on the gap in monolayer and bilayer graphene
• Excitonic Instabilities and Insulating States in Bilayer Graphene
• Influence of hopping selfenergy and quasiparticle degradation on the antiferromagnetic ordering in the bilayer honeycomb Hubbard model

Cited by in corpus (20)

• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Emergent symmetries and coexisting orders in Dirac fermion systems
• Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Twist-tuned quantum criticality in moiré bilayer graphene
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Quantifying the fragility of unprotected quadratic band crossing points
• Quantum field theories of relativistic Luttinger fermions
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Instability of QBC systems to Topological Anderson Insulating phases
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Fermionic criticality with enlarged fluctuations in Dirac semimetals