Quantum superconducting criticality in graphene and topological insulators
arXiv:1210.3576 · doi:10.1103/PhysRevB.87.041401
Abstract
The field theory of the semimetal-superconductor quantum phase transition for graphene and surface states of topological insulators is presented. The Lagrangian possesses the global U(1) symmetry, with the self-interacting complex bosonic order-parameter and the massless Dirac fermions coupled through a Yukawa term. The same theory also governs the quantum critical behavior of graphene near the transition towards the bond-density-wave (Kekule) insulator. The local U(1) gauged version of the theory which describes the quantum semimetal-superconductor transition in the ultimate critical regime is also considered. Due to the Yukawa coupling the transitions are found to be always continuous, both with and without the fluctuating gauge field. The critical behavior is addressed within the dimensional regularization near four space-time dimensions, and the calculation of various universal quantities, including critical exponents and the universal mass-ratio, is reported.
4 pages, no figures +(Supplementary: 6 pages and 5 figures), Published version, New discussion on pairing criticality of surface states of topological crystalline insulator, New references
References in corpus (32)
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Topological Insulators in Three Dimensions
- Topological Crystalline Insulators
- Experimental realization of a topological crystalline insulator in SnTe
- Topological crystalline insulator states in Pb(1-x)Sn(x)Se
- Chiral superconductivity from repulsive interactions in doped graphene
- A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
- The space group classification of topological band insulators
- Interactions and phase transitions on graphene's honeycomb lattice
- Electron fractionalization in two-dimensional graphenelike structures
- Superconducting states of pure and doped graphene
- Unconventional superconductivity on a topological insulator
- Unconventional Josephson Effect in Hybrid Superconductor-Topological Insulator Devices
- Theory of interacting electrons on the honeycomb lattice
- Competing many-body instabilities and unconventional superconductivity in graphene
- Density waves and Cooper pairing on the honeycomb lattice
- Resonating valence bonds and mean-field d-wave superconductivity in graphite
- Relativistic Mott criticality in graphene
- Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
- Quantum phase transitions in d-wave superconductors
- Critical fluctuations in superconductors and the magnetic field penetration depth
- Emergence of supersymmetry at a critical point of a lattice model
- BCS-BEC crossover on the two-dimensional honeycomb lattice
- Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
- Induced superconductivity in the three-dimensional topological insulator HgTe
- Topological insulator in the core of the superconducting vortex in graphene
- Multi-critical behavior of Gross-Neveu-Yukawa theory in graphene
- Dual superfluid-Bose glass critical point in two dimensions and the universal conductivity
- Finite temperature transport at the superconductor-insulator transition in disordered systems
- Anomalous scaling of fermions and order parameter fluctuations at quantum criticality
- Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice
- Critical behavior of Ginzburg-Landau model coupled to massless Dirac fermions
Cited by in corpus (79)
- Four-loop critical exponents for the Gross-Neveu-Yukawa models
- Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
- Fermion-induced quantum critical points
- Emergence of supersymmetry on the surface of three dimensional topological insulators
- Superconducting quantum criticality in three-dimensional Luttinger semimetals
- Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
- Phase diagram of the Kane-Mele-Coulomb model
- Interaction driven phases in the honeycomb lattice from exact diagonalization
- Superconductivity of disordered Dirac fermions
- Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
- Ising and Gross-Neveu model in next-to-leading order
- Superconducting quantum criticality of topological surface states at three loops
- Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
- Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
- Large critical exponents for the chiral Heisenberg Gross-Neveu universality class
- Strain-induced time-reversal odd superconductivity in graphene
- Gauge-field-assisted Kekulé quantum criticality
- Probing quantum criticality using nonlinear Hall effect in a metallic Dirac system
- Continuous and discontinuous topological quantum phase transitions
- Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
- Critical behavior of the QED-Gross-Neveu model: Duality and deconfined criticality
- Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
- Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point
- Fermion-induced quantum critical points in three-dimensional Weyl semimetals
- Critical behavior of the QED-Gross-Neveu-Yukawa model at four loops
- Large quantum field theory
- Fermion-induced quantum critical points in two-dimensional Dirac semimetals
- Superconductivity of disordered Dirac fermions in graphene
- Quantum phase transitions in Dirac fermion systems
- Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system
- Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
- Renormalization group analysis of multi-Dirac-node materials
- Classification of massive and gapless phases in bilayer graphene
- Transition between algebraic and quantum spin liquids at large
- Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
- Fermion bilinear operator critical exponents at in the QED-Gross-Neveu universality class
- Phonon spectral function of the one-dimensional Holstein-Hubbard model
- Phase diagram of interacting spinless fermions on the honeycomb lattice
- Itinerant quantum multi-criticality of two dimensional Dirac fermions
- Momentum dependence of quantum critical Dirac systems
- Yukawa CFTs and Emergent Supersymmetry
- Disordered fermionic quantum critical points
- Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU() Dirac fermions
- Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
- Yukawa interactions at Large Charge
- Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
- Wilson-Fisher fixed points in presence of Dirac fermions
- Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
- Superconductivity in two-dimensional disordered Dirac semimetals
- Quantum critical point in the superconducting transition on the surface of topological insulator
- Emergent Fermi surfaces, fractionalization and duality in supersymmetric QED
- Random-mass disorder in the critical Gross-Neveu-Yukawa models
- Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
- Gapless helical superconductivity on the surface of a three-dimensional topological insulator
- Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
- Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
- Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
- SO(4) multicriticality of two-dimensional Dirac fermions
- Triplet superconductivity in 3D Dirac semimetal due to exchange interaction
- Five loop renormalization of the Wess-Zumino model
- Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry
- Absence of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals
- Nematic order on the surface of a three-dimensional topological insulator
- Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene
- Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
- Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
- Supersymmetry dynamics on Rydberg atom arrays
- Holography of dislocations and ring defects in Einstein-Gauss-Bonnet AdS gravity
- Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
- Quantum entanglement between excitons in two-dimensional materials
- Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
- Critical properties of three-dimensional many-flavour QEDs
- Critical structure and emergent symmetry of Dirac fermion systems
- Topology-driven deconfined quantum criticality in magnetic bilayers
- Axionic quantum criticality of generalized Weyl semimetals
- Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator
- Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet
- Renormalization of supersymmetric chiral theories in rational spacetime dimensions
- Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points