Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter

Abstract

A spatially non-uniform superconducting phase is proposed as the electronic variational ground state for the attractive interactions between nearest neighbors on graphene's honeycomb lattice, close to and right at the filling one half. The state spontaneously breaks the translational invariance of the lattice into the Kekule pattern of bond order parameters, and it is gapped, spin triplet, and odd under the sublattice exchange. With the increase of attractive interactions we first find the transition from the semimetallic phase into the p-Kekule superconductor, defined as being odd under the exchange of Dirac points, with the additional discontinuous superconductor-superconductor transition into the even s-Kekule state, deep within the superconducting phase. Topological excitations of the Kekule superconductor and its competition with other superconducting states on the honeycomb lattice are discussed.

arXiv comment8 RevTex pages, 3 figures; typos corrected, published version

References in corpus (23)

• Quantum Spin Hall Effect in Graphene
• Andreev reflection and Klein tunneling in graphene
• Specular Andreev reflection in graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Superconducting states of pure and doped graphene
• Theory of interacting electrons on the honeycomb lattice
• 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
• Interaction driven instabilities of a Dirac semi-metal
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Massive Dirac fermions in single-layer graphene
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Josephson current in graphene: the role of unconventional pairing symmetries
• Topological insulator in the core of the superconducting vortex in graphene
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• The quantum valley Hall effect in proximity-induced superconducting graphene: an experimental window for deconfined quantum criticality
• Stable Skyrmions in spinor condensates
• Strongly Interacting Two-Dimensional Dirac Fermions
• Anomalous scaling of fermions and order parameter fluctuations at quantum criticality
• Skyrmion in spinor condensates and its stability in trap potentials
• Explanation for the isotropy of the Dirac cone in graphene

Cited by in corpus (112)

• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Dirac materials
• Chiral superconductivity from repulsive interactions in doped graphene
• Artificial graphene as a tunable Dirac material
• Competing many-body instabilities and unconventional superconductivity in graphene
• Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Chiral d-wave superconductivity in doped graphene
• Superconductivity of doped Weyl semimetals: finite-momentum pairing and electronic analogues of the 3He-A phase
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Theory of zero-field superconducting diode effect in twisted trilayer graphene
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Quantum superconducting criticality in graphene and topological insulators
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering
• Ising and Gross-Neveu model in next-to-leading order
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Chiral triplet superconductivity on the graphene lattice
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Strain-induced time-reversal odd superconductivity in graphene
• Tight-binding description of intrinsic superconducting correlations in multilayer graphene
• Gauge-field-assisted Kekulé quantum criticality
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Theory of unconventional quantum Hall effect in strained graphene
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
• Isospin of topological defects in Dirac systems
• Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene
• Magnetic and Kohn-Luttinger instabilities near a Van Hove singularity: monolayer versus twisted bilayer graphene
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Strain Enhanced Superconductivity in Li-Doped Graphene
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Electronic and optical conductivity of kekulé-patterned graphene: Intravalley and intervalley transport
• Observation of competing, correlated ground states in the flat band of rhombohedral graphite
• Topological insulators in strained graphene at weak interaction
• Competing pairing channels in the doped honeycomb lattice Hubbard model
• 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
• Artificial Graphene: Unconventional Superconductivity in a Honeycomb Superlattice
• Inducing topological order in a honeycomb lattice
• Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
• Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice
• Coexistence of extended flat band and Kekulé order in Li-intercalated graphene
• Unconventional superconductivity from magnetism in transition metal dichalcogenide
• Classification of massive and gapless phases in bilayer graphene
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators
• 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
• Theory of integer quantum Hall effect in insulating bilayer graphene
• Disordered fermionic quantum critical points
• Magnetic field induced inequivalent vortex zero modes in strained graphene
• Topological superconductivity in Dirac honeycomb systems
• Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
• Chiral and topological superconductivity in isospin polarized multilayer graphene
• Cooperon condensation and intra-valley pairing states in honeycomb Dirac systems
• Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Critical properties of the Néel/algebraic-spin-liquid transition
• Dynamic polarization and plasmons in kekulé-patterned graphene: Signatures of the broken valley degeneracy
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Topological States with Broken Translational and Time-Reversal Symmetries in a Honeycomb-Triangular Lattice
• Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields
• Wilson-Fisher fixed points in presence of Dirac fermions
• Superconductivity in two-dimensional disordered Dirac semimetals
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Quantum critical point in the superconducting transition on the surface of topological insulator
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Intra-valley Spin-triplet $p+ip$ Superconducting Pairing in Lightly Doped Graphene
• Phases and phase transitions of a perturbed Kekulé-Kitaev model
• Quasiperiodic pairing in graphene quasicrystals
• Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
• Realization of a vortex in the Kekule texture of molecular Graphene, at a Y junction where 3 domains meet
• Inhomogeneous superconductivity in the presence of time-reversal symmetry
• $SO(8)$ unification and the large-N theory of superconductor-insulator transition of two-dimensional Dirac fermions
• Kekule versus hidden superconducting order in graphene-like systems: Competition and coexistence
• Nodal pair density waves from a quarter-metal in crystalline graphene multilayers
• Kekulé superconductivity and antiferromagnetism on the graphene lattice
• Reentrant Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in the honeycomb lattice
• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Conserved charges of order-parameter textures in Dirac systems
• Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Twist-tuned quantum criticality in moiré bilayer graphene
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Superconductivity in graphene stacks: from the bilayer to graphite
• Magnetic Order-Disorder Transitions on a 1/3 - Depleted Square Lattice
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Synthesis of Majorana mass terms in low-energy quantum systems
• Half vortex and fractional electrical charge in two dimensions
• Stabilizing Topological Superfluidity of Lattice Fermions
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Pair density wave in quarter metals from a repulsive fermionic interaction in graphene heterostructures: A renormalization group study
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• Anomalous Superfluid Density in Pair-Density-Wave Superconductors
• Chiral topological superconductivity in twisted bilayer and double bilayer graphene
• Anomalous Phase-Coherence Scaling in a Quantum-Critical Dirac Semimetal
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature