Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene

Abstract

We consider the superconducting and Mott-insulating states for the twisted bilayer graphene, modeled as two narrow-band system of electrons with appreciable intraatomic Coulomb interactions. The interaction induces kinetic exchange which leads to real-space, either triplet- or singlet-spin pairing, in direct analogy to heavy-fermions and high-temperature superconductors. By employing the statistically-consistent Gutzwiller method, we construct explicitly the phase diagram as a function of electron concentration for the spin-triplet $d_{x^2-y^2}+i{d}_{xy}$ paired case, as well as determine the topological edge states. The model reproduces principal features observed experimentally in a semi-quantitative manner. The essential role of electronic correlations in driving both the Mott-insulating and superconducting transitions is emphasized. The transformation of the spin-triplet state into its spin-singlet analogue is also analyzed, as well as the appearance of the phase separated superconducting+Mott-insulating state close to the half filling.

References in corpus (10)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Topological Superconductivity in Twisted Multilayer Graphene
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Wannier Pairs in the Superconducting Twisted Bilayer Graphene and Related Systems
• Phase separation in the particle-hole asymmetric Hubbard model
• Universal properties of high-temperature superconductors from real-space pairing III: The role of correlated hopping and intersite Coulomb interaction within the t-J-U model
• Spin-triplet paired phases inside ferromagnet induced by Hund's rule coupling and electronic correlations: Application to ${\mathrm{UGe}}_2$
• Spontaneous appearance of nonzero momentum Cooper pairing: Possible application to the iron-pnictides
• Statistically-consistent Gutzwiller approach and its equivalence with the mean-field slave-boson method for correlated systems

Cited by in corpus (78)

• Tuning superconductivity in twisted bilayer graphene
• Origin of Magic Angles in Twisted Bilayer Graphene
• Twisted Bilayer Graphene: A Phonon Driven Superconductor
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Strong Correlations and d+id Superconductivity in Twisted Bilayer Graphene
• Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Flatbands in twisted double bilayer graphene
• Magic of high order van Hove singularity
• Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
• Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene
• Nematic superconductivity in twisted bilayer graphene
• Charge-transfer insulation in twisted bilayer graphene
• The Landau Level of Fragile Topology
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
• In-plane critical magnetic fields in magic-angle twisted trilayer graphene
• Valley Jahn-Teller effect in twisted bilayer graphene
• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
• Light-matter coupling and quantum geometry in moiré materials
• Spin-triplet $f$-wave pairing in twisted bilayer graphene near 1/4 filling
• Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Pairing in graphene-based moiré superlattices
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain
• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Twistronics in graphene-based van der Waals structures
• Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles
• Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling
• Symmetry of superconducting correlations in displaced bilayers of graphene
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice
• Harmonic Fingerprint of Unconventional Superconductivity in Twisted Bilayer Graphene
• Constrained Random Phase Approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Electron-K-Phonon Interaction In Twisted Bilayer Graphene
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Possible nodeless $s^{\pm }$-wave superconductivity in twisted bilayer graphene
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Flat-band optical phonons in twisted bilayer graphene
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene
• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Josephson effect in graphene bilayers with adjustable relative displacement
• High-$T_{\text{C}}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\acute{e}$ Superlattices
• Magnetic-impurity resonance states for different pairing symmetries in twisted bilayer graphene
• Topological phases in N-layer ABC-graphene boron-nitride moire superlattices
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Antiferromagnetism and chiral d-wave superconductivity from an effective $t-J-D$ model for twisted bilayer graphene
• Anomalous Higgs oscillations mediated by Berry curvature and quantum metric
• On the nature of the correlated insulator states in twisted bilayer graphene
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Intrinsic non-magnetic ${\varphi }_0$ Josephson junctions in twisted bilayer graphene
• Orbital-Active Dirac Materials from the Symmetry Principle
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Nodal Nematic Superconductivity in Multiple-Flat-Band Land
• Mott transition in the Hubbard model on anisotropic honeycomb lattice with implications for strained graphene: Gutzwiller variational study
• Coulomb-driven band unflattening suppresses $K$-phonon pairing in moiré graphene
• Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields
• Quantum transport of Dirac fermions in selected graphene nanosystems away from the charge-neutrality point
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Atomic frustration-based twistronics