Mean-field theory for superconductivity in twisted bilayer graphene

Abstract

Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the mean-field $s$-wave superconducting state in such a system and show how the state evolves as the twist angle is tuned, and as a function of the doping level. We argue that part of the experimental findings could well be understood to result from an attractive electron--electron interaction mediated by electron--phonon coupling, but the flat-band nature of the excitation spectrum makes also superconductivity quite unusual. For example, as the flat-band states are highly localized around certain spots in the structure, also the superconducting order parameter becomes strongly inhomogeneous.

arXiv comment5+5 pages, 5+1 figures

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• Graphene Bilayers with a Twist
• Origin of Magic Angles in Twisted Bilayer Graphene
• Theory of phonon-mediated superconductivity in twisted bilayer graphene
• Decoupling superconductivity and correlated insulators 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
• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Kohn-Luttinger 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
• Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
• Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene
• Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
• Nematic superconductivity in twisted bilayer graphene
• A Microscopic Perspective on Moiré Materials
• Cold atoms in twisted bilayer optical potentials
• Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene
• The Landau Level of Fragile Topology
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• Simulating twistronics without a twist
• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
• Strong Inter-valley Electron-Phonon Coupling in Magic-Angle Twisted Bilayer Graphene
• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
• Spin-twisted Optical Lattices: Tunable Flat Bands and Larkin-Ovchinnikov Superfluids
• Light-matter coupling and quantum geometry in moiré materials
• Pairing in magic-angle twisted bilayer graphene: role of phonon and plasmon umklapp
• Spin-triplet $f$-wave pairing in twisted bilayer graphene near 1/4 filling
• Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Pairing in graphene-based moiré superlattices
• Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band
• Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene
• Quantum-metric-enabled exciton condensate in double twisted bilayer graphene
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Flat-band ferromagnetism in twisted bilayer graphene
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Twistronics in graphene-based van der Waals structures
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Superconductor versus insulator in twisted bilayer graphene
• Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling
• Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?
• TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene
• Marginal Fermi liquid in twisted bilayer graphene
• Superconductivity induced by the inter-valley Coulomb scattering in a few layers of graphene
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene
• Electron-phonon and electron-electron interaction effects in twisted bilayer graphene
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Coupled superfluidity of binary Bose mixtures in two dimensions
• Metal-insulator transition and dominant $d+id$ pairing symmetry in twisted bilayer graphene
• Evolution of Superconductivity in Twisted Graphene Multilayers
• Harmonic Fingerprint of Unconventional Superconductivity in Twisted Bilayer Graphene
• Double flat bands in kagome twisted bilayers
• Constrained Random Phase Approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene
• Moire Band Structures of the Double twisted Few Layer Graphene
• Time-reversal versus chiral symmetry breaking in twisted bilayer graphene
• 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
• Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition
• Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene
• Geometric superfluid weight of composite bands in multiorbital superconductors
• Kondo effect in twisted bilayer graphene
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Prominent Cooper Pairing Away From the Fermi Level and its Spectroscopic Signature in Twisted Bilayer Graphene
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Theory of plasmonic edge states in chiral bilayer systems
• Moiré Flat Bands of Twisted Few-layer Graphite
• Josephson effect in graphene bilayers with adjustable relative displacement
• Unconventional superconductivity with preformed pairs in twisted bilayer graphene
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• High-$T_{\text{C}}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\acute{e}$ Superlattices
• Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene
• Anomalous Higgs oscillations mediated by Berry curvature and quantum metric
• Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns
• Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• On the nature of the correlated insulator states in twisted bilayer graphene
• Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii-Kosterlitz-Thouless transition
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Defect-induced band restructuring and length scales in twisted bilayer graphene
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Slave-rotor theory on magic-angle twisted bilayer graphene
• Charge order and Mott insulating ground states in small-angle twisted bilayer graphene
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Theoretical determination of the effect of a screening gate on plasmon-induced superconductivity in twisted bilayer graphene
• Nodal Nematic Superconductivity in Multiple-Flat-Band Land
• Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential
• Stacking sensitive topological phases in a bilayer Kane-Mele-Hubbard model at quarter filling
• Moiré plane wave expansion model for scanning tunneling microscopy simulations of incommensurate two-dimensional materials
• Deep-learning design of graphene metasurfaces for quantum control and Dirac electron holography
• Coulomb-driven band unflattening suppresses $K$-phonon pairing in moiré graphene
• Preformed Cooper pairs in flat-band semimetals
• Momentum-resolved spectroscopy of superconductivity with the quantum twisting microscope
• Tuning monolayer superconductivity in twisted NbSe${}_2$ graphene heterostructures
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• 50 years in the Landau Institute environment
• Moiré surface states and enhanced superconductivity in topological insulators
• Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields
• Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
• Quantum Monte Carlo study of magnetism and chiral d+id-wave superconductivity in twisted bilayer graphene
• Energy Spectrum Theory of Incommensurate Systems
• Atomic frustration-based twistronics
• Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• Microscopic theory for electron-phonon coupling in twisted bilayer graphene
• Tracing the main elements and electron orbitals that induce superconducting phase transition