Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene

Abstract

We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.

15 pages, 12 figures; updated discussion and analysis on density wave states

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Cited by in corpus (227)

• Tuning superconductivity in twisted bilayer graphene
• Magic Angle Spectroscopy
• Origin of Magic Angles in Twisted Bilayer Graphene
• All "Magic Angles" Are "Stable" Topological
• 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
• Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
• Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene
• Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
• Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• 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
• Band structure and topological property of twisted double bilayer graphenes
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
• Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: a Hartree-Fock study
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Electronic Compressibility of Magic-Angle Graphene Superlattices
• 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
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
• Nematic superconductivity in twisted bilayer graphene
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Charge-transfer insulation in twisted bilayer graphene
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Flat bands and perfect metal in trilayer moiré graphene
• Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene
• Cold atoms in twisted bilayer optical potentials
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Flat Bands in Twisted Bilayers of Two-Dimensional Polar Materials
• The Landau Level of Fragile Topology
• Internal screening and dielectric engineering in magic-angle twisted bilayer graphene
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene
• A chiral twist on the high-$T_c$ phase diagram in Moiré heterostructures
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice
• Landau levels in twisted bilayer graphene and semiclassical orbits
• Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene
• Simulating twistronics without a twist
• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
• Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene
• Heavy fermion representation for twisted bilayer graphene systems
• Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry
• Giant nonlinear Hall effect in strained twisted bilayer graphene
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• In-plane critical magnetic fields in magic-angle twisted trilayer graphene
• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
• The nature of correlations in the insulating states of twisted bilayer graphene
• Valley Jahn-Teller effect in twisted bilayer graphene
• Supermetal
• Spin-twisted Optical Lattices: Tunable Flat Bands and Larkin-Ovchinnikov Superfluids
• Light-matter coupling and quantum geometry in moiré materials
• Spin-triplet $f$-wave pairing in twisted bilayer graphene near 1/4 filling
• Pairing in magic-angle twisted bilayer graphene: role of phonon and plasmon umklapp
• Flat bands in magic-angle vibrating plates
• Emergent Honeycomb Network of Topological Excitations in Correlated Charge Density Wave
• Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene
• Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene
• Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene
• Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene
• Higher-order van Hove singularity in magic-angle twisted trilayer graphene
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Spin-valley density wave in moiré materials
• Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene
• Superconductivity from collective excitations in magic angle twisted bilayer graphene
• Pairing in graphene-based moiré superlattices
• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
• High-order nonlinear optical response of a twisted bilayer graphene
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain
• Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Kohn-Luttinger superconductivity on two orbital honeycomb lattice
• Isospin and momentum polarized orders in bilayer graphene
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone
• Flat-band ferromagnetism in twisted bilayer graphene
• Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Quantum Geometric Contributions to the BKT Transition: Beyond Mean Field Theory
• Twist Angle Controlled Collinear Edelstein Effect in van der Waals Heterostructures
• A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model
• Gauge phonon dominated resistivity in twisted bilayer graphene near magic angle
• 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
• Classifying superconductivity in Moiré graphene superlattices
• Superconductor versus insulator in twisted bilayer graphene
• Correlated Insulating Phases in the Twisted Bilayer Graphene
• WKB estimate of bilayer graphene's magic twist angles
• TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters
• Symmetry of superconducting correlations in displaced bilayers of graphene
• Topological superconductivity, ferromagnetism, and valley-polarized phases in moire systems: Renormalization group analysis for twisted double bilayer graphene
• TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Marginal Fermi liquid in twisted bilayer graphene
• Degradation of phonons in disordered moiré superlattices
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Inherited and flatband-induced ordering in twisted graphene bilayers
• Ferromagnetism and Spin-Valley liquid states in Moiré Correlated Insulators
• Superconductivity induced by the inter-valley Coulomb scattering in a few layers of graphene
• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Orbital susceptibility of T-graphene: Interplay of high-order van Hove singularities and Dirac cones
• Mott phase in a van der Waals transition-metal halide at single layer limit
• Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Single-orbital realization of high-temperature $s^{\pm }$ superconductivity in the square-octagon lattice
• Engineering flat bands in twisted-bilayer graphene away from the magic angle with chiral optical cavities
• Mott insulating state and $d+id$ superconductivity in an ABC graphene trilayer
• Defect-induced magnetism and Yu-Shiba-Rusinov states in twisted bilayer graphene
• Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
• Spin density wave and electron nematicity in magic-angle twisted bilayer graphene
• Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
• $SU(4)$ Valley + Spin Fluctuation Interference Mechanism for Nematic Order in Magic Angle Twisted Bilayer Graphene: Impact of Vertex Corrections
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• 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
• Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight
• ${\phi }_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state
• Superconductivity from Orbital-Selective Electron-Phonon Coupling in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$
• Symmetry constraints on superconductivity in twisted bilayer graphene: Fractional vortices, $4e$ condensates or non-unitary pairing
• Geometric Induction in Chiral Superconductors
• Correlated states of a triangular net of coupled quantum wires: Implications for the phase diagram of marginally twisted bilayer graphene
• $\text{Ab initio}$ four-band Wannier tight-binding model for generic twisted graphene systems
• Current Switching of Valley Polarization in Twisted Bilayer Graphene
• High transmission in twisted bilayer graphene with angle disorder
• Time-reversal versus chiral symmetry breaking in twisted bilayer graphene
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
• Electron-K-Phonon Interaction In Twisted Bilayer Graphene
• Trions in Twisted Bilayer Graphene
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Fermi Surface Symmetric Mass Generation
• Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number
• Metal-Insulator Transition with Charge Fractionalization
• Superconductivity in twisted WSe${}_2$ from topology-induced quantum fluctuations
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Kondo effect in twisted bilayer graphene
• Geometric superfluid weight of composite bands in multiorbital superconductors
• The strong modulation limit of excitons and trions in moiré materials
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Optical rotation in thin chiral/twisted materials and the gyrotropic magnetic effect
• Odd-frequency pair density wave correlations in underdoped cuprates
• Theory of plasmonic edge states in chiral bilayer systems
• Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene
• Topological Mixed Valence Model for Twisted Bilayer Graphene
• Tuning Superconductivity and Charge Density Wave Order in 2H-TaSe2 by Modulating the Van Hove Singularity
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Three-dimensional Moiré Crystal
• Josephson effect in graphene bilayers with adjustable relative displacement
• Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS${}_2$
• Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover
• Charge density waves and Fermi level pinning in monolayer and bilayer SnSe${}_2$
• High-$T_{\text{C}}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\acute{e}$ Superlattices
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• Magnetic-impurity resonance states for different pairing symmetries in twisted bilayer graphene
• Thermal effects in non-Fermi liquid superconductivity
• Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
• Extended linear-in-$T$ resistivity due to electron-phason scattering in moiré superlattices
• Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice
• Bootstrapped Dimensional Crossover of a Spin Density Wave
• Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene
• Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior
• Antiferromagnetism and chiral d-wave superconductivity from an effective $t-J-D$ model for twisted bilayer graphene
• Spin Hall Effect: Symmetry Breaking, Twisting, and Giant Disorder Renormalization
• On the nature of the correlated insulator states in twisted bilayer graphene
• Symmetric Wannier states and tight-binding model for quantum spin Hall bands in AB-stacked MoTe${}_2$/WSe${}_2$
• Chern-insulator phases and spontaneous spin and valley order in a moiré lattice model for magic-angle twisted bilayer graphene
• The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• Fate of density waves in the presence of a higher order van Hove singularity
• Tunable interface states between Floquet-Weyl semimetals
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist
• Charge order and Mott insulating ground states in small-angle twisted bilayer graphene
• Nodal Nematic Superconductivity in Multiple-Flat-Band Land
• Ultrasonic Delamination Based Adhesion Testing for High-Throughput Assembly of van der Waals Heterostructures
• Probing three-state Potts nematic fluctuations by ultrasound attenuation
• Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential
• Differential entropy per particle as a probe of van Hove singularities and flat bands
• Charge density wave solutions of the Hubbard model in the composite operator formalism
• Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions
• Coulomb-driven band unflattening suppresses $K$-phonon pairing in moiré graphene
• Density Wave States in the Presence of an External Magnetic Field
• Momentum-resolved spectroscopy of superconductivity with the quantum twisting microscope
• Fractal non-Fermi liquids from moiré-Hofstadter phonons
• Signatures of electronic ordering in transport in graphene flat bands
• Network of chiral one-dimensional channels and localized states emerging in a moiré system
• Band theory for heterostructures with interface superlattices
• Tuning monolayer superconductivity in twisted NbSe${}_2$ graphene heterostructures
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Topological phases, van Hove singularities, and spin texture in magic-angle twisted bilayer graphene in the presence of proximity-induced spin-orbit couplings
• Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Collective excitations of the Chern-insulator states in commensurate double moiré superlattices of twisted bilayer graphene on hexagonal boron nitride
• 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
• Analogue of atomic collapse for adatoms on rhombohedral multilayer graphene
• Robust $T$-Linear Resistivity due to SU(4) Valley + Spin Fluctuation Mechanism in Magic Angle Twisted Bilayer Graphene
• Geometry-Driven Moiré Engineering in Twisted Bilayers of High-Pseudospin Fermions
• Van-Hove singularities and competing instabilities in an altermagnetic metal
• Proximity-induced charge density wave in a metallic system
• Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition
• Median-point approximation and its application for the study of fermionic systems
• Particle-hole asymmetric phases in doped twisted bilayer graphene
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions