Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Abstract

Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to such flat bands. In parallel, theory work has discovered that superconductivity and superfluidity is determined by the quantum geometry and topology of the band structure. These recent key developments are merging to a flourishing research topic: understanding the possible connection and ramifications of quantum geometry on the induced superconductivity and superfluidity in moiré multilayer and other flat band systems. This article presents an introduction to how quantum geometry governs superfluidity in platforms including, and beyond, graphene. We explain how a new type of topology discovered in TBG could affect superconductivity, pinpoint the geometric contribution in its Beretzinskii-Kosterlitz-Thouless (BKT) critical temperature, and mention moiré materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moiré materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.

Accepted version, before editing by the journal editors. We recommend the journal version, if you have access to it

References in corpus (31)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Moiré heterostructures as a condensed matter quantum simulator
• Superconductivity in rhombohedral trilayer graphene
• Exponential localization of Wannier functions in insulators
• Topological quantum matter in synthetic dimensions
• Evidence for unconventional superconductivity in twisted bilayer graphene
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Band geometry, Berry curvature and superfluid weight
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Observation of Quantized Conductance in Neutral Matter
• Topological Euler class as a dynamical observable in optical lattices
• Two-terminal transport measurements with cold atoms
• Band structure and insulating states driven by the Coulomb interaction in twisted bilayer graphene
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Competing magnetic orders in a bilayer Hubbard model with ultracold atoms
• Landau levels in twisted bilayer graphene and semiclassical orbits
• Quantum Metric and Correlated States in Two-dimensional Systems
• Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors
• Quantum geometry and flat band Bose-Einstein condensation
• Light-matter coupling and quantum geometry in moiré materials
• Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices
• Heuristic bounds on superconductivity and how to exceed them
• Characterizing two-dimensional superconductivity via nanoscale noise magnetometry with single-spin qubits
• Superconductivity in monolayer FeSe enhanced by quantum geometry
• Phase-induced transport in atomic gases: from superfluid to Mott insulator
• Probing ultracold Fermi gases with light-induced gauge potentials
• Evidence for Flat Band Dirac Superconductor Originating from Quantum Geometry

Cited by in corpus (196)

• Essay: Where Can Quantum Geometry Lead Us?
• Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene
• Quantum geometry in condensed matter
• Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
• Tunable moiré materials for probing Berry physics and topology
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• When Superconductivity Crosses Over: From BCS to BEC
• Local atomic stacking and symmetry in twisted graphene trilayers
• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
• Strong Pairing Originated from an Emergent ${\mathbb{Z}}_2$ Berry Phase in La${}_3$Ni${}_2$O${}_7$
• Nontrivial quantum geometry of degenerate flat bands
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Diamagnetic response and phase stiffness for interacting isolated narrow bands
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Pair Density Waves from Local Band Geometry
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Quantum-geometry-induced anapole superconductivity
• Quantum geometric effect on Fulde-Ferrell-Larkin-Ovchinnikov superconductivity
• Spin-triplet superconductivity from quantum-geometry-induced ferromagnetic fluctuation
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight
• Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model
• Theory of topological exciton insulators and condensates in flat Chern bands
• Anomalous Coherence Length in Superconductors with Quantum Metric
• Localized dynamics arising from multiple flat bands in a decorated photonic Lieb lattice
• Quantum Geometric Kohn-Luttinger Superconductivity
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Coexistence of near-EF flat band and van Hove singularity in a two-phase superconductor
• Pair density wave facilitated by Bloch quantum geometry in nearly flat band multiorbital superconductors
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Instantaneous response and quantum geometry of insulators
• Geometric Stiffness in Interlayer Exciton Condensates
• Experimental demonstration of topological bounds in quantum metrology
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Superfluid weight in the isolated band limit within the generalized random phase approximation
• Extended magic phase in twisted graphene multilayers
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Piezoelectric effect and diode effect in anapole and monopole superconductors
• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
• Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry
• Geometric superfluid weight of composite bands in multiorbital superconductors
• Flat-band ratio and quantum metric in the superconductivity of modified Lieb lattices
• Cooper pairing, flat-band superconductivity and quantum geometry in the pyrochlore-Hubbard model
• Andreev reflection spectroscopy in strongly paired superconductors
• Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
• Quantum geometry encoded to pair potentials
• Theory of Topological Superconductivity and Antiferromagnetic Correlated Insulators in Twisted Bilayer WSe${}_2$
• Quantum entanglement and quantum geometry measured with inelastic X-ray scattering
• Quantum Metric in Step Response
• Quantum geometry of singlet superconductors
• Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures
• Light-induced switching between singlet and triplet superconducting states
• Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators
• Drude weight and the many-body quantum metric in one-dimensional Bose systems
• Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Spectral Density and Sum Rules for Second-Order Response Functions
• Giant Third-Order Nonlinearity Induced by the Quantum Metric Quadrupole in Few-Layer WTe2
• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Drude weight of an interacting flat-band metal
• Quantum Metric Nonlinear Spin-Orbit Torque Enhanced by Topological Bands
• Nonlinear optical responses and quantum geometry in rhombohedral trilayer graphene
• Quantum Geometry and the Hidden Scales in Materials
• Detecting the spread of valence band Wannier functions by optical sum rules
• Kondo screening and coherence in kagome local-moment metals: Energy scales of heavy fermions in the presence of flat bands
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Intercavity polariton slows down dynamics in strongly coupled cavities
• Disorder-Induced Delocalization in Magic-Angle Twisted Bilayer Graphene
• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
• Quarter Metal Superconductivity
• Intrinsic non-magnetic ${\varphi }_0$ Josephson junctions in twisted bilayer graphene
• Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials
• Infrared photoresistance as a sensitive probe of electronic transport in twisted bilayer graphene
• High-$T_c$ Berezinskii-Kosterlitz-Thouless transition in 2D superconducting systems with coupled deep and quasi-flat electronic bands with van Hove singularities
• Flat-band-induced superconductivity in synthetic bilayer optical lattices
• 1/f noise in quantum nanoscience
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Exceeding the Chandrasekhar-Clogston limit in flat-band superconductors: A multiband strong-coupling approach
• Implementation and characterization of the dice lattice in the electron quantum simulator
• Giant chirality-induced spin polarization in twisted transition metal dichalcogenides
• Coherence length and quantum geometry in a dilute flat-band superconductor
• Flattening conduction and valence bands for interlayer excitons in a moiré MoS${}_2$/WSe${}_2$ heterobilayer
• Textured Exciton Insulators
• Electric field induced second-order anomalous Hall transport in unconventional Rashba systems
• Quantum geometric superfluid weight in multiband superconductors: A microscopic interpretation
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Superconductivity from spin fluctuations and long-range interactions in magic-angle twisted bilayer graphene
• Eliashberg Theory and Superfluid Stiffness of Band-Off-Diagonal Pairing in Twisted Graphene
• Universal Wilson Loop Bound of Quantum Geometry
• Superconductivity, generalized random phase approximation and linear scaling methods
• Flat-band Fulde-Ferrell-Larkin-Ovchinnikov State from Quantum Geometric Discrepancy
• Quantum-metric-induced giant and reversible nonreciprocal transport phenomena in chiral loop-current phases of kagome metals
• Emergent spin and orbital angular momentum of light in twisted photonic bilayer
• Geometric and conventional contributions of superconducting diode effect: Application to flat-band systems
• Elf autoencoder: unsupervised exploration of flat-band materials using electronic band structure fingerprints
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Chiral superconductivity from spin polarized Chern band in twisted MoTe${}_2$
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors
• Pair size and quantum geometry in a multiband Hubbard model
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Nonlinear Hall effects with an exceptional ring
• Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Quantum geometric origin of the Meissner effect and superfluid weight marker
• Quantum geometric moment encodes stacking order of moiré matter
• Superconductivity with Wannier-Stark Flat Bands
• Particle dynamics and ergodicity-breaking in twisted-bilayer optical lattices
• Superfluid weight cross-over and critical temperature enhancement in singular flat bands
• Layer Coherence Origin of Planar Hall Effect: from Charge to Multipole and Valley
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Probing fragile topology with a screw dislocation
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Optical conductivity as a probe of the interaction-driven metal in rhombohedral trilayer graphene
• Many-Body Quantum Geometric Dipole
• Superconducting junctions with flat bands
• Thermal and thermoelectric transport in flat bands with non-trivial quantum geometry
• Structure factors and quantum geometry in multiband BCS superconductors
• Bypassing the lattice BCS-BEC crossover in strongly correlated superconductors: resilient coherence from multiorbital physics
• Intertwined Magnetism and Superconductivity in Isolated Correlated Flat Bands
• Functional approach to superfluid stiffness: Role of quantum geometry in unconventional superconductivity
• Magnetic Field Induced Quantum Metric Dipole in Dirac Semimetal Cd3As2
• Quantum geometry induced microwave enhancement of flat band superconductivity
• Effects of the Hubbard interaction on the quantum metric
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• Topological Superfluid Responses of Superconducting Dirac Semimetals
• Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Superfluid stiffness bounds in time-reversal symmetric superconductors
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Common behavior of the scaled condensation energy for both high-$T_c$ and conventional superconductors
• Geometric transport signatures of strained multi-Weyl semimetals
• Transport properties of strongly correlated Fermi systems
• Coexistence of ergodic and non-ergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor
• Phonon spectra, quantum geometry, and the Goldstone theorem
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures
• Berry curvature and quantum metric in copper-substituted lead phosphate apatite
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Kondo-coupled van der Waals antiferromagnet with high-mobility quasiparticles
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Angular momentum of vortex-core Majorana zero modes
• Giant Room-Temperature Third-Order Electrical Transport in a Thin-Film Altermagnet Candidate
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Quenched disorder and the BCS-BEC crossover in the Hubbard model
• Lithography defined semiconductor moires with anomalous in-gap quantum Hall states
• Quantum geometry in correlated electron phases: from flat band to dispersive band
• Moiré spintronics: Emergent phenomena, material realization and machine learning accelerating discovery
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Frustration-free free fermions
• Non-Abelian line graph: A generalized approach to flat bands
• Superfluid Stiffness and Josephson Quantum Capacitance: Adiabatic Approach and Topological Effects
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
• All-optical switching at the two-photon limit with interference-localized states
• Normal state quantum geometry, non-locality and superconductivity
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Scaling behavior of superconductors
• Identifying geometric third-order nonlinear transport in disordered materials
• Superfluid weight in disordered flat-band superconductors as a competition between localization functionals
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Average density of Bloch electrons in a homogeneous magnetic field: A second-order response
• Self-consistent inclusion of disorder in the BCS-BEC crossover near the critical temperature
• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles
• High conductivity from cross-band electron pairing in flat-band systems
• Correlation lengths of flat-band superconductivity from quantum geometry
• The geometry of induced currents in two dimensional media
• Isoperimetric Inequalities in Quantum Geometry
• Intertwined geometries in collective modes of two dimensional Dirac fermions
• Sublattice polarization and filamentary superconductivity in strained graphene
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Chains of nanoparticles for flat-band emission and lasing
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Variational approach for the two-body problem in a multiband extended-Hubbard model
• Flat band mediated photon-photon interactions in 2D waveguide QED networks
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Interaction-driven charge textures and unconventional superconductivity in strained monolayer graphene
• Thermal decoupling in high-$T_c$ cuprate superconductors
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings
• Superconducting magnetoelectric effects in mesoscopic hybrid structures
• Three-dimensional flat bands and possible interlayer triplet pairing superconductivity in the alternating twisted NbSe${}_2$ moiré bulk
• Lattice-induced wavefunction effects on trapped superfluids
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands