Fragile topology and flat-band superconductivity in the strong-coupling regime

Abstract

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.

arXiv comment5 pages, 3 figures + supplemental material (14 pages, 4 figures)

References in corpus (58)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Topological quantum chemistry
• Magic continuum in twisted bilayer WSe2
• Electric Field Tunable Correlated States and Magnetic Phase Transitions in Twisted Bilayer-Bilayer Graphene
• Signatures of Gate-Tunable Superconductivity in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Superfluidity in topologically nontrivial flat bands
• Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
• Correlated states in twisted double bilayer graphene
• High-temperature surface superconductivity in topological flat-band systems
• All "Magic Angles" Are "Stable" Topological
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Fragile Topology and Wannier Obstructions
• 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 touching from real space topology in frustrated hopping models
• Geometric origin of superfluidity in the Lieb lattice flat band
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Band geometry, Berry curvature and superfluid weight
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Deviations from Fermi-liquid behavior above $T_c$ in 2D short coherence length superconductors
• Classification of flat bands according to the band-crossing singularity of Bloch wave functions
• Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
• Topological Euler class as a dynamical observable in optical lattices
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Geometric approach to fragile topology beyond symmetry indicators
• Experimental characterization of fragile topology in an acoustic metamaterial
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• How to Measure the Quantum Geometry of Bloch Bands
• Superconducting Transitions in Flat Band Systems
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• The Landau Level of Fragile Topology
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Stiefel-Whitney classes and topological phases in band theory
• Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study
• Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing
• Flat band superconductivity in strained Dirac materials
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model
• The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Flat band in topological matter: possible route to room-temperature superconductivity
• Flat band superconductivity in the square-octagon lattice
• Fragile topological phases in interacting systems
• Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band
• Universal phase diagrams with superconducting domes for electronic flat bands
• Quantum Geometric Contributions to the BKT Transition: Beyond Mean Field Theory
• Temperature Derivative of the Superfluid Density in the Attractive Hubbard model
• Strain induced superconductor-insulator transition on Lieb lattice
• Magnetization, d-wave superconductivity and non-Fermi liquid behavior in a crossover from dispersive to flat bands
• The gate-tunable strong and fragile topology of multilayer-graphene on a transition metal dichalcogenide
• Correlated Insulating States and Transport Signature of Superconductivity in Twisted Trilayer Graphene Moiré of Moiré Superlattices

Cited by in corpus (73)

• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors
• Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
• Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
• Multicellularity of delicate topological insulators
• General construction of flat bands with and without band crossings based on wave function singularity
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• High-throughput Investigations of Topological and Nodal Superconductors
• Diamagnetic response and phase stiffness for interacting isolated narrow bands
• Quantum geometric effect on Fulde-Ferrell-Larkin-Ovchinnikov superconductivity
• Flat bands with band crossings enforced by symmetry representation
• Non-Compact Atomic Insulators
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Geometric Stiffness in Interlayer Exciton Condensates
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Metal-free Stoner and Mott-Hubbard magnetism in 2D polymers with honeycomb lattice
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Superfluid weight in the isolated band limit within the generalized random phase approximation
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
• Flat-band ratio and quantum metric in the superconductivity of modified Lieb lattices
• Majorana corner states on the dice lattice
• Dynamics of self-dual kagome metamaterials and the emergence of fragile topology
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators
• Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
• Drude weight and the many-body quantum metric in one-dimensional Bose systems
• Effective continuum model of twisted bilayer GeSe and origin of emerging one-dimensional mode
• Kondo-lattice-mediated interactions in flat band systems
• Anomalous Higgs oscillations mediated by Berry curvature and quantum metric
• Electron Doping of a Double Perovskite Flat-band System
• Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Catalogue of Flat-Band Stoichiometric Materials
• Dynamical Fragile Topology in Floquet Crystals
• Disorder-Induced Delocalization in Magic-Angle Twisted Bilayer Graphene
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Flat-band Fulde-Ferrell-Larkin-Ovchinnikov State from Quantum Geometric Discrepancy
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Excitation spectra of strongly interacting bosons in the flat-band Lieb lattice
• Robustness of flat band superconductivity against disorder in a two-dimensional Lieb lattice model
• Superconductivity with Wannier-Stark Flat Bands
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Insulator-pseudogap crossover in the Lieb lattice
• Omnidirectional domain wall modes protected by fragile topological states
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Intertwined Magnetism and Superconductivity in Isolated Correlated Flat Bands
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Fragile topology in nodal-line semimetal superconductors
• Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Common behavior of the scaled condensation energy for both high-$T_c$ and conventional superconductors
• Correlated metallic two-particle bound states in Wannier--Stark flatbands
• Superfluid stiffness of superconductors with delicate topology
• Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials
• In-band supratransmission in nonlinear flat band lattices
• Topologically protected two-fluid edge states
• Mott transition and magnetism in a fragile topological insulator
• Scaling behavior of superconductors
• Non-Abelian line graph: A generalized approach to flat bands
• Design and characterization of all two-dimensional fragile topological bands
• Gaplessness from disorder and quantum geometry in gapped superconductors
• RKKY couplings in the Lieb lattice: flat-band induced frustration
• Quantum Geometric Helical Superconductivity
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• High conductivity from cross-band electron pairing in flat-band systems
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• Orbital magnetization reveals multiband topology