Superconductivity in a Topological Lattice Model with Strong Repulsion

Abstract

The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce a minimal 2D lattice model that incorporates exactly these features: time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall (QSH) insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. At the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the QSH insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be $p$-wave -- reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

30 pages (with 8 figures) + 38 pages supplementary (with 15 figures); v2: updated to match published version

References in corpus (136)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Maximally-localized generalized Wannier functions for composite energy bands
• Cold bosonic atoms in optical lattices
• Tuning superconductivity in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Atomic quantum gases in periodically driven optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Bands for Ultracold Atoms
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Origin of Magic Angles in Twisted Bilayer Graphene
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Computing topological invariants without inversion symmetry
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• All "Magic Angles" Are "Stable" Topological
• Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
• The Hubbard Model
• Wannier representation of Z_2 topological insulators
• Cascade of electronic transitions in magic-angle twisted bilayer graphene
• Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
• High Temperature Superconductivity in Iron Pnictides and Chalcogenides
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Superconductivity in rhombohedral trilayer graphene
• Quantum State Engineering and Precision Metrology using State-Insensitive Light Traps
• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• A Fermi-degenerate three-dimensional optical lattice clock
• Fragile Topology and Wannier Obstructions
• Order and quantum phase transitions in the cuprate superconductors
• 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
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe${}_2$
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Scaling of entanglement support for Matrix Product States
• Band geometry of fractional topological insulators
• Ironing out the details of unconventional superconductivity
• Spin-orbit coupled fermions in an optical lattice clock
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Bad metallic transport in a cold atom Fermi-Hubbard system
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Artificial gauge fields in materials and engineered systems
• Quantum phase transitions across p-wave Feshbach resonance
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Quantum Hall Physics - hierarchies and CFT techniques
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Spin-Orbit Enhanced Superconductivity in Bernal Bilayer Graphene
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Ferromagnetism in narrow bands of moiré superlattices
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Observation of an orbital interaction-induced Feshbach resonance in 173-Yb
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Electron localization in the insulating state: application to crystalline semiconductors
• Spin-orbit coupling and spin Hall effect for neutral atoms without spin-flips
• A strongly interacting gas of two-electron fermions at an orbital Feshbach resonance
• 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
• Strain-induced quantum phase transitions in magic angle graphene
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• An ytterbium quantum gas microscope with narrow-line laser cooling
• Cooling and entangling ultracold atoms in optical lattices
• Multiple topological transitions in twisted bilayer graphene near the first magic angle
• Efficient simulation of moire materials using the density matrix renormalization group
• Ground state phase diagram of the doped Hubbard model on the 4-leg cylinder
• Quantum state engineering of a Hubbard system with ultracold fermions
• Quantum gas microscopy of an attractive Fermi-Hubbard system
• Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions
• Skyrmions without Sigma Models in Quantum Hall Ferromagnets
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Emergence of multi-body interactions in few-atom sites of a fermionic lattice clock
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
• Site-resolved imaging of ytterbium atoms in a two-dimensional optical lattice
• Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• A Fermi-Hubbard Optical Tweezer Array
• Symmetry breaking and skyrmionic transport in twisted bilayer graphene
• State-dependent optical lattices for the strontium optical qubit
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Direct observation of non-local fermion pairing in an attractive Fermi-Hubbard gas
• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• A scaling hypothesis for matrix product states
• Quantum Metric Induced Phases in Moiré Materials
• Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
• Hamiltonian engineering of spin-orbit coupled fermions in a Wannier-Stark optical lattice clock
• Pairing symmetry of twisted bilayer graphene: a phenomenological synthesis
• Topological superconductivity in the doped chiral spin liquid on the triangular lattice
• Topological superconductivity in doped magnetic moiré semiconductors
• Fragile topological phases in interacting systems
• Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Local Matrix Product Operators: Canonical Form, Compression, & Control Theory
• Doping-induced quantum spin Hall insulator to superconductor transition
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Probing transport and slow relaxation in the mass-imbalanced Fermi-Hubbard model
• Chiral non-linear sigma-models as models for topological superconductivity
• Doping the Kane-Mele-Hubbard model: A Slave-Boson Approach
• The Luther-Emery liquid: Spin gap and anomalous flux period
• Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study
• From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Narrow bands in magnetic field and strong-coupling Hofstadter spectra
• Upper critical field for anisotropic superconductivity. A tight-binding approach
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Topological superconductivity in Dirac honeycomb systems
• Triplet $p+ip$ paring correlation in doped Kane-Mele-Hubbard model: A quantum Monte Carlo study
• Trions in Twisted Bilayer Graphene
• Competing orders in the Hofstadter t-J model
• State-dependent potentials for the ${}^1{\text{S}}_0$ and ${}^3{\text{P}}_0$ clock states of neutral ytterbium atoms
• BCS theory of time-reversal-symmetric Hofstadter-Hubbard model
• How quantum phases on cylinders approach the 2d limit
• Hofstadter-Hubbard model with opposite magnetic fields: Bardeen-Cooper-Schrieffer pairing and superfluidity in the nearly flat butterfly bands
• Edge superconducting state in attractive U Kane-Mele-Hubbard model

Cited by in corpus (5)

• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Spin-orbital magnetism in moiré Wigner molecules
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes