Origin of flat-band superfluidity on the Mielke checkerboard lattice

Abstract

The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invariant, i.e., the so-called quantum metric tensor of the single-particle bands, in the inverse effective mass tensor of the Cooper pairs.

9 pages with 7 figures

References in corpus (6)

• Band geometry, Berry curvature and superfluid weight
• Exotic electronic states in the world of flat bands: from theory to material
• Superconducting Transitions in Flat Band Systems
• Observation of flat band for terahertz spoof plasmon in metallic kagomé lattice
• Superfluid stiffness for the attractive Hubbard model on a honeycomb optical lattice
• Hofstadter-Hubbard model with opposite magnetic fields: Bardeen-Cooper-Schrieffer pairing and superfluidity in the nearly flat butterfly bands

Cited by in corpus (22)

• Two-body problem in a multiband lattice and the role of quantum geometry
• Designer Flat Bands: Topology and Enhancement of Superconductivity
• Anomalous Coherence Length in Superconductors with Quantum Metric
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states
• Superfluid density and collective modes of fermion superfluid in dice lattice
• 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
• Prediction of polarization vortices, charge modulation, flat bands, and moiré magnetism in twisted oxide bilayers
• Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system
• Correlation functions and characteristic lengthscales in flat band superconductors
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Quantum geometric superfluid weight in multiband superconductors: A microscopic interpretation
• Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system
• Superfluid weight cross-over and critical temperature enhancement in singular flat bands
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Non-Abelian line graph: A generalized approach to flat bands
• Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings