Flat-band ratio and quantum metric in the superconductivity of modified Lieb lattices
arXiv:2404.12993 · doi:10.1038/s42005-025-01964-y
Abstract
Flat bands may offer a route to high critical temperatures of superconductivity. It has been predicted that the quantum geometry of the bands as well as the ratio of the number of flat bands to the number of orbitals determine flat band superconductivity. However, such results have assumed at least one of the following: an isolated flat band, zero temperature, mean-field theory, and/or uniform pairing. Here, we explore flat band superconductivity when these assumptions are relaxed. We consider an attractive Hubbard model for different extensions of the Lieb lattice. The superconducting order parameter, critical temperature, superfluid weight, and Berezinskii-Kosterlitz-Thouless (BKT) temperature are calculated within dynamical mean-field theory. We find that for isolated flat bands, the flat-band ratio and quantum geometry are in general good indicators of superconductivity even at finite temperatures. For non-isolated flat bands, a good guideline of the BKT temperature is provided by the zero-temperature superfluid weight and the flat-band ratio.
arXiv commentJournal version
References in corpus (37)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
- Continuous-time Monte Carlo methods for quantum impurity models
- Quantum Cluster Theories
- Graphene Bilayers with a Twist
- Superfluidity in topologically nontrivial flat bands
- Ultracold Atoms in a Tunable Optical Kagome Lattice
- From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
- Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States
- Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
- Geometric origin of superfluidity in the Lieb lattice flat band
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
- Band geometry of fractional topological insulators
- Flat bands in topological media
- Sublattice Interference in the Kagome Hubbard Model
- Band geometry, Berry curvature and superfluid weight
- Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
- Relations between topology and the quantum metric for Chern insulators
- Fragile topology and flat-band superconductivity in the strong-coupling regime
- Effective theory and emergent symmetry in the flat bands of attractive Hubbard models
- Superfluid weight bounds from symmetry and quantum geometry in flat bands
- Theoretical possibilities for flat-band superconductivity
- Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study
- Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
- Aharonov-Bohm Caging and Inverse Anderson transition in Ultracold Atoms
- Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
- High T_c superconductivity due to coexisting wide and narrow bands: A fluctuation exchange study on the Hubbard ladder as a test case
- Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
- Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices
- Origin of flat-band superfluidity on the Mielke checkerboard lattice
- Spatial Adiabatic Passage of Massive Quantum Particles
- Designer Flat Bands: Topology and Enhancement of Superconductivity
- Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states
- Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice
- Topological Heavy Fermion Principle For Flat (Narrow) Bands With Concentrated Quantum Geometry
- Engineering topological chiral transport in a flat-band lattice of ultracold atoms
Cited by in corpus (11)
- Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
- Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
- Functional approach to superfluid stiffness: Role of quantum geometry in unconventional superconductivity
- Altermagnetism and its induced higher-order topology on the Lieb lattice
- Superfluid stiffness of superconductors with delicate topology
- Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
- Low-temperature scaling laws in unconventional flat-band superconductors
- Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
- Quantum geometry in correlated electron phases: from flat band to dispersive band
- Superconductivity and geometric superfluid weight of a tunable flat band system
- Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction