Pair size and quantum geometry in a multiband Hubbard model
arXiv:2409.14921 · doi:10.1103/PhysRevB.111.014502
Abstract
We study the size of two-body bound states and Cooper pairs within a multiband Hubbard model that features time-reversal symmetry and uniform pairing on a generic lattice. Our analysis involves (i) an exact calculation of the localization tensor to determine the size of lowest-lying two-body bound state in vacuum, and (ii) an evaluation of the analogous tensor to estimate the average size of Cooper pairs within the mean-field BCS-BEC crossover theory at zero temperature. Beyond the conventional intraband contribution that depends on Bloch bands, we show that pair size also has a geometric contribution governed by the quantum-metric tensor of the Bloch states and their band-resolved quantum-metric tensors. As a concrete example, we investigate the pyrochlore-Hubbard model numerically and demonstrate that, while the pair size diverges in the weakly interacting BCS regime of dispersive bands, it remains finite and relatively small in the flat-band regime, even for infinitesimal interaction, perfectly matching the exact two-body result in the dilute limit.
arXiv comment8 pages with 3 figures; to appear in PRB
References in corpus (18)
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- The Insulating State of Matter: A Geometrical Theory
- Essay: Where Can Quantum Geometry Lead Us?
- Determination of the Fermion Pair Size in a Resonantly Interacting Superfluid
- The Ginzburg-Landau theory of flat band superconductors with quantum metric
- Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids
- Two-body problem in a multiband lattice and the role of quantum geometry
- Pair Density Waves from Local Band Geometry
- Spin-triplet superconductivity from quantum-geometry-induced ferromagnetic fluctuation
- Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model
- "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
- Geometric Stiffness in Interlayer Exciton Condensates
- Observation of Flat Bands and Dirac Cones in a Pyrochlore Lattice Superconductor
- Geometric superfluid weight of composite bands in multiorbital superconductors
- Cooper pairing, flat-band superconductivity and quantum geometry in the pyrochlore-Hubbard model
- Quantum geometry encoded to pair potentials
- Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings
- Coherence length and quantum geometry in a dilute flat-band superconductor
Cited by in corpus (5)
- Structure factors and quantum geometry in multiband BCS superconductors
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- Normal state quantum geometry, non-locality and superconductivity
- Correlation lengths of flat-band superconductivity from quantum geometry
- Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles