Superfluid weight in the isolated band limit within the generalized random phase approximation

Abstract

The superfluid weight of a generic lattice model with attractive Hubbard interaction is computed analytically in the isolated band limit within the generalized random phase approximation. Time-reversal symmetry, spin rotational symmetry, and the uniform pairing condition are assumed. It is found that the relation obtained in [https://link.aps.org/doi/10.1103/PhysRevB.106.014518] between the superfluid weight in the flat band limit and the so-called minimal quantum metric is valid even at the level of the generalized random phase approximation. For an isolated, but not necessarily flat, band it is found that the correction to the superfluid weight obtained from the generalized random phase approximation $D_{\mathrm{s}}^{(1)}=D_{\mathrm{s},\mathrm{c}}^{(1)}+D_{\mathrm{s},\mathrm{g}}^{(1)}$ is also the sum of a conventional contribution $D_{\mathrm{s},\mathrm{c}}^{(1)}$ and a geometric contribution $D_{\mathrm{s},\mathrm{g}}^{(1)}$, as in the case of the known mean-field result $D_{\mathrm{s}}^{(0)}=D_{\mathrm{s},\mathrm{c}}^{(0)}+D_{\mathrm{s},\mathrm{g}}^{(0)}$, in which the geometric term $D_{\mathrm{s},\mathrm{g}}^{(0)}$ is a weighted average of the quantum metric. The conventional contribution is geometry independent, that is independent of the orbital positions, while it is possible to find a preferred, or natural, set of orbital positions such that $D_{\mathrm{s},\mathrm{g}}^{(1)}=0$. Useful analytic expressions are derived for both the natural orbital positions and the minimal quantum metric, including its extension to bands that are not necessarily flat. Finally, using some simple examples, it is argued that the natural orbital positions may lead to a more refined classification of the topological properties of the band structure.

28 pages, 3 figures, referee feedback implemented

References in corpus (7)

• Transient supersolid properties in an array of dipolar quantum droplets
• Long-lived and transient supersolid behaviors in dipolar quantum gases
• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Band geometry, Berry curvature and superfluid weight
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Topological and geometrical aspects of band theory
• Interplay and competition between disorder and flat band in an interacting Creutz ladder

Cited by in corpus (16)

• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Instantaneous response and quantum geometry of insulators
• Geometric superfluid weight of composite bands in multiorbital superconductors
• Enhanced quantum metric due to vacancies in graphene
• Quantum Geometry and the Hidden Scales in Materials
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Superfluid weight cross-over and critical temperature enhancement in singular flat bands
• Superconducting junctions with flat bands
• Superfluid stiffness bounds in time-reversal symmetric superconductors
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Superfluid stiffness of superconductors with delicate topology
• Supersolid phase in two-dimensional soft-core bosons at finite temperature
• Unconventional excitonic insulators in two-dimensional topological materials
• Quantum Geometric Helical Superconductivity
• Superfluid weight in disordered flat-band superconductors as a competition between localization functionals