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arXiv · 2403.04270

Cooper pairing, flat-band superconductivity and quantum geometry in the pyrochlore-Hubbard model

M. Iskin
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Abstract

We investigate the impacts of the quantum geometry of Bloch states, specifically through the band-resolved quantum-metric tensor, on Cooper pairing and flat-band superconductivity in a three-dimensional pyrochlore-Hubbard model. First we analyze the low-lying two-body spectrum exactly, and show that the pairing order parameter is uniform in this four-band lattice. This allowed us to establish direct relations between the superfluid weight of a multiband superconductor and ($i$) the effective mass of the lowest-lying two-body branch at zero temperature, ($ii$) the kinetic coefficient of the Ginzburg-Landau theory in proximity to the critical temperature, and ($iii$) the velocity of the low-energy Goldstone modes at zero temperature. Furthermore, we perform a comprehensive numerical analysis of the superfluid weight and Goldstone modes, exploring both their conventional and geometric components at zero temperature.

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M. Iskin. 2024-03-07. Cooper pairing, flat-band superconductivity and quantum geometry in the pyrochlore-Hubbard model. https://doi.org/10.1103/physrevb.109.174508

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