Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Physical Review B, Volume 106, issue 1
A central result in superconductivity is that flat bands, though dispersionless, can still host a nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is incomplete, which can lead to severe quantitative and even qualitative errors. We derive the complete equations and demonstrate that the minimal quantum metric, the metric with minimum trace, is related to the superfluid weight in isolated flat bands. We complement this result with an exact calculation of the Cooper pair mass in attractive Hubbard models with the uniform pairing condition. When the orbitals are located at high-symmetry positions, the Cooper pair mass is exactly given by the quantum metric, which is guaranteed to be minimal. Moreover, we study the effect of closing the band gap between the flat and dispersive bands, and develop a mean field theory of pairing for different band-touching points via the S-matrix construction. In mean field theory, we show that a nonisolated flat band can actually be beneficial for superconductivity. This is a promising result in the search for high-temperature superconductivity as the material does not need to have flat bands that are isolated from other bands by the thermal energy. Our work resolves a fundamental caveat in understanding the relation of multiband superconductivity to quantum geometry, and the results on band touchings widen the class of systems advantageous for the search of high-temperature flat band superconductivity.
Funding Information: We thank A. Julku, L. Liang, S. Peotta, G. Salerno, and G. Topp for useful discussions. We acknowledge support by the Academy of Finland under Projects No. 303351 and No. 327293. K.-E.H. acknowledges support from the Magnus Ehrnrooth Foundation. B.A.B. and A.C. were supported by the ONR Grant No. N00014-20-1-2303, the Schmidt Fund for Innovative Research, Simons Investigator Grant No. 404513, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, and the Gordon and Betty Moore Foundation's EPiQS Initiative, Grant No. GBMF11070. Further support was provided by the NSF-MRSEC Grant No. DMR2011750, the BSF Israel US foundation Grant No. 2018226, and the Princeton Global Network Funds. B.A.B. acknowledges support from the Office of Naval Research Grant No. N00014-20-1-2303 and from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 101020833). J.H.-A. is supported bya Marshall Scholarship funded by the Marshall Aid Commemoration Commission and a Hertz Fellowship. A.C. is supported by a Moore Postdoctoral Fellowship from the Gordon and Betty Moore Foundation. Publisher Copyright: © 2022 American Physical Society.
superconductivity, flat band, quantum geometry
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Huhtinen, K E, Herzog-Arbeitman, J, Chew, A, Bernevig, B A & Törmä, P 2022, ' Revisiting flat band superconductivity: Dependence on minimal quantum metric and band touchings ', Physical Review B, vol. 106, no. 1, 014518, pp. 1-23 .