TY - JOUR
T1 - Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands
AU - Herzog-Arbeitman, Jonah
AU - Peri, Valerio
AU - Schindler, Frank
AU - Huber, Sebastian D.
AU - Bernevig, B. Andrei
N1 - Funding Information:
J. H.-A. thanks Zhi-Da Song and Dylan King for useful discussions, and gratefully acknowledges insight from Päivi Törmä. J. H-A. is supported by a Marshall Scholarship funded by the Marshall Aid Commemoration Commission. V. P., and S. D. H. acknowledge support from the Swiss National Science Foundation, the NCCR QSIT, the Swiss National Supercomputing Centre (CSCS) under Project No. eth5b, and the European Research Council under the Grant Agreement No. 771503 (TopMechMat). F. S. was supported by a fellowship at the Princeton Center for Theoretical Science. B. A. B thanks funding from the European Research Council under the Grant Agreement No. 101020833 (SuperFlat). B. A. B. was also supported by the U.S. Department of Energy (Grant No. DE-SC0016239) and was partially supported by the National Science Foundation (EAGER Grant No. DMR 1643312), a Simons Investigator Grant (No. 404513), the Office of Naval Research (ONR Grant No. N00014-20-1-2303), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US foundation (Grant No. 2018226), the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation, and the NSF-MRSEC (Grant No. DMR2011750). The auxiliary-field QMC simulations were carried out with the ALF package available at .
Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/2/25
Y1 - 2022/2/25
N2 - Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms - even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.
AB - Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms - even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.
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U2 - 10.1103/PhysRevLett.128.087002
DO - 10.1103/PhysRevLett.128.087002
M3 - Article
C2 - 35275691
AN - SCOPUS:85125602283
SN - 0031-9007
VL - 128
JO - Physical review letters
JF - Physical review letters
IS - 8
M1 - 087002
ER -