Band geometry, Berry curvature and superfluid weight

Long Liang, Tuomas I. Vanhala, Sebastiano Peotta, Topi Siro, Ari Harju, Päivi Törmä

Research output: Contribution to journalArticleScientificpeer-review

103 Citations (Scopus)
548 Downloads (Pure)


We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can berealized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.
Original languageEnglish
Article number024515
Pages (from-to)1-16
JournalPhysical Review B
Issue number2
Publication statusPublished - 27 Jan 2017
MoE publication typeA1 Journal article-refereed


  • Condensed Matter - Superconductivity
  • Condensed Matter - Quantum Gases


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