Band geometry, Berry curvature, and superfluid weight

Long Liang, Tuomas I. Vanhala, Sebastiano Peotta, Topi Siro, Ari Harju, and Päivi Törmä
Phys. Rev. B 95, 024515 – Published 27 January 2017

Abstract

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 be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.

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  • Received 6 October 2016
  • Revised 10 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.024515

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

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

  • COMP Centre of Excellence, Department of Applied Physics, Aalto University, Helsinki, Finland

  • *ari.harju@aalto.fi
  • paivi.torma@aalto.fi

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Issue

Vol. 95, Iss. 2 — 1 January 2017

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