Superfluidity of flat band Bose-Einstein condensates revisited

Aleksi Julku*, Grazia Salerno, Päivi Törmä*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose-Einstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing the free energy with respect to it. We find that the superfluid weight has a contribution arising from the change in the condensate density and chemical potential upon the phase twist that has been neglected in the previous literature. We also point out that the speed of sound and the excitation fraction are proportional to orbital-position-independent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (Fubini-Study metric) and the Hilbert-Schmidt quantum distance only in special cases. We derive a second-order perturbation correction to the dependence of the speed of sound on the generalized quantum metric, and show that it compares well with numerical calculations. Our results provide a consistent connection between flat band BEC and quantum geometry, with physical observables being independent of the orbital positions for fixed hopping amplitudes, as they should, and complete formulas for the evaluation of the superfluid weight within the Bogoliubov theory. We discuss the limitations of the Bogoliubov theory in evaluating the superfluid weight.

Original languageEnglish
Pages (from-to)701-713
Number of pages13
JournalLow Temperature Physics
Issue number6
Publication statusPublished - 1 Jun 2023
MoE publication typeA1 Journal article-refereed


  • Bogoliubov theory
  • flat band Bose-Einstein condensate
  • Fubini-Study metric
  • Hilbert-Schmidt quantum distance
  • quantum geometry.
  • superfluid weight


Dive into the research topics of 'Superfluidity of flat band Bose-Einstein condensates revisited'. Together they form a unique fingerprint.

Cite this