Unconventional superfluidity and quantum geometry of topological bosons

TL;DR

This paper uncovers a novel superfluid phase in topological bosonic bands characterized by unconventional order parameter modulation and non-zero sound speed even in flat bands, highlighting the influence of quantum geometry.

Contribution

It introduces a new superfluid phase with unique symmetry-breaking and provides detailed theoretical expressions for superfluid weight and BKT temperature in topological bands.

Findings

Discovery of a new superfluid phase with unconventional order parameter modulation.

Non-zero Bogoliubov excitations and sound speed in flat topological bands.

Re-entrant superfluid behavior observed in the Haldane model.

Abstract

We investigate superfluidity of bosons in gapped topological bands and discover a new phase that has no counterparts in the previous literature. This phase is characterized by a highly unconventional modulation of the order parameter, breaking the crystallographic symmetry, and for which the condensation momentum is neither zero nor any other high-symmetry vector of the Brillouin zone. This unconventional structure impacts the spectrum of Bogoliubov excitations and, consequently, the speed of sound in the system. Even in the case of perfectly flat bands, the speed of sound and Bogoliubov excitations remain nonvanishing, provided that the underlying topology and quantum geometry are nontrivial. Furthermore, we derive detailed expressions for the superfluid weight using the Popov hydrodynamic formalism for superfluidity and provide estimates for the Berezinskii-Kosterlitz-Thouless temperature, which is significantly enhanced by the nontriviality of the underlying quantum metric. These results are applicable to generic topological bosonic bands, with or without dispersion. To illustrate our findings, we employ the Haldane model with a tunable bandwidth, including the narrow lowest-band case. Within this model, we also observe a re-entrant superfluid behavior: As the Haldane's magnetic flux is varied, the Berezinskii-Kosterlitz-Thouless transition temperature initially decreases to almost zero, only to resurface with renewed vigor.