Swallow-tail dispersions of moving solitons in a two-dimensional fermionic superfluid

TL;DR

This paper investigates the unique swallow-tail dispersion relations of localized solitons in a two-dimensional Fermi superfluid, revealing complex behaviors like diverging effective mass and multiple dispersion branches.

Contribution

It provides the first detailed analysis of soliton dispersion relations in 2D Fermi superfluids using Bogoliubov-de Gennes equations, highlighting novel swallow-tail features.

Findings

Solitons exhibit swallow-tail shaped dispersion relations with cusps.

Effective mass of solitons diverges and changes sign at the cusp.

Dispersion behavior differs from 3D Fermi superfluids.

Abstract

Soliton-like localised wave solutions in a two-dimensional Fermi superfluid are studied by solving the Bogoliubov-de Gennes equations in the BCS regime of weak pairing interactions. The dispersion relations of these solitons are found to exhibit a peculiar swallow-tail shape, with cusps and multiple branches. The effective mass of the solitons is found to diverge and change sign at the cusp. This behavior is in contrast to the smooth dispersion relations and negative effective masses of solitons in the three-dimensional Fermi superfluid. The swallow-tail dispersion relations are shown to be a consequence of counterflow of the superfluid and sign-changing contributions to the superfluid current from different transverse momenta in the Bogoliubov-de Gennes formalism. The results are relevant for the understanding of solitonic excitations in two-dimensional Fermi superfluids, such as ultracold atomic gases and high-temperature superconductors.