Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids

TL;DR

This paper presents exact, self-consistent soliton solutions in unconventional Fermi superfluids using the Bogoliubov-de Gennes formalism, revealing complex phenomena like Majorana states and mixed superfluid dynamics.

Contribution

It generalizes previous soliton solutions to multicomponent systems with $SU(d)$ symmetry, including new filling states and fermion types, and explores rich dynamical phenomena.

Findings

Derivation of multicomponent soliton solutions using inverse scattering theory.

Identification of Majorana triplet states and SU(2)-DHN breathers.

Visualization of order parameters with spherical harmonics.

Abstract

Exact self-consistent soliton dynamics based on the Bogoliubov-de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $SU(d)$-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the $ d=2 $ systems, which describe the mixture of singlet $s$-wave and triplet $p$-wave superfluids, exhibit a variety of phenomena such as SU(2)-DHN breathers, Majorana triplet states, $s$-$p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and $N$-flavor generalization are discussed.