Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids

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.

25 pages, 1 figure, 1 table, 18 animations. Higher-quality avi files and gif animation files are available at (may need chrome to view): https://drive.google.com/folderview?id=0Bxd4vPIq2or8UlFadjRNYlk2X0k

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• Collective modes of a soliton train in a Fermi superfluid
• Duality study of chiral Heisenberg Gross-Neveu model in 1+1 dimensions
• Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
• Emergent chirality and superfluidity of parity-doubled baryons in neutron stars
• Tsunami Solitons Emerging from Superconducting Gap
• Appropriate conditions to realize a $p$-wave superfluid state starting from a spin-orbit coupled $s$-wave superfluid Fermi gas
• SU(N) affine Toda solitons and breathers from transparent Dirac potentials