Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $\text{SU}(d)$ -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 rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ 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.Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $\text{SU}(d)$-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 rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ 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.

arXiv:1509.04242Physical review. B./Physical review. BJan 19, 201613 citations

ON THE THEORY OF SUPERFLUIDITY

Nikolay N. Bogolubov

Elsevier eBooksJan 1, 197152 citations

Aspects of a model of superfluidity

James R. Johnston, F.W. Cummings

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BJul 1, 19682 citations

Unconventional superfluidity and quantum geometry of topological bosons

Lukin, Ilya, Andrii Sotnikov, Alexander Kruchkov

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.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.

arXiv:2307.08748Jul 17, 20230 citations

On the theory of superfluidity

Yongle Yu

arXiv:cond-mat/0609711Annals of PhysicsJul 11, 20087 citations

Fulde-Ferrell-Larkin-Ovchinnikov states and topological Bogoliubov Fermi surfaces in altermagnets: An analytical study

Zhao Liu, Hui Hu, Xia-Ji Liu

We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting $d$ -wave altermagnetic spin splitting under $s$ -wave pairing. Within the Bogoliubov-de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper-type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and $s$ -wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting $d$-wave altermagnetic spin splitting under $s$-wave pairing. Within the Bogoliubov-de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper-type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and $s$-wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.

arXiv:2508.07813Physical review. B./Physical review. BJan 13, 20266 citations

Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an

\text{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 rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ 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.

We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting

d

-wave altermagnetic spin splitting under

s

-wave pairing. Within the Bogoliubov-de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper-type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and

s

-wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.