We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The field is analogue Rashba spin-orbit coupling. Upon squashing SO(3) to one- or two-dimensional shapes, we find continuously undergoes change from identified by estimating winding numbers and helicity. All emerged Skyrmions are physically understandable concept helical modulation in...

In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and crystalline superconductors, their physical consequences such as helical chiral Majorana fermions. We start article with the minimal model that captures essence materials. The central part is devoted to superfluid $^3$He, which serves rich repository novel quantum phenomena originating from intertwining symmetries topologies. particular, it emphasized fluid...

The putative spin-triplet superconductor ${\mathrm{UTe}}_{2}$ exhibits multiple superconducting phases under applied pressure [Braithwaite et al., Commun. Phys. 2, 147 (2019)]. clarification of pairing mechanisms and symmetries gap functions are essentially important for understanding the multiple-phase diagram. Since coexistence ferromagnetic antiferromagnetic spin fluctuations with Ising-like anisotropy is suggested from measurements magnetic susceptibilities neutron scattering...

It is proposed that the spatially modulated superfluid phase, or Fulde-Ferrell-Larkin-Ovchinnikov state could be observed in resonant fermion atomic condensates which are realized recently. We examine optimal experimental setups to achieve it by solving Bogoliubov-de Gennes equation for both idealized one-dimensional and realistic three-dimensional cases. The spontaneous modulation of this shown directly imaged as density profiles either optical absorption Stern-Gerlach experiments.

The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along z axis comparing energies other competing non-axis-symmetric or singular vortices. phase diagram is thereby established a plane rotation drive vs total magnetization. Their stability also checked calculating...

We study the textures of $F=2$ spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On basis analysis SOC energy and numerical calculation Gross-Pitaevskii equation, we demonstrate that originate from helical modulation order parameter (OP) due to SOC. In particular, cyclic OP consists two-dimensional lattice textures, such as hexagonal $\frac{1}{3}$ vortex lattice, commonly understandable network modulations.

We here demonstrate that the superfluid $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}B$ under a magnetic field in particular direction stays topological due to discrete symmetry, is, symmetry protected order. Because of order, helical surface Majorana fermions $B$ phase remain gapless and their Ising spin character persists. unveil competition between Zeeman dipole interaction involves an anomalous quantum transition which takes place together with spontaneous breaking. Based on...

It is shown by microscopic calculations for trapped imbalanced Fermi superfluids that the gap function has always sign changes, i.e., Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state like, up to a critical imbalance $P_c$, beyond which normal becomes stable, at temperature T=0. A phase diagram constructed in $T$ vs $P$, where BCS without change stable only $T\neq 0$. We reproduce observed bimodality density profile identify its origin and evaluate $P_c$ as functions of coupling strength. These...

The visualization of chiral p-wave superfluidity in Fermi gases near Feshbach resonances is theoretically examined. It proposed that the becomes detectable entire BCS-BEC regimes through (i) vortex by density depletion inside core and (ii) intrinsic angular momentum vortex-free states. revealed both are closely connected with Majorana zero energy mode edge mode, which survive until strong coupling BCS regime approached from weak limit vanish Bose-Einstein condensation regime.

We investigate the topological aspect of spin-triplet $f$-wave superconductor UPt$_3$ through microscopic calculations edge- and vortex-bound states based on quasiclassical Eilenberger Bogoliubov-de Gennes theories. It is shown that a gapless linear dispersion exists at edge $ab$-plane. This forms Majorana valley, protected by mirror chiral symmetry. also demonstrate that, with increasing magnetic field, quasiparticles undergo phase transition from topologically trivial in double-core vortex...

We self-consistently study surface states of superconducting topological insulators. clarify that, if a topologically trivial bulk $s$-wave pairing symmetry is realized, parity mixing the pair potential near anomalously enhanced by Dirac fermions, opening an additional gap larger than one. In contrast to classical superconductors, resulting density state hosts extra coherent peak at induced besides conventional gap. also find that no such appears for odd-parity superconductors with...

Owing to the richness of symmetry and well-established knowledge bulk superfluidity, superfluid (3)He has offered a prototypical system study intertwining topology symmetry. This article reviews recent progress in understanding topological superfluidity multifaceted manner, including considerations, Jackiw-Rebbi's index theorem, quasiclassical theory. Special focus is placed on protected superfuidity (3)He-B confined slab geometry. The under magnetic field separated two different sub-phases:...

Superconducting spintronics explores the interplay between superconductivity and magnetism, sparking substantial interest in nonunitary superconductors as a platform for magneto-superconducting phenomena. However, identifying remains challenging. We demonstrate that spin current driven by thermal gradients sensitively probes nature of condensate superconductors. Spin polarization momentum space induces superconducting Seebeck effect, where is generated along without thermoelectric charge...

The stability of doubly quantized vortices in dilute Bose-Einstein condensates 23Na is examined at zero temperature. eigenmode spectrum the Bogoliubov equations for a harmonically trapped cigar-shaped condensate computed and it found that vortex spectrally unstable towards dissection into two singly vortices. By numerically solving full three-dimensional time-dependent Gross-Pitaevskii equation, intertwine before decaying. This work provides an interpretation recent experiments [A. E....

We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC) with the ferromagnetic spin-interaction by numerically solving Gross-Pitaevskii equation. The BEC under slow rotation can sustain a rich variety exotic vortices due to multi-component order parameters, such as Mermin-Ho and Anderson-Toulouse coreless (the 2-dimensional skyrmion meron) non-axisymmetric sifting vortex cores. Here, we present spin texture various states at higher rates in...

The structure and stability of various vortices in $F=1$ spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both axisymmetric nonaxisymmetric covering a wide range ferromagnetic antiferromagnetic interactions. topological defect called Mermin-Ho (Anderson-Toulouse) vortex is shown to be case. phase diagram established plane external rotation $\ensuremath{\Omega}$...

We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight line, driven by a parametric resonance between quadrupole mode and pair modes opposite momenta. Subsequently, rapidly decay longer wavelengths emitting sound process. present modified wave dispersion relation for superfluids propose simple method excite specific number.

Multiply quantized vortices in the BCS-to-BEC evolution of p-wave resonant Fermi gases are investigated theoretically. The vortex structure and low-energy quasiparticle states discussed, based on self-consistent calculations Bogoliubov-de Gennes gap equations. We reveal direct relation between macroscopic vortices, such as particle densities, low-lying state. In addition, net angular momentum for multiply with a vorticity $\kappa$ is found to be expressed by simple equation, which reflects...

We investigate how the vortex-vortex separation changes Majorana zero modes in vicinity of BCS-BEC (Bose-Einstein condensation) topological phase transition $p$-wave resonant Fermi gases. By analytically and numerically solving Bogoliubov--de Gennes equation for spinless superfluids with plural vortices, it is demonstrated that quasiparticle tunneling between neighboring vortices gives rise to quantum oscillation low-lying spectra on scale wavelength addition exponential splitting. This...

We theoretically investigate the effect of intertube tunneling in topological superfluid phases a quasi-one-dimensional Fermi gas with Rashba-type spin–orbit interaction. It is shown that effective Hamiltonian analogous to nanowire superconductor multibands. Using hidden mirror symmetry system, we introduce new number ensures existence non-Abelian Majorana zero modes even presence tunneling. demonstrated from full numerical calculation self-consistent equations some survive against...

In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, thermal excitations with finite decay rates. On other hand, a lattice vacancy traps flux even in ground state, resulting stable realization of mode vacancy. We demonstrate that spin-spin correlation functions between two sites exhibit long-range arising from fractionalized character spite strong bulk correlations. Remarkably, this nonlocal does not decrease distance...

The recent measurement of the de Haas-van Alphen effect in spin-triplet superconductor UTe2 [D. Aoki et al., J. Phys. Soc. Jpn. 91, 083704 (2022)] supports cylindrical electron and hole Fermi surfaces, which implies that is trivial as a 3D time-reversal-invariant topological superconductor. Inspired by this observation, we investigate possible realization crystalline protected symmetry UTe2. We examine Majorana surface states mirror two-fold rotational symmetries for all symmetry-allowed...

We find theoretically that the vortex core in Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from ordinary for a simple topological reason. The intersection point of and nodal plane FFLO empties excess spins. This leads to observable consequences spatial structure spontaneous magnetization. analyze this based on low lying excitation spectrum by solving microscopic Bogoliubov--de Gennes equation clarify its physical origin.