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Europhysics Letters (EPL)

Vortical configurations in mesoscopic superconducting square loop with mixed pairing orders

Guo-Qiao Zha

Published Jul 21, 2020• 10 citations
Publisher

Abstract

Based on the microscopic Bogoliubov-de Gennes theory, we study vortical configurations in a mesoscopic superconducting square loop with mixed pairing orders. By choosing appropriate interaction strengths and chemical potential, the spin-triplet p -wave and subdominant spin-singlet d -wave pairing symmetries can be stabilized. In a small external magnetic field, unusual elliptical-like vortices in chiral p -wave orders as well as elongated vortices in the d -wave order tend to form in sample diagonals. For an enlarged flux, we find a two-quanta skyrmionic mode for the p -wave components, while the closed domain wall does not appear compared to the previous studies in superconducting systems with a pure p -wave state. Particularly, a novel multi-skyrmionic pattern containing four single-quanta skyrmions takes place with increasing flux. Such a single-quanta vortex structure consisting of two spatially separated half-quantum vortices is analogous to the nematic skyrmion with unit topological charge. In addition, several complex hybrid or multiple skyrmionic configurations are revealed in the strong flux range.

DOI
10.1209/0295-5075/130/67005

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Based on the microscopic Bogoliubov-de Gennes theory, we study vortical configurations in a mesoscopic superconducting square loop with mixed pairing orders. By choosing appropriate interaction strengths and chemical potential, the spin-triplet p -wave and subdominant spin-singlet d -wave pairing symmetries can be stabilized. In a small external magnetic field, unusual elliptical-like vortices in chiral p -wave orders as well as elongated vortices in the d -wave order tend to form in sample diagonals. For an enlarged flux, we find a two-quanta skyrmionic mode for the p -wave components, while the closed domain wall does not appear compared to the previous studies in superconducting systems with a pure p -wave state. Particularly, a novel multi-skyrmionic pattern containing four single-quanta skyrmions takes place with increasing flux. Such a single-quanta vortex structure consisting of two spatially separated half-quantum vortices is analogous to the nematic skyrmion with unit topological charge. In addition, several complex hybrid or multiple skyrmionic configurations are revealed in the strong flux range.
The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.
Magnetic skyrmions in proximity to superconductors offer a route to engineering topological superconductivity due to the synthetic spin-orbit coupling engendered by the spin twist of the skyrmion texture. Previous theoretical works show that this leads to Majorana zero modes (MZMs) in skyrmion-vortex pairs for s-wave superconductors. Here we investigate this mechanism in fully gapped d+is and d+id superconductors. We find the surprising result that while stable MZMs are found in large parts of the phase diagram, strongly enhanced d-wave pairing or stronger skyrmion-induced spin twisting can in fact destroy topology unlike in s-wave superconductors. This effect can be understood from the non-trivial spatial structure of the d-wave pairing, and mixing of odd and even angular-momentum pairing channels in a rotated frame which untwists the skyrmion texture. Our results inform the feasibility of realizing MZMs with unconventional superconductors in such heterostructures.
As an example of the skyrmion lattice, the structure of Mermin-Ho vortex lattice in superfluids 3He^{3}\text{H}\text{e}3He is studied by self-consistent Eilenberger theory and by Bogoliubov-de Gennes theory. We identify how the intrinsic orbital angular momentum l\mathbf{l}l of ppp-wave Cooper pairs contributes to spatial structures of the pair potential, current flow, and quasiparticle states. There are two types of vortices depending on the l\mathbf{l}l direction relative to rotation. Only one of them has zero-energy bound states appearing even in coreless vortices due to intrinsic topological reasons.
We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two-dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from ppp-wave at very low electron fillings to ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a Van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise subdominant triplet solution over the singlet ddd-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time-reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasiparticle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap as well as the chiral triplet gap solution.
We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.
Triple-Core Structure of the Double-Core Vortex in Superfluid 3^33He-B
Abstract The order parameter of superfluid 3^33 3 He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid 3^33 3 He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.