Abstract: We report characteristic vortex configurations in s + id superconductors with time-reversal symmetry breaking, exposed to magnetic field. A vortex in the s + id state tends to have an opposite phase winding between s- and d-wave condensates. We find that this peculiar feature together with the competition between s- and d-wave symmetry results in three distinct classes of vortical configurations. When either s or d condensate absolutely dominates, vortices form a conventional lattice. However, when one condensate is relatively dominant, vortices organize in chains that exhibit skyrmionic character, separating the chiral components of the s +/- id order parameter into domains within and outside the chain. Such skyrmionic chains are found stable even at high magnetic field. When s and d condensates have comparable strength, vortices split cores in two chiral components to form full-fledged skyrmions, i.e., coreless topological structures with an integer topological charge, organized in a lattice. We provide characteristic magnetic field distributions of all states, enabling their identification in, e.g., scanning Hall probe and scanning SQUID experiments. These unique vortex states are relevant for high-T-c cuprate and iron-based superconductors, where the relative strength of competing pairing symmetries is expected to be tuned by temperature and/or doping level, and can help distinguish s + is and s + id superconducting phases.

Abstract: We investigate the effects related to vortex-core deformations when vortices approach each other. As a result of these vortex-core deformations, the vortex-vortex interaction effectively acquires an attractive component leading to a variety of vortex patterns typical for systems with nonmonotonic repulsive-attractive interaction, such as stripes and labyrinths. The core deformations are anisotropic and can induce frustration in the vortex-vortex interaction. In turn, this frustration has an impact on the resulting vortex patterns, which are analyzed in the presence of additional random pinning, as a function of the pinning strength. This analysis can be applicable to vortices in multiband superconductors or to vortices in Bose-Einstein condensates.

Abstract: The effect of proximity-induced interactions such as Rashba spin-orbit coupling (SOC) and exchange interaction on the electronic and optical properties of n-type monolayer (ML) MoS2 is investigated. We predict and demonstrate that the Rashba SOC can induce an in-plane spin splitting with terahertz (THz) energy, while the exchange interaction lifts the energy degeneracy in different valleys. Thus, spin polarization can be achieved in an n-type ML MoS2 and valley Hall or optical Hall effect can be observed using linearly polarized THz radiation. In such a case, the transverse optical conductivity sigma(xy) (omega) results from spin-flip transition within spin-split conduction bands and from the fact that contributions from electrons with different spin orientations in different valleys can no longer be canceled out. Interestingly, we find that for fixed effective Zeeman field (or exchange interaction) the lowest spin-split conduction band in ML MoS2 can be tuned from one in the K valley to another one in the K' valley by varying the Rashba parameter lambda(R). Therefore, by changing lambda(R) we can turn the sign of the spin polarization and Im sigma(xy) (omega) from positive to negative. Moreover, we find that the dominant contribution of the selection rules to sigma(xx)(omega) is from electrons in the K valley and to sigma(xy) (omega) is from electrons in the K' valley. These important and interesting theoretical findings can be helpful to experimental observation of the optical Hall effect in valleytronic systems using linearly polarized THz radiation fields.