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 a 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-Tc 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. * lingfeng.zhang@uantwerpen.be † spzhou@shu.edu.cn 1 Milorad V. Milošević and Andrea Perali, "Emergent phenomena in multicomponent superconductivity: An introduction to the focus issue," Supercond. Sci. Technol. 28, 060201 (2015). 2 Masatoshi Sato and Yoichi Ando, "Topological superconductors: a review," Rep. Prog. Phys. 80, 076501 (2017). 3 Andrew Peter Mackenzie and Yoshiteru Maeno, "The superconductivity of Sr2RuO4 and the physics of spin-triplet

No abstract

No abstract

Recent scanning tunneling microscopy ͑STM͒ measurements of the proximity effect in Au/ La 2−x Sr x CuO 4 and La 1.55 Sr 0.45 CuO 4 / La 2−x Sr x CuO 4 bilayers showed a proximity-induced pseudogap ͓O. Yuli, I. Asulin, Y. Kalcheim, G. Koren, and O. Millo, Phys. Rev. Lett. 103, 197003 ͑2009͔͒. We describe the proximity effect in mesoscopic superconductor/normal-metal bilayers by using the Bogoliubov-de Gennes equations for a tightbinding Hamiltonian with competing antiferromagnetic and d-wave superconductivity orders. The temperaturedependent local density of states is calculated as a function of the distance from the interface. Bound state due to both d-wave and spin-density wave gaps are formed in the normal metal for energies less than the respective gaps. If there is a mismatch between the Fermi velocities in the two layers we observe that these states will shift in energy when spin-density wave order is present, thus inducing a minigap at finite energy. We conclude that the STM measurement in the proximity structures is able to distinguish between the two scenarios proposed for the pseudogap ͑competing or precursor to superconductivity͒.

The effect of next-nearest-neighbor ͑nnn͒ hopping on the antiferromagnetism and vortex charges for doped high-temperature superconductors is investigated by numerically solving the Bogoliubov-de Gennes equations based on a model Hamiltonian with competing antiferromagnetic ͑AFM͒ and d-wave superconductivity interactions. We find that the AFM order magnitude in the vortex core is first enhanced and then suppressed for an optimally doped sample, accompanied with vortex charge sign change from positive to negative when the relative nnn hopping strength increases from 0 to 0.4. It is also found that positive vortex charges can be observed at a large nnn hopping strength even though the AFM order remains strong for an underdoped sample. In addition, transitions between isotropic two-dimensional and one-dimensional structures of vortex charge and spin-density wave orders may occur by tuning the nnn hopping strength.