Vortex States In The Ising Superconductors On Honeycomb Lattice

By self-consistently solving the Bogoliubov-de Gennes equations of a model Hamiltonian built on the honeycomb lattice, we study the roles played by the Ising spin-orbital coupling (ISOC) pertinent to the transition metal dichalcogenides (TMDs) in the presence of a magnetic field. It is shown that the presence of ISOC enables the superconductivity to survive in a high in-plane magnetic field, otherwise it would be destroyed completely by the magnetic field. For the vortex states produced by a perpendicular magnetic field, the ISOC will induce a weak ferromagnetic order within the vortex core region. The rapid increase of the ferromagnetic order at very low temperatures prevents the vortex core size from further shrinks with temperature decreasing, and results in a larger saturation value at low temperatures. More importantly, the ISOC also has the effect in shifting the energy levels of the finite energy vortex bound states and tends to merge them into the near zero-energy bound state, and thus obscures the discrete energy level feature for the energy dependence of the local density-of-state. The results in some way account for the experimental observations, and suggest that the ISOC in the TMDs may be an intrinsic factor apart from the thermal broadening to give rise to the near zero-energy peak observed in experiments on the vortex states of TMDs' superconductors.