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.

通过自洽求解建立在蜂窝晶格上的模型哈密顿量的 Bogoliubov-de Gennes 方程，我们研究了与过渡金属二硫属元素化物 (TMD) 相关的 Ising 自旋轨道耦合 (ISOC) 在存在磁场。结果表明，ISOC的存在使超导性能够在高面内磁场中存活，否则将被磁场完全破坏。对于由垂直磁场产生的涡旋态，ISOC 将在涡旋核心区域内感应出弱铁磁有序。极低温度下铁磁阶数的快速增加阻止了涡核尺寸随着温度降低而进一步收缩，并导致低温下更大的饱和值。更重要的是，ISOC 还具有改变有限能量涡流束缚态的能级的作用，并倾向于将它们合并到接近零能量的束缚态，从而模糊了局部密度的能量依赖性的离散能级特征。 -状态。结果在某种程度上解释了实验观察结果，并表明 TMD 中的 ISOC 可能是一个内在因素，除了热展宽导致在 TMD 超导体涡流状态实验中观察到的接近零能量峰值.