By solving the Bogoliubov–de Gennes equations we study fermion bound states in the core of a vortex of a two-dimensional superconductor. The metallic surface states of a strong topological insulator become superconducting via proximity effect with an $s$-wave superconductor. The strong spin-orbit coupling locks the spin perpendicular to the momentum (Rashba interaction) giving rise to a zero-energy Majorana state. We investigate the case of a large first excitation energy of the order of the superconducting gap (${\Delta }_{\infty }$), i.e. for the Fermi level close to the apex of the Dirac cone. We obtain the local density of states (LDOS) for the bulk and the bound states. The particle-hole symmetry is broken in the LDOS for up-spin as a consequence of the spin-orbit coupling and the chirality of the vortex. On the other hand, the down-spin LDOS is particle-hole symmetric. The spin-polarization of the bound state peaks is studied in detail. We present a waterfall-like spectrum that shows that for a distance less than 3 times the coherence length $\xi$ from the core, the bound states can be observed.

通过求解 Bogoliubov-de Gennes 方程，我们研究了二维超导体涡旋核心中的费米子束缚态。强拓扑绝缘体的金属表面态通过邻近效应变为超导$s$波超导体。强自旋轨道耦合锁定垂直于动量的自旋（Rashba 相互作用），从而产生零能量马约拉纳状态。我们研究了超导间隙量级的大第一激发能量的情况（${\Delta }_{\infty }$)，即对于接近狄拉克锥顶点的费米能级。我们获得了体态和束缚态的局部态密度 (LDOS)。由于自旋轨道耦合和涡旋的手性，在 LDOS 中，由于自旋轨道耦合和旋涡的手性，粒子-空穴对称性被打破。另一方面，下自旋 LDOS 是粒子-空穴对称的。详细研究了束缚态峰的自旋极化。我们提出了一个类似瀑布的光谱，它表明距离小于相干长度的 3 倍$\xi$从核心可以观察到束缚态。