标题： 在超导体上的磁性原子链中，拓扑平凡和非平凡 Yu-Shiba-Rusinov 带的同时存在 显示英文标题

标题： Coexistence of topologically trivial and non-trivial Yu-Shiba-Rusinov bands in magnetic atomic chains on a superconductor

摘要： 马约拉纳零能模（MZMs）被认为是马约拉纳量子比特的有前景的基础，为拓扑量子计算提供了巨大的潜力。这种模式可能出现在超导体上的磁性原子链的末端。通常情况下，链的一端只有一个马约拉纳零能模存在，但对称性可以保护同一端的多个马约拉纳零能模。在这里，我们利用第一性原理计算以及扫描隧道显微镜和谱学实验，研究了在Nb(110)和Ta(110)衬底上构建的Mn链激发的Yu-Shiba-Rusinov（YSR）带的拓扑性质。我们证明了相对于包含链的对称平面反射时，偶数和奇数YSR态具有不同的色散，并且它们都可以分别导致马约拉纳零能模的出现。尽管自旋-轨道耦合会导致带之间的杂化，但由于镜面对称性，仍然可能存在多个马约拉纳零能模。这些发现强调了对称性在解释马约拉纳零能模候选物的光谱特征方面的影响。 显示英文摘要

摘要： Majorana zero modes (MZMs) have been proposed as a promising basis for Majorana qubits offering great potential for topological quantum computation. Such modes may form at the ends of a magnetic atomic chain on a superconductor. Typically only a single MZM may be present at one end of the chain, but symmetry may protect multiple MZMs at the same end. Here, we study the topological properties of Yu-Shiba-Rusinov (YSR) bands of excitations in Mn chains constructed on a Nb(110) and on a Ta(110) substrate using first-principles calculations and scanning tunneling microscopy and spectroscopy experiments. We demonstrate that even and odd YSR states with respect to mirroring on the symmetry plane containing the chain have different dispersions, and both of them may give rise to MZMs separately. Although the spin-orbit coupling leads to a hybridization between the bands, multiple MZMs may still exist due to the mirror symmetry. These findings highlight the influence of symmetries on interpreting the spectroscopic signatures of candidates for MZMs.