Topological Superconducting Vortex From Trivial Electronic Bands

Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or Cooper-paired electron wavefunctions, is crucial for enabling Majorana zero modes. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivial superconductors with topological electronic band structures. Here we show that the Majorana-carrying vortex is not a privilege of bulk-state topology, but can arise from superconducting trivial bands as well. Notably, even for superconductors with topological band structures, the existence of ubiquitous low-energy trivial bands can significantly change the conclusion of vortex Majorana physics that is based on simplified topological-band-only models. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topology that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and a new experimental "smoking gun" are also discussed. Our work provides new guidelines for Majorana search in general superconductors.