Near zero energy Caroli–de Gennes–Matricon vortex states in the presence of impurities

Caroli-de Gennes-Matricon (CdGM) states are localized with a discrete energy spectrum bound to the core of vortices in superconductors. In topological superconductors, CdGM predicted coexist zero-energy, chargeless widely known as Majorana zero modes (MZMs). Due their difference, current experiments rely on scanning tunneling spectroscopy methods distinguish between them. This work shows that electrostatic inhomogeneities can push trivial arbitrarily close non-topological systems where no MZM is present. Furthermore, BCS charge suppressed under same mechanism. Through exploration impurity parameter space, we establish these two phenomena generally happen consonance. Our results show and shifts may be enough imitate spectroscopic signatures MZMs even cases estimated level spacing (in absence impurities) much larger than typical experimental broadening.