Can Caroli-de Gennes-Matricon and Majorana vortex states be distinguished in the presence of impurities?

Majorana zero modes states (MZMs) are predicted to appear as bound states in vortices of topological superconductors. MZMs are pinned at zero energy and have zero charge due to particle-hole symmetry. MZMs in vortices of topological superconductors tend to coexist with other subgap states, named Caroli-de Gennes-Matricon (CdGM) states. The distinction between MZMs and CdGM is limited since current experiments rely on zero-bias peak measurements obtained via scanning tunneling spectroscopy. In this work, we show that a local impurity potential can push CdGM states to zero energy. Furthermore, the finite charge in CdGM states can also drop to zero under the same mechanism. We establish, through exploration of the impurity parameter space, that these two phenomena generally happen in consonance. This means that energy and charge shifts in CdGM may be enough to imitate spectroscopic signatures of MZMs.