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

TL;DR

This paper demonstrates that impurities can cause trivial vortex core states in superconductors to mimic Majorana zero modes by shifting their energy close to zero and suppressing their charge, complicating experimental identification.

Contribution

It reveals how electrostatic inhomogeneities can push trivial CdGM states near zero energy and suppress their charge, challenging the distinction from MZMs in topological superconductors.

Findings

Impurities can push trivial CdGM states arbitrarily close to zero energy.

Electrostatic inhomogeneities suppress the BCS charge of CdGM states.

Energy and charge shifts can mimic MZM signatures in experiments.

Abstract

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