Majorana Bound States in the Presence of Half-Smeared Potential

Abstract

The Majorana bound state can be realized in one-dimensional chain, in form of two well-localized and separated states at both ends of the chain. In this paper, we discuss the case when the potential is smeared at one end of the system. In our investigation, we assume the smearing in the form of a quadratic function of position. We show that the smearing potential leads to the emergence of extra in-gap states, and effectively decreases the local gap (around the smeared potential). The Majorana states are still preserved in the system, however, their localization depends on the smearing. Moreover, the symmetric localization of the Majorana states from both sides of the system is no longer preserved in the presence of the smearing potential.