Majorana bound states in the presence of the half-smeared potential

TL;DR

This paper investigates how a quadratic smearing potential at one end of a 1D chain affects Majorana bound states, revealing the emergence of extra in-gap states and altered localization properties.

Contribution

It introduces a model with a quadratic smearing potential and analyzes its impact on Majorana states, highlighting changes in localization and the preservation of Majorana modes.

Findings

Extra in-gap states emerge due to smearing.

Majorana states remain but with altered localization.

Symmetric localization of Majorana states is broken.

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 form of a quadratic function of position. We show that the smearing potential lead to the emergence of extra in-gap states, and effectively decrease the local gap (around the smeared potential). The Majorana states are still preserved in the system, however, their localization depend on the smearing. Moreover, the symmetric localization of the Majorana states from both side of the system is no longer preserved in the presence of the smearing potential.