Majorana correlations in quantum impurities coupled to a topological wire

TL;DR

This study uses density matrix renormalization group methods to analyze Majorana correlations in quantum impurities coupled to a topological wire, revealing exponential decay, interaction effects, and Coulomb blockade phenomena affecting Majorana states.

Contribution

It provides detailed numerical analysis of Majorana correlations in impurity-wire systems, highlighting the influence of electron interactions and impurity occupation on Majorana states.

Findings

Correlations decay exponentially with distance.

Electron interactions strengthen correlation effects.

Coulomb blockade peaks influence Majorana correlations.

Abstract

In this work we investigate Majorana correlations in quantum impurities coupled to a topological superconducting wire. By employing a density matrix renormalization group approach, we have calculated the Majorana correlation functions in the ground state of the system for different positions of the impurities along the wire. We observe that the correlations decreases exponentially with the distance between the impurities and the ends of the wire. Moreover, different electron-electron interactions on the wire and on the impurities were also analyzed, and the results showed a stronger effect as the electron occupation in the wire is increased. Moreover, changing the occupation of the impurities by tuning their energy levels, we observe that for specific values of $\epsilon$ the absolute value of correlation is highly peaked when the chemical potential lies within the window of the topological regime. These peaks are associated to coulomb blockade phenomena in the impurities, revealing very clearly its effect on the Majorana bound states in the topological phase of the system.