Effect of interatomic repulsion on Majorana zero modes in a coupled quantum-dot-superconducting-nanowire hybrid system

TL;DR

This paper investigates how interatomic repulsion influences Majorana zero modes in a topological superconductor-quantum dot hybrid system, revealing significant effects in short wire configurations through a Hartree-Fock analysis.

Contribution

It introduces a detailed Hartree-Fock study of Coulomb interactions' impact on Majorana states in a Kitaev chain coupled to a quantum dot, highlighting limitations of simplified models.

Findings

Majorana states are affected by Coulomb repulsion in short wires.

The low-energy spectrum shows a 'diamond' shape dependence on quantum dot energy.

Simplest effective models may not fully capture the physics in realistic systems.

Abstract

We study the low-energy eigenstates of a topological superconductor wire modeled by a Kitaev chain, which is connected at one of its ends to a quantum dot through nearest-neighbor (NN) hopping and NN Coulomb repulsion. Using an unrestricted Hartree-Fock approximation to decouple the Coulomb term, we obtain that the quality of the Majorana end states is seriously affected by this term only when the dependence of the low-lying energies with the energy of the quantum dot shows a "diamond" shape, characteristic of short wires. We discuss limitations of the simplest effective models to describe the physics. We expect the same behavior in more realistic models for topological superconducting wires.