Interplay of correlations and Majorana mode from local solution perspective

TL;DR

This paper analyzes how Coulomb interactions influence the spectral properties of Majorana modes in a hybrid quantum dot-topological superconductor system, providing exact solutions and potential experimental verification methods.

Contribution

It offers an exact analytical solution revealing the interplay between Coulomb repulsion and Majorana modes, advancing understanding beyond previous Hubbard-based approximations.

Findings

Spectral weight of Majorana mode depends on quantum dot energy and Coulomb repulsion.

Analytical expressions quantify coexistence of zero-energy and finite-energy states.

Potential for experimental detection via spin-polarized Andreev spectroscopy.

Abstract

We study the quasiparticle spectrum of a hybrid system, comprising a correlated (Anderson-type) quantum dot coupled to a topological superconducting nanowire hosting the Majorana boundarymodes. From the exact solution of the low-energy effective Hamiltonian, we uncover a subtle interplay between Coulomb repulsion and the Majorana mode. Our analytical expressions show that the spectral weight of the leaking Majorana mode is sensitive to both the quantum dot energy level and the repulsive potential. We compare our results with estimations by L.S. Ricco et al. Phys. Rev. B 99, 155159 (2019) obtained for the same hybrid structure using the Hubbard-type decoupling scheme, and analytically quantify the spectral weight of the zero-energy (topological) mode coexisting with the finite-energy (trivial) states of the quantum dot. We also show that empirical verification of these spectral weights could be feasible through spin-polarized Andreev spectroscopy.