Majorana zero modes in Y-shape interacting Kitaev wires

TL;DR

This paper analytically and numerically investigates Majorana zero modes in Y-shaped Kitaev wires, revealing multi-site MZMs near the junction that are robust against Coulomb interactions, with implications for quantum computing.

Contribution

It provides the first analytical solutions for MZMs in Y-shaped Kitaev wires and analyzes their stability under Coulomb repulsion using DMRG.

Findings

Multi-site MZMs are located near the junction center.

Multi-site MZMs are as topologically protected as single-site MZMs.

Analytical wave-functions for MZMs at the sweet spot are derived.

Abstract

Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in $Y$-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot ($t_h=\Delta$) and derive the exact form of MZM wave-functions in this geometry. The novelty of our result is the observation of multi-site MZMs located near the junction center on the nearby edge sites of each leg. This result is important for potential braiding of Majoranas and the performance of $Y$-junctions made from arrays of quantum dots. Furthermore, we study the stability of local (single-site) and multi-site MZMs modes in the presence of Coulomb repulsion, using density matrix renormalization group theory. Our local density-of-states calculation shows that these multi-site MZMs are as equally topologically protected as the single-site MZMs when in the presence of Coulomb repulsion or when away from the sweet-spot.