Majorana zero modes in Y-shape interacting Kitaev wires

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.

8 pages and 5 figures

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• Spin Signature of Majorana Fermions in Topological Nodal-Point Superconductors
• Superconducting triangular islands as a platform for manipulating Majorana zero modes
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• Effect of interatomic repulsion on Majorana zero modes in a coupled quantum-dot-superconducting-nanowire hybrid system
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Superconducting magnetoelectric effects in mesoscopic hybrid structures