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

Majorana zero modes in Y-shape interacting Kitaev wires