Fig. 1: Possible system setups and our major predictions.

a Illustration of our system that consists of four or more MZMs on opposite sides of the nanowire. Two of them (γ1 and γ2) are coupled with the strength ν, and only γ1 and γ4) are connected to leads. b The CB peak conductance through our Majorana-hosted island that is tuned to the half-filling. For more intuitiveness, we use logarithmic coordinates and find that it is non-monotonic in temperature. Inset: the monotonic temperature-dependence peak conductance of normal CB peaks. c Illustration of another possible realization of our system. d A picture on what happens after the hybridization of f1. Upper panel: for non-local transport, the hybridization of f1 changes the status of MZMs, including γ4 (which is essential for “teleportation”) near the right lead, and also γ1, γ2 near the left lead. The latter two are also influenced by a finite coupling ν, which is another element that both manifests non-locality and also distinguishes our work from the MT of ref. 32. This structure leads to a great modification of the tunneling across the island. Lower panel: for local transport, the hybridization of the site next to the right lead simply reduces the effective size of the island, leading to a minor modification of the tunneling.