Electron Teleportation in Multi-Terminal Majorana Islands: Statistical Transmutation and Fractional Quantum Conductance

We study a topological superconductor island with spatially separated Majorana modes coupled to multiple normal metal leads by single electron tunneling in the Coulomb blockade regime. We show that low-temperature transport in such Majorana island is carried by an emergent charge-$e$ boson composed of a Majorana mode and an electron from the leads. This transmutation from Fermi to Bose statistics has remarkable consequences. For noninteracting leads, the system flows to a non-Fermi liquid fixed point, which is stable against tunnel couplings anisotropy or detuning away from the charge-degeneracy point. As a result, the system exhibits a universal conductance at zero temperature, which is a fraction of the conductance quantum, and low-temperature corrections with a universal power-law exponent. In addition, we consider Majorana islands connected to interacting one-dimensional leads, and find different stable fixed points near and far from the charge-degeneracy point.