Exponential localization of zero modes in Majorana islands
Majorana modes, predicted to emerge at the ends of some 1D superconductors, are half-fermions whose quantum states can be manipulated by adiabatic braids. Such manipulations are protected, up to a splitting which is predicted to vanish exponentially as the modes become spatially separated.
I will summarize our recent experimental test of the exponentially small splitting. Coulomb peak spacings are used to measure electron addition energies of superconducting nanowire quantum dots. At finite magnetic fields, a low-energy state consistently emerges. Addition energies exponentially approach zero for long wire lengths, consistent with protected, end-localized Majorana modes.