Charge and Spin Transports Through a Normal Lead Coupled to an S‐Wave Superconductor and Majorana Fermions

Abstract

Charge and spin transports through a normal lead coupled to an s‐wave superconductor and Majorana fermions at the ends of the nanowire are investigated using the Green's function method. In the limit of the superconducting gap Δ → ∞ , the analytical expressions of charge conductance G normalc and spin conductance G s n false^ are obtained at zero temperature. For different values of coupling constant x between the normal lead and s‐wave superconductor, the impacts of Majorana fermions coupling energy ε m, temperature kT, and superconducting gap Δ on charge conductance G normalc and spin conductance G sz are discussed. As x increases, G normalc changes from peak to valley and then to peak at bias eV = ± ε m. The conductance of peaks and valleys is equal to quantum conductance 2 e 2 / h , which corresponds to Majorana fermions. Moreover, G sz decreases as x increases. For kT > 0 , the charge (spin) conductance of peaks and valleys cannot reach 2 e 2 / h ( e / 4 π ) . These results can help probe and understand Majorana fermions in experiments.