Equivalence of NEGF and scattering approaches to electron transport in the Kitaev chain

Abstract

We consider electron transport in a Kitaev chain connected at its two ends to normal metallic leads kept at different temperatures and chemical potentials. Transport in this set-up is usually studied using two frameworks -- the nonequilibrium Green's function (NEGF) approach or the scattering approach. In the NEGF approach the current and other steady state properties of a system are expressed in terms of Green's functions that involve the wire properties and self-energy corrections arising from the leads. In the scattering approach, transport is studied in terms of the scattering amplitudes of plane waves incident on the wire from the reservoirs. Here we show explicitly that these two approaches produce identical results for the conductance of the Kitaev chain. Further we show that the NEGF expression for conductance can be written in such a way that there is a one-to-one correspondence of the various terms in the NEGF expression to the amplitudes for normal transmission, Andreev transmission and Andreev reflection in the scattering approach. Thereby, we obtain closed form expressions for these. We obtain the wavefunctions of zero energy Majorana bound states(MBS) of the wire connected to leads and prove that they are present in the same parameter regime in which they occur for an isolated wire. These bound states give rise to perfect Andreev reflection responsible for zero bias quantized conductance peak. We discuss the dependence of the width of this peak on different parameters of the Hamiltonian and relate it to the MBS wavefunction properties. We find that the peak broadens if the weight of the MBS in the reservoirs increases and vice versa.