Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain

TL;DR

This paper analytically investigates how impurity scattering influences odd-frequency spin-triplet pairing and Majorana edge states in a Kitaev chain, revealing tunable local density of states and pairing amplitudes near impurities.

Contribution

It provides an analytical calculation of the Green's function in a semi-infinite Kitaev chain with impurities, elucidating impurity effects on Majorana modes and odd-frequency pairing.

Findings

Impurity position near the edge affects LDOS and pairing amplitude.

Zero-energy LDOS and odd-frequency pair amplitude share the same spatial profile.

Majorana wave functions explain the LDOS spatial dependence.

Abstract

We study a Kitaev chain model, which is the simplest model of topological superconductors hosting Majorana fermion, appearing as a zero-energy state at the edge. We analytically calculate the Green's function of the semi-infinite Kitaev chain with a delta-function-type impurity potential within the quasi-classical regime to obtain the spatial dependence of the induced odd-frequency pairing. It is found that if the position of the impurity is not far from the edge, the spatial profile of the local density of states (LDOS) and the odd-frequency spin-triplet $s$-wave pair amplitude is tunable as a function of the strength of the impurity potential. Moreover, the zero-energy LDOS and low-frequency odd-frequency pair amplitude are found to have the same spatial dependence. The spatial profile of the zero-energy LDOS is analyzed based on the wave function of Majorana fermions.