Zero-energy states in the Kitaev finite and semi-infinite model

The Kitaev chain models a p-wave superconductor and hosts two Majorana bound states at the ends of the chain in the topological phase, for example if mu = 0, Delta = t, where mu, Delta and t are chemical potential, superconducting pairing potential, and the next-nearest neighbor hopping amplitude, respectively. We consider finite and semi-infinite chains with close parameters mu = 0 and Delta = t +epsilon where.. is small, near the point Delta - t = 0. Using the Dyson equation and the Green's function for the infinite Kitaev chain, we analytically study the conditions for the appearance of zero-energy states, as well as their wave functions. We have proven that in the finite chain such states exist only if Delta > t and the number of sites is odd. Zero-energy states disappear in the finite chain in the presence of an impurity potential, which indicates their instability. But in the semi-infinite chain, for Delta > t there is a single Majorana state and it is robust against an impurity.Thus the bulk-boundary correspondence may be violated for the Kitaev chain near the singular point.

Automated summary

This study analytically investigates the conditions and properties of zero-energy states in the Kitaev chain model. They find that in finite chains, zero-energy states exist only when the chemical potential is greater than the superconducting pairing potential and the number of sites is odd, while in semi-infinite chains, a single stable Majorana state exists as long as the superconducting pairing potential is greater than the chemical potential.