Notes on the Kitaev \leftrightarrow Tight-binding correspondence

TL;DR

This paper explores the relationship between the Kitaev chain, a topological superconductor model, and a specific tight-binding lattice, enabling exact solutions for energy levels and states under certain conditions.

Contribution

It establishes a precise correspondence between the Kitaev chain and a tailored tight-binding model, allowing exact solutions for specific parameters.

Findings

Exact energy levels and eigenstates for the Kitaev chain at t=|Δ| and μ=0

Identification of a geometric tight-binding model corresponding to the Kitaev chain

Insights into localized edge states in topological systems

Abstract

In this project, we study the properties of a non-trivial topological system which exhibits localized edge states. In our study, we adress the Kitaev chain, a one-dimensional chain of atoms deposited on top of a p-wave superconductor that induces superconductivity in the chain by proximity effect. We establish a correspondence between the Kitaev chain and a tight-binding lattice with a particular geometry for a particular case of the system parameters. This correspondence allows one to find the exact energy levels and eigenstates of the Kitaev chain when t=|\Delta| and \mu=0 for an arbitrary chain size.