Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point

TL;DR

This paper explores a non-Hermitian Kitaev chain with imaginary p-wave pairing, revealing phase transitions at exceptional points where resonant Cooper pair generation occurs, and proposes a dynamic scheme to produce superconducting states.

Contribution

It provides an exact solution for the non-Hermitian Kitaev chain, identifying exceptional points and their role in resonant Cooper pair generation, along with a scheme for dynamic superconducting state creation.

Findings

Phase diagram with real and complex spectra separated by an exceptional line.

Resonant generation of specific Cooper pair states at exceptional points.

Proposal of a dynamic method to generate superconducting states.

Abstract

We investigate a non-Hermitian extension of Kitaev chain by considering imaginary $p$-wave pairing amplitudes. The exact solution shows that the phase diagram consists two phases with real and complex \ Bogoliubov-de-gens spectra, associated with $\mathcal{PT}$-symmetry breaking, which is separated by a hyperbolic exceptional line. The exceptional points (EPs) correspond to a specific Cooper pair state $( 1+c_{k}^{\dagger }c_{-k}^{\dagger }) \left\vert 0\right\rangle $\ with movable $k$ when the parameters vary along the exceptional line. The non-Hermiticity around EP supports resonant generation of such a pair state from the vacuum state $% \left\vert 0\right\rangle $ of fermions via the critical dynamic process. In addition, we propose a scheme to generate a superconducting state through a dynamic method.