Dark Andreev States in Superconductors

TL;DR

This paper integrates Migdal-Eliashberg theory with BdG equations to reveal new high-energy bound states called dark Andreev states and a shadow gap near the Debye energy in superconductors.

Contribution

It introduces a novel approach combining frequency-dependent pairing with BdG equations, uncovering new spectral features in superconductors.

Findings

Discovery of a shadow superconducting gap near the Debye energy

Prediction of high-energy dark Andreev bound states

Experimental signatures in tunneling measurements

Abstract

The conventional Bardeen-Cooper-Schrieffer (BCS) model of superconductivity assumes a frequency-independent order parameter, which allows a relatively simple description of the superconducting state. In particular, its excitation spectrum readily follows from the Bogoliubov-de-Gennes (BdG) equations. A more realistic description of a superconductor is the Migdal-Eliashberg theory, where the pairing interaction, the order parameter, and electronic self-energy are strongly frequency dependent. This work combines these ingredients of phonon-mediated superconductivity with the standard BdG approach. Surprisingly, we find qualitatively new features such as the emergence of a shadow superconducting gap in the quasiparticle spectrum at energies close to the Debye energy. We show how these features reveal themselves in standard tunneling experiments. Finally, we also predict the existence of additional high-energy bound states, which we dub "dark Andreev states."