Wave function for odd frequency superconductors

TL;DR

This paper proposes a BCS-like wave function for odd-frequency superconductors, capturing the composite boson condensate and explaining their gapless excitations and critical coupling transition.

Contribution

It introduces a new wave function model for odd-frequency superconductors based on composite boson condensation, advancing understanding of their broken symmetry state.

Findings

Quasiparticle excitations are gapless.

Superconducting transition requires a critical coupling.

Wave function recovers known properties of odd-frequency superconductors.

Abstract

We revisit the question of nature of odd-frequency superconductors, first proposed by Berezinskii in 1974. \cite{berezinskii1974} We start with the notion that order parameter of odd-frequency superconductors can be thought of as a time derivative of the odd-time pairing operator. It leads to the notion of the composite boson condensate.\cite{abrahams1995} To elucidate the nature of broken symmetry state in odd-frequency superconductors, we consider a wave function that properly captures the coherent condensate of composite charge $2e$ bosons in an odd-frequency superconductor. We consider the Hamiltonian which describes the equal-time composite boson condensation as proposed earlier in Phys. Rev. B $\textbf{52}$, 1271 (1995). We propose a BCS-like wave function that describes a composite condensate comprised of a spin-0 Cooper pair and a spin-1 magnon excitation. We derive the quasiparticle dispersion, the self-consistent equation for the order parameter and the density of states. We show that the coherent wave function approach recovers all the known proposerties of odd-frequency superconductors: the quasi-particle excitations are gapless and the superconducting transition requires a critical coupling.