From phase- to amplitude-fluctuation driven superconductivity in systems with precursor pairing

TL;DR

This paper explores the transition from phase- to amplitude-fluctuation driven superconductivity in a system of electrons and localized pairs, highlighting how doping affects Cooperon properties and the nature of superconductivity.

Contribution

It introduces a model showing how Cooperon mass and lifetime influence the crossover from phase- to amplitude-fluctuation driven superconductivity with doping.

Findings

High n_B Cooperons are heavy and long-lived; reducing n_B decreases their mass and lifetime.

Superconductivity at high n_B is phase-stiffness driven; at low n_B, it is amplitude-fluctuation driven.

The phase diagram resembles high T_c superconductors, with key factors being Cooperon mass and lifetime.

Abstract

The change-over from phase- to amplitude-fluctuation driven superconductivity is examined for a composite system of free electrons (Fermions with concentration n_F) and localized electron-pairs (hard-core Bosons with concentration n_B) as a function of doping-changing n_B. The coupling together of these two subsystems via a charge exchange term induces electron pairing below a certain T^* (showing up in form of a pseudogap) and ultimately superconductivity in the Fermionic subsystem. T^* steadily decreases with decreasing n_B. Below T^* this electron pairing leads to electron-pair resonant states (Cooperons) with quasi-particle features which strongly depend on $n_B$. For high concentrations, (n_B \simeq 0.5), correlation effects between the hard-core Bosons lead to itinerant Cooperons having a heavy mass m_p, but are long-lived. Upon reducing n_B, the mass as well as the lifetime of those Cooperons is considerably reduced. For high values of n_B, a superconducting state sets in at a T_c, being controlled by the phase stiffness D_\phi=\hbar^2 n_p/m_p of those Cooperons, where n_p denotes their density. Upon reducing n_B, the phase stiffness steadily increases, and eventually exceeds the pairing energy k_B T^*. The Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high T_c superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.