Internal structure of preformed Cooper pairs

TL;DR

This paper investigates the internal structure of preformed Cooper pairs in high-temperature superconductors by calculating a pair structure function using the Bethe-Salpeter equation, considering different symmetries and interaction potentials.

Contribution

It introduces a detailed calculation of the pair structure function for preformed pairs, accounting for various symmetries, potentials, and physical parameters, advancing understanding of pseudogap states.

Findings

Dependence of pair structure on center of mass momentum

Impact of interaction strength and temperature on pair structure

Differences between s-wave and d-wave pairing structures

Abstract

In order to obtain information about the internal structure of the preformed pairs in the pseudogap state of high $T_c$ superconductors, we calculate the propagator of a singlet pair with center of mass coordinate $\mathbf{r}$, and relative distance $\pmb{\rho}$, by solving the Bethe-Salpeter equation, representing the sum over repeated two-particle scattering events due to a distance dependent attraction. We define then a ``pair structure function'' $g_{P}(\mathbf{P},\pmb{\rho}) $ that depends on the internal distance $\pmb{\rho}$ between the partners and on the momentum $\mathbf{P}$ of the pair. We calculate this function both for a local potential and $s-$wave symmetry of the order parameter and for a separable potential and $d-$wave symmetry of the order parameter. The influence of the center of mass momentum, strenght of the interaction, temperature, density of particles and of the pseudogap in the one-electron spectrum is studied for both cases.