Boltzmann equation for fluctuation Cooper pairs in Lawrence-Doniach model. Possible out-of-plane negative differential conductivity

TL;DR

This paper models out-of-plane fluctuation conductivity in layered cuprates using the Lawrence-Doniach model within TDGL theory, revealing conditions for negative differential conductivity and potential THz oscillation generation.

Contribution

It introduces a Boltzmann equation approach for fluctuation Cooper pairs in the Lawrence-Doniach model, linking the TDGL correlator to particle dynamics and conductivity behavior.

Findings

Transition from normal to superconducting phase involves negative differential conductivity.

Fluctuation conductivity depends on particle distribution over Josephson phase.

Negative differential conductivity could enable THz oscillation generation.

Abstract

The differential conductivity for the out-of-plane transport in layered cuprates is calculated for Lawrence-Doniach model in the framework of time-dependent Ginzburg-Landau (TDGL) theory. The TDGL equation for the superconducting order parameter is solved in the presence of Langevin external noise, describing the birth of fluctuation Cooper pairs. The TDGL correlator of the superconducting order parameter is calculated in momentum representation and it is shown that the so defined number of particles obeys the Boltzmann equation. The fluctuation conductivity is given by an integral over the Josephson phase \theta of the particles distribution, depending on that phase, n(\theta) and their velocity v(\theta). It is demonstrated that in case of overcooling under T_c the transition from normal to superconducting phase while reducing the external electric field runs via annulation of the differential conductivity. The presented results can be used for analysis and experimental data processing of measurements of differential conductivity and fluctuation current in strong electric and magnetic fields. The possible usage of a negative differential conductivity (NDC) for generation of THz oscillations is shortly discussed.