Kinetics and Boltzmann kinetic equation for fluctuation Cooper pairs

Abstract

The Boltzmann equation for excess Cooper pairs above Tc is derived in the framework of the timedependent Ginzburg-Landau (TDGL) theory using Langevin's approach of the stochastic differential equation. The Newton dynamic equation for the momentum-dependent drift velocity is obtained and the effective drag force is determined by the energy dependent life time of the metastable Cooper pairs. The Newton equation gives just the Drude mobility for the fixed momentum of Cooper pairs. It is shown that the comparison with the well-known result for Aslamazov-Larkin paraconductivity and BCS treatment of the excess Hall effect can give the final determination of all the coefficients of TDGL theory. As a result the intuitive arguments used for an interpretation of the experimental data for fluctuation kinetics are successively introduced. The presented simple picture of the degenerated Bose gas in τ -approximation near the Bose-Einstein condensation temperature can be used for analysis of fluctuation conductivity for the cases of high frequency and external magnetic field for layered and bulk superconductors. The work of the Boltzmann equation is illustrated by frequencydependent Aslamazov-Larkin conductivity in nanowires, in the two-dimensional case and in the case of strong electric field where the TDGL equation is solved directly. There are also derived explicit formulas for the current in the case of arbitrary time dependence of electric field up to THz range, the distribution of fluctuation Cooper pairs for nonparabolic dispersion, the influence of the energy cut-off and the self-consistent equation for the reduced temperature. The general theory is illustrated by formulas for fluctuation conductivity in nanowires and nanostructured superconductors.

Phonon mode spectroscopy, electron-phonon coupling, and the metal-insulator transition in quasi-one-dimensionalM2Mo6Se6

“…This clearly cannot explain our data, since we observe ∆T c to increase linearly as H increases. However, Mishonov et al 29 derived a quasi-1D Ginzburg parameter for a superconducting nanowire:…”

“…33 Unfortunately, the majority of these previously developed models are unlikely to be applicable to M 2 Mo 6 Se 6 since they generally assume a 2D or 3D electronic ground state. Relatively little work has addressed the one-dimensional problem directly, although Mishonov et al 34 derived a quasi-1D Ginzburg parameter for a superconducting nanowire,…”

Paraconductivity of underdopedLa2−xSrxCuO4thin-film superconductors using high magne

“…A total energy cutoff had also been introduced by other groups. [26][27][28] For small values of ⑀, the measured divergence of ⌬ is not expected to depend on the exact variation of N , however, for larger values of ⑀, the choice made for the normal state becomes relevant, in particular, when studying the power-law decrease of ⌬. As a matter of fact, in the underdoped YBa 2 Cu 3 O 7−␦ and Bi 2 Sr 2 CaCu 2 O 8+␦ analyses, the normal state resistivity could only be hypothesized since T C is too high to be suppressed by the magnetic fields typically available in the laboratory.…”

Generation of Terahertz oscillations by thin superconducting film in fluctuation regime

“…The general expression for the nonlinear current accounting for the fluctuation conductivity in the case of a two dimensional (2D) superconductor can be obtained in the vicinity of critical temperature in different ways: using Boltzmann transport equation for fluctuation Cooper pairs above T c0 , in the frameworks of the TDGL formalism, and in diagrammatic approach. [2][3][4][5]10 We will take it in the form, valid both below and above critical temperature…”