Flow equation approach to the linear response theory of superconductors

Abstract

We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions we reproduce the standard response kernel of the BCS superconductor. We next generalize this non-perturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.

Fluctuation conductivity due to the preformed local pairs

“…We treat on equal footing the boson and fermion degrees of freedom, by means of the continuous unitary transformation [25,26] that is reminiscent of the numerical renormalization group techniques [27]. Such nonperturbative scheme has been used by us [28] to determine the response function beyond the BCS approximation [29]. Here we focus on its physical implications for the real part of the frequency-dependent conductance due to the preformed local pairs.…”

Electromagnetic Response of the BCS Superconductor: Flow Equation Approach

“…The present procedure can be generalized on the nontrivial case when ∆ k is treated as the quantum eld [4].…”

“…We have applied such approach to the bosonfermion model and examined the pseudogap state where the preformed pairs are incoherent above T c [4]. We were motivated by the experimental data of the torque magnetometry [6] revealing the residual diamagnetism in cuprates above T c .…”

“…We focus on the technical details concerning determination of the currentcurrent response function for the BCS superconducting which have been omitted in our previous work [4]. We also point out how this treatment can be used for studying the uctuations and various non-equilibrium phenomena.…”

Renormalization Group Approach for the Double Exchange Ferromagnets

“…Particular choice of this canonical generator depends on the subtleties of the considered problem [12]. We have applied such unitary transformations for BCS superconductors [13] and for the systems of coherent and incoherent preformed pairs [14]. Now, we shall try to extend such algorithm for the strong ferromagnetic coupling limit which is relevant to the manganites.…”