Title: Derivation of the high-Tc version of the BCS optical conductivity of conventional superconductors using the spin polaron theory and matsubara green s functions

Abstract

In this article we derived the energy gap function, the normal and anomalous Green’s functions, and eventually the optical conductivity of ‘dirty’ high-Tc superconductors at the zero-temperature limit. This process in particular is primarily done by using the Heisenberg equation of motion, the effective Hamiltonian from spin polaron theory, and Matsubara (finite temperature) Green’s functions. Having done this, we proceeded to calculate the optical conductivity of ‘dirty’ high-T¬c superconductor by assuming energy conservation but not momentum and by evaluating the Kubo formula. This Kubo formula expresses the current-current correlation function, now as functions of the high-T¬c forms of the normal and anomalous Green’s functions. Then by using the Wick’s theorem made it possible to simplify the product of operators (holons as spinless fermions and bosons as normal bosons). Subsequently, the frequency summations were evaluated using the coherence factors approach. Analytic continuation was then applied in order to obtain the retarded current-current correlation function; after which the zero-temperature limit was taken. The optical conductivity, as a function of the momentum and frequency, was then obtained from the imaginary part of the retarded current-current correlation function. Our result, which is mathematically similar in form as that of conventional superconductors, reveals that the incident photon is absorbed by having its energy converted into two quasiparticles with separate energies.