Optical conductivity the optical conductivity resonance from an exact description of the electronic states around the Fermi energy

Abstract

In this paper we show that the optical conductivity can be calculated to agree with experiment if the details of the electronic states around the Fermi level are taken into account with some care. More precisely, we present a calculation of the optical conductivity in YBa$_{2}$Cu$_{3}$O$_{7}$ on the basis of an exact (ab initio) three dimensional electronic band structure calculation from which we extract the information on the bands near the Fermi energy that can be associated with the CuO$_{2}$ plane-carrier states. To simulate the superconducting state, we superimpose a gap on these bands alone. On these basis, from the known Kubo-Greenwood formula we calculate the optical conductivity in the normal and in the superconducting state. Our calculation agrees with the experimental result even in the higher part of the frequency spectrum. Our way of calculating the resonance suggests a model of evolution for the bands under the effect of doping consistent with the recent experimental findings that the optical resonance can disappear while the sample remains superconducting. An important conclusion of this paper is that the resonance depends mostly on the details of the electronic band structure. It is enough to take into account the effect of the superconducting transition through a single parameter (the gap). No details on the mechanism are needed, so no mechanism can be tested on this basis. Our calculation suggests a model of evolution for the bands around the Fermi energy under doping that gives some microscopic foundations to the recent experiments that show unambiguously that the resonance cannot be the cause of superconductivity. Most importantly, it indicates how the background is built up and depends on the electronic excitations accessible through values of the energy transfer on a wider interval than the one contributing directly to the resonance. These electronic excitations are determined by the optical transitions allowed. From this point of view, it is an obvious consequence that the background is with small differences, common to all the cuprates having a CuO$_{2}$ plane. But the most important conclusion is that the background contains essentially the same physics as the resonance does, and so it does not have any detailed information on the superconducting mechanism as well, contrary to the conclusions of recent work.