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 YBa2Cu3O7 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 to the CuO2 plane-carrier states. To simulate the superconducting state we superimpose a gap to these bands alone. On these basis, we calculate from the known Kubo-Greenwood formula, 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 the recent experiments that show unambiguously that the resonance cannot be the cause of superconductivity.