Optical conductivity the optical conductivity resonance from an exact description of the electronic states around the Fermi energy
F. Puch*, R. Baquero**
* Departamento de Física, Universidad de Zacatecas, Zacatecas, México.
** Departamento de Física, CINVESTAV, Apartado Postal 14–740, México D.F
Recibido el 30 de marzo de 2006 ]]> Aceptado el 30 de mayo de 2006
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 with the CuO2 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 CuO2 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.
Keywords: Superconductivity, mechanism, YBa2Cu3O7, Optical Conductivity, resonante.
Resumen
En esta carta mostramos que la conductividad óptica puede calcularse con base en el cálculo detallado de los estados electrónicos reales en las cercanías del nivel de Fermi. Más exactamente, presentamos aquí el cálculo de la conductividad óptica para el material superconductor YBa2Cu3O7 basado en un cálculo tridimensional ab initio en el cual hemos identificado las bandas que pueden asociarse al plano de CuO2. Para simular el estado superconductor, imponemos a mano una brecha a esas bandas exclusivamente. Nuestro cálculo es pues bidimensional pero usa información de un cálculo tridimensional. Usamos la conocida fórmula de Kubo–Greenwood, sin hacer uso de la brecha para obtener el cálculo en el estado normal e imponiendo la brecha en la forma descrita para el estado superconductor. Ambos resultados se ajustan muy bien con los experimentos conocidos incluso en la parte alta del espectro. Nuestra forma de calcular sugiere un modelo para la evolución de las bandas en función del contenido de oxígeno que es consistente con el hallazgo reciente de que la resonancia desaparece antes de que la muestra deje de ser superconductora. Una conclusión importante de este trabajo es que la resonancia depende en forma muy directa de los detalles de la estructura de bandas y, por lo tanto, no incluir esos detalles, tiene un efecto quizás irremediable. Por otro lado, el modelo muestra que la superconductividad misma, puede ser bastante simple. Fue suficiente incluir un solo parámetro, la brecha, sin hacer referencia a ningún mecanismo, para obtener el resultado. Este cálculo sugiere un modelo para la evolución de las bandas con el contenido de oxígeno que le da un fundamento microscópico a los experimentos recientes y que muestra, por el contrario, que la resonancia no puede explicar el mecanismo. Lo mismo vale para el ruido de fondo al cual se le atribuyó importancia, en este sentido, recientemente. Más importante aun, este cálculo muestra como el ruido de fondo está determinado por las transiciones ópticas permitidas en las frecuencias aledañas a la resonancia. Todas vienen del plano de CuO2 y, en ese sentido, es normal que el ruido de fondo sea, detalle más, detalle menos, común a todos los cupratos. Pero la conclusion más importante es que el ruido de fondo no contiene ninguna información sobre el mecanismo, conclusión que es contraria a la de algunos trabajos recientes.
Descriptores: Superconductividad; mecanismo; YBa2Cu3O7; conductividad óptica; resonancia.
]]> PACS: 74.20–z; 74.25.Gz; 74.72.Bk
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