OPTICAL PROPERTIES OF HIGH Tc SUPERCONDUCTORS

Abstract

After one century of the historic landmark discovery of superconductivity by Heike Kamerlingh Onnes (1911), now has grown a rich heritage in experimental as well as in theoretical sectors. This journey has acquired several milestones during this long period can be divided into two major segments, namely; Conventional superconductivity period (1911-1985) and era of high temperature superconductivity (1986 and onwards). The era of conventional superconductivity includes the investigations; namely: perfect diamagnetism and total expulsion of magnetic flux- Meissner and Ochsenfeld effect (1933); two fluid model of Gorter and Casimir; isotope effect by Maxwell and Reynolds et al.; London equations by F. and H. London (1934); phenomenological ‘macroscopic theory’ of superconductivity of Vitaly Ginzburg and Lev Landau(1950); investigation of type-I and type-II superconductors and Abrikosov (1957) Vortex formation; microscopic theory of superconductivity-BCS theory by John Bardeen, Leon Cooper and Robert Schrieffer(1957); Correspondence between GL theory and BCS theory by Lev Gorkov (1959); Josephson effect and various technological applications of superconductors, e.g., magnetic levitation, superconducting transformers, etc. The BCS theory appeared as a most successful theory which explained the phenomenon of superconductivity. New area of research started with the breakthrough discovery of first high temperai ii ture superconductor (cuprate superconductors) by Bednorz and Muller (1986). The long awaited unique problem of anharmonic phonon-electron interactions in high temperature superconductors attracted the physicist with the verity that anharmonicity is responsible for many different dynamical properties of the solids. Some of the proposed mechanisms of high temperature superconductivity considered that phonon helps to join the two electrons into superconducting pairs (cooper pairs, bipolarons, and pairons). Various remarkable conclusions shows that the anharmonicity less than 1% can induced superconductivity even in the presence of coulomb repulsion. A near consensus to decide the building blocks to understand the high temperature superconductivity has been emerged out as follows: (i) Dimensionality plays an important role in the phenomenon of high temperature superconductivity. The action of conduction occurs primarily in the Cu-O planes, which attracts the attention of experimental as well as of theoretical physicist on the behavior of planar excitations and focus on the two best studied systems, YBCO and LSCO. (ii) The presence of binding layers (charge reservoir layers) provides a source for the hole doping in copper oxide planes. The transition temperature and superconductivity depends upon the concentration of holes. Material should be layered with one or more planes there should be a layer that acts reservoir layer. The YBCO is the basic representative superconductor with the unique dynamical properties of high temperature superconductors like thermal properties, optical properties and electronic properties. The vibrations of apical oxygen ions along c-direction shows influenced effect of defects and anharmonicity. The discovery of high temperature superconductors in cuprates was actually inspired by possible strong electron-phonon interaction in oxides owing to polaron formation or in mixed valence systems. The theory of electrons interacting with harmonic phonons studied by Migdal and Eliashberg leading to the description of superconductivity in phonon mediated superconductors. Shortly after the discovery, several experiments lead some people to believe that electron-phonon coupling may not be relevant to high temperature superconductivity instead, strong electron-electron correlation has been proposed to be the mechanism of high temperature superconductivity. Now iii to study the various dynamical properties of high temperature superconductors and quantum dynamics of phonon and electron the Green’s function method of Zubarev has been taken as the state of the art with almost a complete crystal Hamiltonian. By using this method phonon density of states and electron density of states has been studied with in a new frame work. It is observed that the theories of superconductivity so far deal with the Hamiltonian which include (i) unperturbed phonon part, (ii) the electron-phonon part and (iii) the BCS part. The complete picture of the interactions cannot be accorded by mere consideration of these three and becomes impossible to describe dynamical properties of high temperature superconductors with a reasonable competence. Since the anharmonicity does not vanish even at ultra low temperature and the localization effects due to the substitutional impurities change the energy spectrum drastically. We have rarely come across the various theories which simultaneously deal with the problem of anharmonicities as well as that of impurities in the problem of superconductivity. This probed us to undertake the study of dynamical properties of high temperature superconductors when the impurities, anharmonicities and electron-phonon effects play a vital role in simultaneity. The problem of anharmonic effects is a bit too complicated in simple solids and this becomes more complex when the effects of defects are included. These effects in the high temperature superconductors are not studied up to a satisfactory extent and need to be explored and critically analyzed. Since the number of atoms per unit cell in the superconducting systems is found large and hence the possibility of impurity interaction as well as that of anharmonic interactions is quite large as compared to the simple solids. There pending a very interesting problem in the respect of Born-Mayer potential. We see that in earlier theories the parameters of Born-Mayer potential has been taken as constant, which is needs to be critically analyzed. Taking the anharmonic, defect and electron-phonon contribution the infrared absorption also a very complicated and unique problem. In this our work we have tried to solve both of the problems with in a new frame work.