THERMODYNAMIC PROPERTIES OF HIGH TEMPERATURE SUPERCONDUCTORS BASED ON THE t-J-d MODEL

Abstract

Many theories that attempt to describe the superconducting state have suffered significant failures, leaving the t-J model as the only model which effectively captures the physics of the strong correlations inherent in this problem. However, many aspects of this model are quite complex and the thermodynamic properties of the superconducting state need to be analyzed carefully. In this thesis, second quantization techniques involving Bogliubov Valatin transformation have been used to diagonalize the t-J model Hamiltonian so that the thermodynamic properties of high temperature superconductors can be studied. Formulae for ground state energy, , specific heat, , and entropy, , of high temperature superconductors have been derived in the framework of the t-J model. Additionally, the superconducting dipole Hamiltonian has been diagonalized and the sum of the t-J and dipole Hamiltonians obtained resulting in what is now referred to as the „t- J-d model‟. Transition temperature for LSCO in the t-J formalism is obtained as and in the t-J-d system. Transition temperature for YBCO in the t-J formalism is obtained as and in the t-J-d model. Both models predict Tc that is higher than the experimental value of 90K but remarkably close to the known values. Highest heat capacity of the superconducting state of the t-J model is found to be while the highest entropy value is 3.15×10-3 eV/K for high-Tc superconductors. The total energy of the system increases exponentially with the temperature.