טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBar-Lev Yevgeny
SubjectAnalysis of a Boson Model for Cuprate Superconductors
DepartmentDepartment of Physics
Supervisor Professor Ady Mann


Abstract

A model suggested by Iachello for superconductivity in cuprate materials is analyzed. This model tries to reconcile conflicting experiments, which show different symmetries of the macroscopic wavefunction of copper oxide superconductors in bulk-sensitive and surface-sensitive experiments. While bulk sensitive experiments yield substantial s symmetry, surface sensitive experiments yield d symmetry. The model follows the proposal of Müller that a reconciliation of the conflicting experiments was possible if the superconducting wavefunction were a sum of two components, namely, one of s symmetry and one of d symmetry, and varied as a function of the distance from the surface. The model consists of s and d pairs in a two-dimensional Fermi system with a surface, which is then bosonized in analogy to a similar case in nuclear physics. This model was first introduced by Bassichis and Foldy, as a boson model exhibiting phase transition. The transition occurs between a phase in which the system is a condensate of one of the bosons, and a phase which is a mixture of bosons. In the current work exact solution of the ground state energy and the lowest excited states is obtained for a given number of particles, N<100. Then the exact solution is compared to perturbative expansion, Hartree-Fock, Bogoliubov and RPA approximations. The validity ranges of the approximations for this model are discussed. A reduced Hamiltonian for the model is introduced and phase diagram and thermodynamical properties are investigated. A control parameter for a transition is proposed.