M.Sc Student | Bar-Lev Yevgeny |
---|---|

Subject | Analysis of a Boson Model for Cuprate Superconductors |

Department | Department of Physics |

Supervisor | Professor Ady Mann |

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.