On a theoretical model for d-wave to mixed s- and d-wave transition in cuprate superconductors

A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. 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 two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases and the temperature dependence of the heat capacity.