Specific heat for high temperature superconductors

Full text: Superconductivity arises from the formation and condensation of Cooper pairs. For pairs to form, an attractive interaction which somehow avoids the instantaneous Coulomb repulsion must be present. In conventional superconductors, this attraction is provided by a temporally retarded interaction mediated by phonons. In high temperature superconductors, it is believed that spin fluctuations might play the same role. Many of the detailed properties of superconductors depend on the precise microscopic mechanism. On the other hand, many interesting qualitative features of superconductivity can be studied without worrying about the precise origin of the attraction and the attractive Hubbard Hamiltonian has proven to be a very useful model to study qualitative features of superconducting phase transitions, for example the coexistence of a sharp Fermi surface with a Bose-like spin gap, and the competition of superconductivity and ordering into insulating charge density wave states. Experimental data for the specific heat of cuprates, such as YBaCu3O6+x [1], Bi2Sr2CuO6-x [2] and Bi2Sr2CaCu2O8-x [2] with different dopings x have been available for ten years. We calculate the specific heat for the two-dimensional attractive Hubbard model on a square lattice. We use Quantum Monte Carlo methods to obtain the energy as a function of temperature and different procedures to extract both the specific heat and entropy. This is done for different electronic densities so that one can observe how the position and intensity of the peaks change with doping, signaling to the so called density induced breaking of pairs. Comparisons with the experimental data are made. [1] J. W. Loram, K. A. Mirza, J. R. Cooper, and W. Y. Liang, Phys. Rev. Lett. 71 1740, (1993); [2] A. Chakraborty, A. J. Epstein, D. L. Cox, E. M. McCarron, and W. E. Farneth, Phys. Rev. Lett. 39 12267, (1989). (author)