Ponto crítico quântico supercondutor em sistemas multi-bandas - Oliveira, Aline Ramires Neves de (2010)
The study of quantum phase transitions provides a new route to ¯nd and understand unconventional phases in Condensed Matter Physics. The past decades have seen a sub- stantial rejuvenation of interest in this area of study, driven by experiments on the cuprate superconductors, heavy fermions' materials, organic conductors and related compounds. Nevertheless, the transitions involving superconducting phases are not as well explored theoretically as transitions involving magnetic phases. Thus, the study of superconduct- ing systems with treatments beyond mean ¯eld theories seems to be necessary to verify the behavior of °uctuations in the normal phase near the transition to the superconductor state. We propose a generalization of the equation of motion method for equilibrium Green's functions to handle systems with time-dependent perturbations. This generalization is based on the properties of Green's functions and in the adiabatic application of the disturbance. We study a two band s-wave superconductor with hybridization, based on an attractive Hubbard model. We consider the system under the action of a fictitious field, time and wave vector dependent, which couples to the superconducting order parameter. We calculate the zero order propagators in the field, using the conventional equation of motion method, and the first order ones, using the generalized equation of motion. The response to the field is given by a generalized susceptibility, which in the one-band case reduces to the one obtained by Thouless. We associate the emergence of superconductivity with the divergence of the static part of the generalized susceptibility. The advantage of this method is its simplicity, because we only deal with single-particle propagators. We analyze this superconducting susceptibility, which allows us to find a critical hybridization above which there is no superconducting phase, determine the critical and the crossover lines and determine the dynamical critical exponent z for this system. Therefore we can predict the behavior of some quantities measured experimentally at low temperatures close to the superconducting quantum critical point.