Transient dynamics of unconventional superconductors: d-wave symmetry and strong correlations

This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.