Abstract
Optimizing various properties of materials have been under intensive focus for many decades. In recent years, the exposure of ultrafast techniques enhance the possibility of seizing this goal. As by employing these techniques, one can expose the system under strong short fields, and investigate the transient response of various low-lying excitations. Such studies will strengthen our understanding of interplays among various degrees of freedom in correlated materials, and thereby facilitate the chance to manipulate different properties of these systems. Of our particular attention is the electron-lattice dynamics, where modulating a particular vibrational mode of the crystal lattice, will lead to the emergence of new quasi stable'' lattice structures as well as novel transient phenomena. Aside from these experimental prospects, the above mentioned goals were also the subject of an extensive theoretical studies.
In this thesis, we investigated the in and out of equilibrium dynamics of electronic systems which are interacting with lattice degrees of freedom. We employed the two-time Keldysh Green's function within the framework of the dynamical mean field theory to conduct our researches on this subject. In our first attempt, we studied the dynamical response of a one-electron system under a linear electron-lattice interaction. We explored the real-time formation of a bound quasiparticle, known as a polaron, under various parameter regimes of the model. We presented that when the carrier is suddenly coupled to the lattice degrees of freedom, the long-time response of the system in the strong coupling limit exhibits both bound, polaronic, and unbound, delocalized, states. We characterized the nature of such a mixed state using the adiabatic picture of the model. We also showed that the formed polaron is dressed by excited phononic states, in contrast to its equilibrium counterpart, where the ground-state phononic states are bounding the electron.
We also addressed the response of a many-body electronic system, weakly coupled to a bosonic bath,
under various time dependent excitations, which brings the system to a bad-metallic phase. We employed a model which treated the Coulomb repulsive interaction locally.
We presented that the relaxation of this excited state varies by the strength of the electron-electron interaction. We demonstrated that, for both insulating and metallic regimes of the system, a slow relaxation dynamics can be observed close to the phase transition from the metallic to insulating regimes of the system.
Our analysis revealed that in the metallic side, this slow evolution is rooted in the spin-related physics of the problem.
However, in the insulating regimes of the model, our results showed that presence of a gap in the spectral density of the insulating system prohibits the relaxation of the excited particles. We also studied the associated timescale for the adiabatic dynamics near the Mott transition. Our results exhibited that there is a nonadiabatic window'' in the metallic side of the phase transition, in which the adiabatic timescale is extremely long. We pointed out that the presence of such a window is intertwined with the slow relaxation timescale of the spin-related dynamics close to the Mott transition.
We also captured an induced metallic phase near metal-to-insulator transition out of equilibrium. We initiated this study using the slave-rotor impurity solver, which is been coupled to the self-energies obtained from the first-order Luttinger-Ward functional for the Phonon degrees of freedom.
We presented the emergence of the larger spectral density at small frequencies both in metallic and insulating phases close to the phase transition, which is surrounded by pseudo gaps. We explored the physics of such spectral densities as well as their dependencies on the phononic parameters. We postulated that this response of the system is due to the evolution of the system, in a non-thermal mechanism, towards a temperature which is less than the initial temperature of the system, before coupling to the bath. We also pointed out that the associated very slow relaxation dynamics is the result of the formation of psuedo-gaps around the quasiparticle peak.
