Dynamical mean-field theory for solids with strong coupling to the electromagnetic field

Abstract

Recent advances in the study of quantum cooperative effects in coupled light-matter systems open up unprecedented pathways to manipulate the properties of materials without external drive. This is due to vacuum fluctuations of the electromagnetic field, which hybridize with matter degrees of freedom even in thermal equilibrium and thereby influence the behavior of the system. In this thesis, we focus on the theoretical study of such photon-induced effects. We first present a collective theory for single-mode models and then apply dynamical mean-field theory (DMFT) to macroscopic solids interacting with a continuum of electromagnetic modes. The collective theory is based on diagrammatic techniques and assumes a linear dipolar coupling to one single cavity mode. It allows expressing the electric susceptibility of the system inside the cavity in terms of the bare matter response. We find that the radiative corrections of the static susceptibility vanish in the thermodynamic limit if the single-particle coupling is finite. Moreover, the formalism proves that nonlinearities in the matter response play a crucial role in affecting the equilibrium state of finite-size systems. As an example, we apply the theory to a simple model of a quantum paraelectric with dipole-dipole interactions and demonstrate that the cavity mode leads to an enhancement of the static electric response in small clusters of material. DMFT, however, is most appropriate for extended solids consisting of a macroscopic number of atoms or molecules. Therefore, we consider a setting, where a continuum of electromagnetic modes gives rise to a non-vanishing total effect even in the thermodynamic limit. The modes correspond to surface plasmon polaritons (SPPs) at a dielectric-metal interface. We study two different model systems: In the first case, we consider a two-dimensional solid that couples to the vacuum fluctuations of the SPPs via a linear dipolar interaction. Within static mean-field approximation, the material exhibits a ferroelectric phase transition that is not affected by the electromagnetic radiation field. Bosonic DMFT provides a more accurate description and reveals that the light-matter interaction enhances the ferroelectric order and stabilizes the ferroelectric phase. In the second case, we study a two-dimensional Hubbard model, which couples to the electromagnetic modes via Peierls phase factors. Even without light-matter interaction, the system may undergo a Mott metal-isulator transition. We follow a diagrammatic approach to incorporate photon-induced effects into the DMFT formalism. Our results suggest that the coupling to the electromagnetic field favors the metallic state over the Mott insulating phase. In summary, this thesis demonstrates that the interplay of light and matter opens up new possibilities to modify the static response of microscopic systems and to control phase transitions in macroscopic solids, even in thermal equilibrium. Moreover, it highlights that DMFT can serve as a valuable theoretical tool to study quantum cooperative effects in systems with strong light-matter interactions.