## 71.35.Lk Collective effects (Bose effects, phase space filling, and excitonic phase transitions)

### Refine

#### Keywords

Nanoengineering and laser optics allow for the fabrication of a wide range of systems that subject fermionic particles to geometric restrictions. In addition to strong correlations, the fermions may couple to internal or external bosonic fields, such as quantized lattice vibrations or light fields. This thesis considers the theoretical description of two such systems. One is a molecular junction, i.e., a small organic molecule contacted by metallic electrodes or leads. Itinerant electrons induce molecular vibrations and deformations, corresponding to phonon modes of considerable energy. The thesis investigates the effects of this local electron-phonon interaction on the electric and thermoelectric transport through the junction. Starting with an Anderson-Holstein quantum dot model, our ansatz is based on the application of a variational Lang-Firsov transformation that accounts for the polaronic character of the dot state. We solve the steady-state Kadanoff-Baym equations and derive a self-consistent approximation to the polaronic self-energy that accounts for finite densities and multi-phonon scattering processes. The optimal variational parameter is determined numerically by minimizing the thermodynamical potential. This allows a detailed study of the electronic dot spectral function for all interaction strengths and adiabaticity regimes. For instance, we discuss how a voltage dependent polaronic renormalization of the dot-lead coupling and the dot level causes negative differential conductance and novel conductance features. The investigation of the second system is motivated by recent experiments on the Bose-Einstein condensation of excitons in small semiconducting cuprous oxide crystals. At ultra cold temperatures three species of para- and orthoexcitons are caught in stress induced potential traps. Their decay luminescence is the primary method of detection. This thesis considers the thermodynamics of this system in terms of a multicomponent gas of weakly interacting bosons in external potentials. The coupled equations of motion are solved within a Hartree-Fock-Bogoliubov-Popov approximation. For typical experimental parameters the density distributions of the interacting species are calculated numerically. Based on the luminescence formula by Shi and Verechaka we discuss, e.g., how the spectrum of the direct decay of thermal paraexcitons may reveal the formation of a nonluminescent paraexciton condensate as well as the spatial separation of strongly repulsive orthocondensates. First results for an extended luminescence theory are presented, which takes into account the polariton effect.

In this thesis we have revisited the formation of the excitonic insulator (EI), which realizes an exciton condensate. In contrast to optically created exciton condensates, the EI forms in thermal equilibrium and is solely driven by the Coulomb attraction between electrons and holes. The EI phase is anticipated to occur near the semimetal-semiconductor (SM-SC) transition at low temperatures. Depending from which side the EI is approached, it forms due to a BCS-type condensation of electron-hole pairs or a Bose-Einstein condensation (BEC) of excitons. The extended Falicov-Kimball model (EFKM) is the minimal model the EI can be described with. This model describes spinless fermions in two dispersive bands (f band and c band), that interact via a local Coulomb repulsion. The EFKM is also used to describe electronic ferroelectricity (EFE). Both phases, the EI and EFE-type ordering, are characterized by a spontaneous f-c hybridization in the EFKM. We have presented the EI phase, the EFE phase, and the orderings they compete with. Moreover, we have determined the ground-state phase diagram of the EFKM. We have focused particularly on the anticipated BCS-BEC crossover within the EI and have analyzed the formation scenarios. The exciton spectrum and the exciton density in the normal phase close to the critical temperature give information about relevant particles and therefore the nature of the transition. We have demonstrated that the whole EI is surrounded by a halo", that is, a phase composed of electrons, holes and excitons. However, on the SM side, only excitons with a finite momentum exist. These excitons appear only in a small number and barely influence the SM-EI transition. This phase transition is driven by critical electron-hole fluctuations, generated by electrons and holes at the Fermi surface. On the SC side, excitons with arbitrary momenta exist. Most notably, we have found the number of zero-momentum excitons to diverge at the SC-EI transition, signaling the BEC of these particles. Within the EI phase, there is a smooth crossover from the BCS regime to the BEC regime. One of the promising candidates to observe the EI experimentally, is the transition-metal dichalcogenide 1T-TiSe2. Strong evidences were found favoring an EI scenario of the charge-density-wave (CDW) formation in this material. However, some aspects point to a lattice instability to drive the CDW transition. We have addressed this issue by analyzing the recently discovered chiral property of the CDW in 1T-TiSe2. We have found that the EI scenario is insufficient to explain a stable, long range chiral charge ordering. Lattice degrees of freedom must be taken into account. In particular, nonlinear electron-phonon coupling and phonon-phonon interaction are crucial. By estimating appropriate model parameters for 1T-TiSe2, we have suggested a combination of excitonic and lattice instability to drive the CDW transition in this material. Experiments in 1T-TiSe2 and other materials suggest that the coupling to the lattice is non-negligible. We have extended therefore the model by an explicit exciton-phonon interaction, and have analyzed crucial effects of this interaction. While the single-particle spectrum is not modified qualitatively, the electron-hole pair spectrum changes significantly. The inclusion of the phonons lead to a massive collective mode in the ordered ground state in contrast to the case for vanishing exciton-phonon coupling, where the mode is acoustic. We have suggested that a gapless collective mode leads to off-diagonal long range order. This questions that the ground state for finite exciton-phonon coupling represents a condensate.