Titolo della tesi: Charge-density waves, quantum-anharmonicity, polar responses and resonant Raman in 1D conjugated systems
Systems with reduced dimensionality are known to display many fascinating phenomena, with properties often showing pathological behaviors. In this context, one of the most studied aspect regards the insurgence of a modulation of the electronic charge density, i.e. a charge density wave (CDW). The interest in CDWs physics is very broad as they are present in many systems, ranging from 1D and 2D materials, to high Tc superconductors and transition metal dichalcogenides. CDWs usually manifest as a broken-symmetry state, that in 1D chains of atoms results in the presence of a bond-length alternation, commonly explained as a consequence of the interplay between an instability of electronic origin and the coupling between electronic and lattice degrees of freedom. It is commonly understood that the interplay of these elements in 1D systems regulates the competition between a dimerized, less symmetric, configuration and an undimerized, more symmetric, one. In particular, a diatomic chain of atoms presents a second-order phase transition between these two phases. However, a part for these two ingredients, many other different elements are actually at play in the creation of a CDW. Indeed, there are evidences that the presence of a CDW in the infinitely-long straight chains of carbon atoms, called carbyne, is strongly affected by quantum and anharmonic fluctuations, as well as from the effect of an external environment, as we confirm and discuss in our study. The aim of the present work is thus, on one hand, to unveil the contribution of each element to the manifestation of a CDW, and, on the other hand, to study the properties of 1D systems that host CDWs. Indeed, the instability at the boundaries of the structural phase transition suggests the presence of interesting and peculiar polar responses. Following this idea, in our work, we show how 1D systems such as conjugated polymers present a huge enhancement of the effective charges, with values up to 30 times that of the nominal electronic charge at the critical point of the transition, and of the piezoelectric coefficients, which in principle present a diverging behavior in proximity of the phase boundary. In the task of determining the properties of these materials, it is then fundamental to resort to particular experimental techniques, such as resonance Raman spectroscopy. However, at date, a theory which permits to accurately describe experimental results on 1D systems is lacking. We address this problem in our work, introducing a framework that allows for the calculation of resonance Raman spectra beyond the commonly adopted Placzek approximation, even in systems beyond the simple 1D case.