New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Optoelectronic investigation of defects in hybrid metal halide perovskites

The growing demand for flexible and low-cost electronics has driven research towards the study of novel semiconducting materials to replace traditional semiconductors like silicon and germanium, which are limited by mechanical rigidity and high production cost. Some of the most promising semiconductors in this sense are metal halide perovskites (MHPs), which combine low-cost fabrication and solution processability with exceptional optoelectronic properties like high absorption coefficient, long charge carrier lifetime, and high mobility. These properties, combined with an impressive effort by many research groups around the world, have enabled the fabrication of solar cells with record-breaking efficiencies, and photodetectors with better performance than commercial ones. However, MHP devices are still affected by issues that are hindering their commercialization, such as degradation under humidity and illumination, ion migration, electronic defects, and limited resistance to mechanical stress. The aim of this thesis work is the experimental characterization of these phenomena. We investigated the effects of several factors, such as X-ray irradiation, exposure to environmental gases, and atmosphere during synthesis, on the optoelectronic properties of MHP single crystals. We achieved this by means of optical spectroscopy, electrical measurements, and chemical analyses. We identified the cause of mechanical delamination in MHP/silicon tandem solar cells by atomic force microscopy measurements. We characterized electronic defects and ion migration in MHP single crystals by applying for the first time the photo-induced current transient spectroscopy technique to this class of materials. This research allowed to gain insight into both intrinsic defects, like ion migration and electron trapping, and extrinsic defects, induced by X-ray irradiation, mechanical stress, and exposure to humidity. This research paves the way to the development of methods that heal and passivate these defects, enabling improved performance and stability of MHP optoelectronic devices.