Fundamentals of Condensed Matter: Disorder, Interfaces, Topology and Discovery
In this thesis, we tackle the challenge of exploring condensed matter phenomena observed not only in theoretical but also in experimental settings. Along this journey, we merged techniques from ab initio density functional theory (DFT), topological-band theory, and data science. We examine in-depth the effects of disorder in the form of defects and amorphous phases in topological materials. Our investigation of two-dimensional Na3Bi shows that defects, while preserving time-reversal symmetry (TRS), significantly reduce the electronic transmission of trivial states tunnelling through the band edges, while maintaining transmission for dissipationless states. This finding enables controlled experiments on topological states. We demonstrate how one might filter the response of the topological metallic states at the edges and design a switching device controlled by an electric field. We explore the effect of defects in the penetration depth of the topological edge states in bismuthene. We discuss certain conditions in which these edge states hybridize across the sample, creating scattering channels without breaking the symmetries that would destroy topological protection. We extensively study the topological protection on amorphous flat bismuthene and demonstrate how the transport and topological classification change with increasing amorphization degree, spin-orbit coupling (SOC) strength and even in the presence of a splitting field. We also show that in three dimensions, the topological character of layered chalcogenide (Bi2Se3) seems to be weaker than in two dimensions for bismuthene. Next, we target materials discovery through data-driven methods. We construct a machine-learning workflow that allows for general property prediction and classification. First, we apply our protocol to discover new two-dimensional topological insulators. Next, the same technique is used for investigating the interface between graphene oxide and nanocellulose. Additionally, we create a machine learning workflow for bypassing the computational overhead of Kohn-Sham density functional theory calculations and allow for faster ab initio simulations. Finally, in the last part of this thesis, we apply these different methodologies on problems observed experimentally, we use DFT and ab initio molecular dynamics (AIMD) to understand the stability and rupture of a mono-atomic ionic wire made of ZrO2, as observed through high-resolution transmission electron microscopy (HRTEM), and we apply ML to filter, cluster, and extract information from the lignin-microfibrillated cellulose interface using atomic force microscopy (AFM) force-distance (F–d ) curves data.