Inversion of Disorder Signatures in Complex Systems

Abstract

In an attempt to understand nature, we are constantly seeking the causal factor behind everyday observations. We categorise this kind of endeavour as an inverse problem - the problem of inverting the arrow of time, the direction of measurement, to understand the instrumental parameters that brought a system into its current state. In this thesis, we will approach inverse problems in the realm of condensed matter physics to devise a methodology capable of revealing the primary factors behind observed spectral signals. With this method, we will be able to identify the structural properties of a variety of systems from the nano to the mesoscopic scale, revealing the different types of disorder found within.

In particular, we will approach two major systems - the transition metal dichalcogenide (TMD) Molybdenum Disulfite (MoS2), and the neuromorphic random nanowire network of memristors. After having established the theory to approach disordered crystals, we will apply the devised inversion methodology to recover the concentration of chalcogen vacancies in the MoS2, the most common type of disorder in this system. This will be done for a variety of quantities including a qualitative inversion of experimental measurements. Later we will analyse this system with an extra level of complexity by introducing AuCl3 coordinated complexes on the TMD surface as disorder. The weak effect that this scatterer has in the spectral functions offers a challenge to our inversion method. By performing this inversion, we will probe the reliability of the methodology. Finally, we will shift gears into treating nanowire networks of memristors that can assume a particular conductive behaviour denominated "winner takes all", where the sourced current travels through one single path within the network. We will identify and characterize the network parameters responsible for this neuromorphic behaviour and predict its occurrence.

The work presented in this thesis contributes to the development of research on inversion problems in condensed matter physics and opens the door for quantitative work in the field of inversion, as well as for tackling the inverse problem of signal-based material design. By obtaining domain over the field of inverse problems, we are one step closer to observing and controlling matter to our will.