Interactions, external fields and disorder in low-dimensional systems

Resum

Condensed matter physics could be distinguished as one of the most prolific fields of contemporary physics research. It is devoted to studying the physical properties of condensed phases of matter, both at the microscopic and the macroscopic levels. Physicists pursue to understand the diverse and unexpected phenomena that arise when matter is formed from its fundamental constituents. Discoveries of novel phases of matter and many technological inventions present in our everyday life have been developed as a result of the research in this branch of physics. Due to the diversity of topics with which is related, this active field is deeply connected to other scientific disciplines such as biology, chemistry, material science, nanotechnology and mathematics. A detailed revision of the scope of condensed matter physics and the fertile and multitudinous phenomena found under this name is given in the general and very complete book Introduction to Condensed Matter Physics by F. Duan and J. Guojun [1]. For a short inspect, in the webpage of the Institute of Physics (United Kingdom) a booklet that addresses the main challenges of this area of research and examples of some recent scientific advances can be found [2]. Traditionally, this field is divided in soft and hard condensed matter physics, differentiating between them as a function of the energy and length scale where the interactions between constituents happen. Hard condensed matter, usually known as solid state physics, deals with materials with structural rigidity such as crystalline solids. Their physical properties are fundamentally governed by atomic forces and quantum mechanics. However, soft condensed matter is centred on the study of liquids, membranes, polymers and biological materials. The energy scale at which their physical behaviours occur is comparable to room temperature multiplied by the Boltzmann constant. Therefore, quantum effects generally do not play any role, and their properties are mainly described by classical mechanics [1]. However, the boundary separating the two branches is becoming diffuse, and they are framed in the new paradigm of condensed matter physics, which emphasises many-body effects and broken symmetry [1]. This Thesis is embodied itself in the study of structures that operate in the quantum regime. The main purpose of this work is to explore different problems that have been faced in the past and in the present in the framework of theoretical hard condensed matter. The building blocks of this research are settled on the foundations of quantum mechanics, which in the early 20th century revolutionised the way we understand matter. Quantum physics was the seed from which many other theories and models emerged and provided insights on the interaction between particles and the effects of external potentials on microscopic systems [3]. On the other hand, during the second half of the 20th century another important step in understanding the physical properties of matter was gained by the advances in nanotechnology [4]. In artificial nanostructures electrons are confined in one, two or three dimensions. When the size of the confinement is large enough to modify the optical, transport and magnetic properties of the system compared to the ones observed in the bulk material, the nanosize structure is subjected to quantum effects. This opens the door to explore scales where the interaction among matter constituents becomes significant. Therefore, the better the understanding of the physical laws present at that scale, the better the tailoring of the physical properties and the subsequent designing of electronic devices. Theoretical studies, although having a smaller impact on commercial applications, constitute a fundamental step for understanding observed phenomena and predicting new ones. Inspired by the recent developments and experiments in the nanoscale regime, in this Thesis previous theoretical models are revised and new models are proposed to calculate, explain and augur physical properties in diverse quantum systems. The low-dimensional systems under study include two-dimensional (2D) systems such as graphene and quantum rings (QRs), one-dimensional (1D) structures like quantum wires (QWs) and zero-dimensional (0D) geometries such as artificial atoms or quantum dots (QDs). Specifically, this work is divided in three distinct areas of research related to fundamental mechanisms that govern the behaviour of particles in the quantum regime. We study different approaches for modelling the interaction with other particles, the effects of external fields on detectable properties of the system and finally, the way that imperfections could modify the particles’ wave function behaviour. Each of these themes is introduced below. The reader will see that the connection of the chapters with the main topics of this Thesis does not follow a chronological scheme because they appear simultaneously along all the work. However, the chapters are self-contained and a full description of their theoretical framework is given at their beginning in order to make them more understandable.