Transport phenomena in quantum wells and wires in presence of disorder and interactions

Abstract: Popular Abstract in Undetermined All of our present information technology culture with computers, internet, smart-phones, Bluetooth links, 3D-Tv, iPad tablets, programmable washing/cooking machines, car engines, navigation computers, etc. (the list goes on and on) is based on small electrical circuits. The smaller these circuits can be made, the faster and the better microelectronics can perform. There is much more round the corner: nano-chip technology could soon dim the boundary between living and non-living entities, and perhaps even between us and what is just outside our body: the external world. Some of our capabilities could be improved or fully regained from deficit situations (think of people recovering neural abilities, improving their eyesight, using cyber-prostethics, having real-time monitoring of non-perfect vital functions, etc.) It is fair to say that some of these developments could impel us to deal with novel bio-ethical conflicts (voices of concern exist already), but science has forced us before to face dilemmas of this sort. Past experience over the last few millennia shows that each time humanity has made a great discovery (e.g. the fire, the wheel, the printing press, the steam engine, the electricity, penicillin, the transistor, internet) the subsequent technological evolution has always proceeded in one direction: forward. Regaining a more down-to-earth perspective, present-day electrical circuits have reached such small dimensions that the laws of physics which govern the microscopic world, called quantum mechanics, are becoming center-stage. Even within the status-quo of technological development (we refer to it as "nanoelec- tronics"), it is becoming increasingly important to have a basic understanding of how small systems with a finite number of atoms and electrons behave when subjected to perturbing agents, for example by electric current passing through them. The knowledge we have of such systems relies, first and foremost, on elaborate and careful experiments. However, experimental data can be difficult to interpret, because even such small systems are in-fact many-particle systems. The analysis can be (and usually is) further complicated by the fact that samples are "disor- dered", i.e. we have incomplete knowledge and control of the kind of atoms and their positions in the sample. In principle, theoretical research can contribute significantly to this endeavor, by answering a number of important questions. In practice, often a major obstacle is the lack of accurate theoretical information on how interactions among particles and disorder affect the results. This thesis is about research work in this direction, namely theoretical investi- gations of the electric current in different nano-structures. We have analyzed quan- tum wells (layered slices of semiconductors), and quantum wires (one-dimensional conducting aggregates of atoms). Both are man-made artificial structures where, as their name suggests, quantum effect play an important role in the current trans-mission. These systems have great potential for technological breakthroughs. We have employed rather different theoretical techniques, aimed to look directly into the behavior of the current in the steady-state (where the current does not change in time), or to follow how the current changes in time to reach such steady state. We have used the Boltzmann’s equation, a method with a long and eminent ser- vice record in physics, but also a rather new approach (called "density functional theory"), which uses the total electron density as a basic but only variable and therefore requires significantly less computing power than traditional methods. In the end, the actual common denominator to the different parts of our thesis work is the presence of disorder in our systems. Disorder is ubiquitous in nature: in fact, in many instances, the notion of order corresponds more to our need for simple conceptualizations of reality, than to reality itself (that is, in most cases, in nature, order exists only in an approximate way). Nanoscale systems are no exception and, in fact, the effects of disorder are expected to be strong in these small systems. From the outside, and especially to the eye of the professional physicist, these considerations can seem a rather tenuous link to thread together somewhat differ- ent subjects, systems and methodologies in the same thesis. For us, who worked on these topics for several years, this thesis is a confirmation that, as life itself, scientific research is often made of pieces whose mutual connection is not imme- diately apparent, and that, in the end, there is beauty in all different parts of Physics.