Quantum Chaos in Disordered Two-Dimensional Nanostructures

Chaos is ubiquitous and plays an important part in most fields of science. On the classical side, it is widely acknowledged that dynamics is difficult to predict due to chaos. However, on the quantum side, we can push the limit further by employing quantum coherence for our benefit. A quantum scar is a striking visual manifestation of quantum mechanical suppression of classical chaos: the condensation of the probability density in the vicinity of unstable classical periodic orbits.

This Thesis presents a self-contained introduction to a new class of quantum scarring discovered in disordered nanostructures. Counterintuitively, adding randomly scattered perturbations can actually reveal hidden (classical) regularities in a quantum system. In this pertubation-induced scarring, some of the high-energy states of a perturbed system are strongly scarred by the periodic orbits of the unperturbed counterpart. Interestingly, this type of scarring is characteristic for disordered nanostructures. This fact is further supported by the physical scarring mechanism presented in the Thesis. Furthermore, the studied scarring phenomenon sheds light upon understanding the fundamental disconnection posed by reconciling quantum formalism with the classical concept of chaos. Several quantum measures, including both conventional and modern statistical methods, have shown that the scarring is connected to the suppression of chaos in eigenvalue statistics.

From the point of view of future nanoelectronics, the results presented in this Thesis provide insights into the physics of disordered nanostructures. In particularly, it has been shown that the existence, geometry and orientation of perturbationinduced scars can be controlled with experimentally feasible schemes. Together, these properties could lead to a new field of “scartronics”, where the local conductance of a nanoscale system is modulated by inducing and manipulating scarred states.