Open quantum dots in graphene: Scaling relativistic pointer states

Relativistic quantum chaos-An emergent interdisciplinary field

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Conductance stability in chaotic and integrable quantum dots with random impurities

For a quantum dot system of fixed geometry, in the presence of random impurities the average conductance over an appropriate range of the Fermi energy decreases as the impurity strength is increased. Can the nature of the corresponding classical dynamics in the dot region affect the rate of decrease? Utilizing graphene quantum dots with two semi-infinite, single-mode leads as a prototypical model, we address the device stability issue by investigating the combined effects of classical dynamics and impurities on the average conductance over the energy range of the first transverse mode. We find that, for chaotic dot systems, the rate of decrease in the average conductance with the impurity strength is in general characteristically smaller than that for integrable dots. We develop a semiclassical analysis for the phenomenon and also obtain an understanding based on the random matrix theory. Our results demonstrate that classical chaos can generally lead to a stronger stability in the device performance, strongly advocating exploiting chaos in the development of nanoscale quantum transport devices.

Effect of geometrical rotation on conductance fluctuations in graphene quantum dots

Conductance fluctuations are ubiquitous in quantum transport through nanoscale devices, and how to modulate or control the fluctuation patterns is of considerable interest. We use two-terminal graphene devices as a prototypical system and articulate a scheme based on geometrical rotation of the device to effectively modulate the conductance fluctuations. To facilitate a systematic calculation of the conductance as a function of the Fermi energy and the rotation angle, we use a layer-by-layer based, recursive non-equilibrium Green's function approach, which is demonstrated to be computationally extremely efficient. Our study indicates that relative rotation of the device, which is experimentally feasible, can markedly affect the degree of conductance fluctuations, and we provide physical explanations of this behavior based on the emergence of edge states.