Shot noise in the chaotic-to-regular crossover regime

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.

Current control by resonance decoupling and magnetic focusing in soft-wall billiards

The isolation of energetically persistent scattering pathways from the resonant manifold of an open electron billiard in the deep quantum regime is demonstrated. This enables efficient conductance switching at varying temperature and Fermi velocity, using a weak magnetic field. The effect relies on the interplay between magnetic focusing and soft-wall confinement, which rescale the scattering pathways and decouple quasibound states from the attached leads, the field-free motion being forwardly collimated. The mechanism proves robust against billiard shape variations and qualifies as a nanoelectronic current control element.

Finite frequency quantum noise in an interacting mesoscopic conductor

We present a quantum calculation based on scattering theory of the frequency-dependent noise of current in an interacting chaotic cavity. We include interactions of the electron system via long range Coulomb forces between the conductor and a gate with capacitance C. We obtain explicit results exhibiting the two time scales of the problem, the cavity's dwell time tau(D) and the RC time tau(C) of the cavity in relation to the gate. The noise shows peculiarities at frequencies of the order and exceeding the inverse charge relaxation time tau(-1) = tau(D)(-1) + tau(C)(-1).

Pseudopath semiclassical approximation to transport through open quantum billiards: Dyson equation for diffractive scattering

We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the semiclassical Green's function we develop a diagrammatic expansion that allows a systematic summation over classical and pseudopaths, the latter consisting of classical paths joined by diffractive scatterings ("kinks"). This renders the inclusion of an exponentially proliferating number of pseudopath combinations numerically tractable for both regular and chaotic billiards. For a circular billiard and the Bunimovich stadium the path sum leads to a good agreement with the quantum path length power spectrum up to long path length. Furthermore, we find excellent numerical agreement with experimental studies of quantum scattering in microwave billiards where pseudopaths provide a significant contribution.