This grant supports theoretical research on transport through semiconductor quantum dots in the mesoscopic regime. The systems under consideration are small enough that quantum interference and the finite dwell time of the electrons play an important role, while they are big enough, and with irregular shape, so that the (classical) dynamics is chaotic and statistical methods, such as random matrix theory, need to be used to describe a sample, or an ensemble of samples.
The research consists of two parts: time-dependent transport and the interference of resonant and non-resonant paths through quantum dots. A unifying theme of both parts is the interplay of chaotic dynamics, quantum interference, and electron-electron interactions. The primary focus of the research is how, in quantum dots, electron-electron interactions manifest themselves through Coulomb blockade and dephasing.
The first part of the grant is centered around the adiabatic quantum electron pump which has recently been realized experimentally. The idea is that if any two parameters of a (quantum mechanical) system are varied, a d.c. current will flow through it. In the experiment, the parameters that are varied are gate voltages that control the shape of the quantum dot. In this case, one can show that the pumped current is entirely of a quantum interference nature, hence the name quantum pump. The current flow is in a random direction, set by microscopic details of the dot. Basic aspects of the experiment can be understood from a simple scattering matrix formula. The research to be done here is aimed at improvement in our understanding of the experiment (effect of dephasing), and to prediction of properties (relationship between voltage and current, which appears not to be given by the dot's conductance), through a more detailed analysis and extension of the scattering matrix formula, as well as entering new directions by inclusion of electronic interactions (Coulomb blockade) into formalism for time-dependent transport.
The second part of the research is about interference of direct transmitting and resonant paths through a quantum dot. This interference gives rise to Fano resonances in the transmission through the dot. Fano resonances have been observed recently and are described by a resonance width and by a complex Fano parameter q. Both the resonance width and q vary randomly from resonance to resonance. This research aims at a calculation of the distribution of q for a chaotic quantum dot. Further possible activities include the study of the interplay and mutual connection of Coulomb blockade, direct transmitting paths, dephasing, and the Kondo effect, which all occur in one and the same system. %%% This grant supports theoretical research on transport through semiconductor quantum dots in the mesoscopic regime. This area of research is related to the current interest in nanotechnology. The systems under consideration are small enough that quantum interference and the finite dwell time of the electrons play an important role, while they are big enough, and with irregular shape, so that the (classical) dynamics is chaotic and statistical methods, such as random matrix theory, need to be used to describe a sample, or an ensemble of samples.
The research consists of two parts: time-dependent transport, and the interference of resonant and non-resonant paths through quantum dots. A unifying theme of both parts is the interplay of chaotic dynamics, quantum interference, and electron-electron interactions. The primary focus of the research is how, in quantum dots, electron-electron interactions manifest themselves through Coulomb blockade and dephasing. While the research is of a fundamental scientifc nature, the results will also be of great interest to those interested in constructing nanoscale devices. ***
