在開放式彈道量子點中的量子傳輸

Abstract

本論文研究電子在開放式彈道量子點中的傳輸特性。我們探討了電導G與化學位能m 的關係。當電子的化學位能m 為量子點內的共振態(resonant states)時，G會急速的下降或上昇。這些共振態與盒子模型(particle-in-a-box model)估計出來的能階非常接近。這一致性相當出人意料之外，因為此開放式量子點開放端的寬度已是其本身寬度的1/2。但並非所有的共振態為準束縛態(quasibound states)。我們探討了不形成準束縛態的物理原因，並由電子在量子點內的住留時間(dwell time)的分析，洞察到了一些物理的內涵。此外，我們亦研究了時間調變位能對G特性的效應。我們發現了額外的急降結構，此結構與由準束縛態分出來的側能帶(sideband)有關。最後，我們探討了不同結構的開放式量子點的G特性。

We study the transmission of electrons through a ballistic open quantum dot. The dependence of the conductance $G$ on the chemical potential $\mu$ is investigated. Dip as well as Fano-like structures are found in $G$ whenever $\mu$ aligns with the resonant states formed in the dot. The energy levels of these resonant states correspond closely to those estimated from a particle-in-a-box model. This correspondence is surprisingly well even for widely open dots when the opening width is up to $1/2$ of the dot size. Not all resonant levels in the dot give rise to quasibound states, however. The physical origin and implications of these missing quasibound states are investigated. More insights are obtained from analyzing the dwell time of the transmitting particle in the dot. Furthermore, we study the effect of a time-modulated potential on the $G$ characteristics. Additional dip structures which correspond to the sidebands splitted away from the unperturbed quasibound states are found. Finally, we have investigated dots that differ in the configuration of its two openings and the correlations with the $G$ characteristics.