Simulation of electron transport through a quantum dot with soft walls

Abstract

We numerically investigate classical and quantum transport through a soft-wall cavity with mixed dynamics. Remarkable differences to hard-wall quantum dots are found which are, in part, related to the influence of the hierarchical structure of classical phase space on features of quantum scattering through the device. We find narrow isolated transmission resonances which display asymmetric Fano line shapes. The dependence of the resonance parameters on the lead mode numbers and on the properties of scattering eigenstates are analyzed. Their interpretation is aided by a remarkably close classical-quantum correspondence. We also searched for fractal conductance fluctuations. For the range of wave numbers kF accessible by our simulation we can rule out their existence.

Conductance fluctuations in chaotic bilayer graphene quantum dots

“…To gain a physical understanding of the persistent sharp conductance fluctuations in BGQDs, we analyze the resonance width, the localized states, and the local current patterns. Specifically, the transmission resonance is characterized by Fano profiles [74], where the width of the resonance can be related to the localization of the electronic states [53,57,75,76], leading to sharp conductance fluctuations. In particular, the quantum transport system can be effectively regarded as an isolated quantum dot described by a Hamiltonian matrix H, which is weakly coupled to two leads, one on each side of the dot region.…”

Fano resonances in the conductance of quantum dots with mixed dynamics

“…20 More recently, Fano resonances have also been found in numerical investigations on the influence of a smooth confining potential ͑leading to mixed dynamics͒ on open quantum dots. 21,22 These findings triggered proposals for interesting applications, such as controlling Fano line shapes 23 and using them for the readout of single spins. 24 Given this wealth of theoretical work, why is the experimental observation of Fano line-shape resonances so elusive in open quantum dots?…”

Resonance Eigenfunction Hypothesis for Chaotic Systems

“…For the structure of resonance eigenfunctions some aspects have been studied, e.g. for open billiards [38][39][40][41][42], optical microcavities [43][44][45][46][47][48], potential systems [35], and maps [32,[49][50][51][52][53][54][55][56]. However, there exists no analogue to the semiclassical eigenfunction hypothesis for scattering systems.…”