Simulation of Electron Transport through a Quantum Dot with Soft Walls

TL;DR

This paper numerically explores classical and quantum electron transport in a soft-wall quantum dot, revealing unique resonance behaviors and a close classical-quantum correspondence, while ruling out fractal conductance fluctuations within the studied parameters.

Contribution

It demonstrates the impact of soft-wall boundaries on transport properties and resonance features, highlighting differences from hard-wall quantum dots and analyzing classical-quantum relationships.

Findings

Identification of narrow Fano-shaped transmission resonances.

Close classical-quantum correspondence in scattering features.

No evidence of fractal conductance fluctuations within the studied wave number range.

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 $k_F$ accessible by our simulation we can rule out their existence.