Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights

TL;DR

This paper investigates how the internal chaotic dynamics of quantum dots influence Coulomb blockade peak heights, revealing that chaos modulates these peaks and differs from purely random wavefunction assumptions.

Contribution

It demonstrates that internal dynamics modulate Coulomb blockade peaks, challenging the assumption of complete randomness and providing semiclassical analysis for chaotic and integrable dots.

Findings

Chaos modulates Coulomb blockade peaks.

Semiclassical results align with numerical calculations.

Experimental observations may already reflect this modulation.

Abstract

The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in this case the conductance has a peak. In a small grain with quantized electron states, referred to as a quantum dot, the magnitude of the conductance peak is directly related to the magnitude of the wavefunction near the contacts to the dot. Since dots are generally irregular in shape, the dynamics of the electrons is chaotic, and the characteristics of Coulomb blockade peaks reflects those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random. Here we show that the specific internal dynamics of the dot, even though it is chaotic, modulates the peaks: because all systems have short-time features, chaos is not equivalent to randomness. Semiclassical results are derived for both chaotic and integrable dots, which are surprisingly similar, and compared to numerical calculations. We argue that this modulation, though unappreciated, has already been seen in experiments.