Research Projects

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Research conducted by: Steven Tomsovic,Nicholas Cerruti, Evgenii Narimanov (Bell Laboratories--Lucent Technologies), Harold Baranger (Duke University)

Introduction

The electrostatic energy of an additional electron on a quantum dot -- a mesoscopic island of confined charge with quantized states -- blocks the flow of current through the dot, an effect known as the Coulomb blockade. Current can flow only if two different charge states of the quantum dot are tuned to have the same energy; this produces a peak in the conductance of the dot whose magnitude 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 reflect those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random and uncorrelated with each other.

Our work

We developed a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that the dynamics in the dot leads to a large modulation of the peak height. The corrections to the standard statistical theory of peak height distributions, power spectra, and correlation functions are non-universal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The resulting correlation function oscillates as a function of peak number in a way defined by such orbits; in addition, the correlation of adjacent conductance peaks is enhanced. Both of these effects are in agreement with recent experiments.

Figures

The peak conductance from tunneling through subsequent energy levels for the stadium billiard shown in the inset. Each peak is placed at the wavevector k corresponding to its level; R is the radius of the half-circle parts of the stadium. A Gaussian lead wavefunction appropriate for tunneling from a single transverse mode is used.