Parametric Conductance Correlation for Irregularly Shaped Quantum Dots

TL;DR

This paper introduces a conductance peak height autocorrelator as a signature of chaotic electron dynamics in quantum dots, providing analytical results and experimental accessibility for understanding underlying chaos.

Contribution

It derives a universal autocorrelation function for conductance peaks in quantum dots using random matrix theory, including a semiclassical approach for magnetic field effects.

Findings

Analytical autocorrelation function derived for broken time-reversal symmetry.

Universal behavior of the autocorrelation function independent of system details.

Validation through numerical diagonalization of conformal billiard with magnetic flux.

Abstract

We propose the autocorrelator of conductance peak heights as a signature of the underlying chaotic dynamics in quantum dots in the Coulomb blockade regime. This correlation function is directly accessible to experiments and its decay width contains interesting information about the underlying electron dynamics. Analytical results are derived in the framework of random matrix theory in the regime of broken time-reversal symmetry. The final expression, upon rescaling, becomes independent of the details of the system. For the situation when the external parameter is a variable magnetic field, the system-dependent, nonuniversal field scaling factor is obtained by a semiclassical approach. The validity of our findings is confirmed by a comparison with results of an exact numerical diagonalization of the conformal billiard threaded by a magnetic flux line.