Static and dynamical properties of elliptic quantum corrals

TL;DR

This paper investigates the static and dynamic behaviors of elliptic quantum corrals, including their response to external perturbations and the effects of impurities, providing insights relevant for experimental comparisons.

Contribution

It offers a detailed analysis of elliptic quantum corrals' properties, including impurity interactions and robustness, using numerical methods for realistic parameters.

Findings

System dynamics involve few excited states, indicating robustness.

Impurities form singlet or triplet states depending on filling, with a dominant single peak in spin dynamics.

Large superexchange J leads to impurity decorrelation similar to Kondo transition.

Abstract

Due to their focalizing properties, elliptic quantum corrals present very interesting physical behaviors. In this work, we analyze static and dynamical properties of these systems. Results are presented for realistic values of the parameters, which might be useful for comparison with experiments. We study noninteracting corrals and their response to several kinds of external perturbations, observing that, for realistic values of the Fermi level, the dynamics involves only a few number of excited states, making the system quite robust with respect to possible sources of decoherence. We also study the system in the presence of two S=1/2 impurities located at its foci, which interact with the electrons of the ellipse via a superexchange interaction J. This system is diagonalized numerically and properties such as the spin gap and spin-spin static and dynamical correlations are studied. We find that, for small J, both spins are locked in a singlet or triplet state, for even or odd filling, respectively, and its spin dynamics consists mainly of a single peak above the spin gap. In this limit, we can define an effective Heisenberg Hamiltonian to describe the low-energy properties. For larger J, more states are involved and the localized spins decorrelate in a manner similar to the Ruderman-Kittel-Kasuya-Yosida-Kondo transition for the two-impurity problem.