Quantum chaos in nanoelectromechanical systems

TL;DR

This paper theoretically investigates quantum chaos in nanoelectromechanical systems by analyzing electron-phonon interactions and spectral statistics, revealing conditions under which GOE or GUE distributions emerge, including an unusual GUE case in time-reversal invariant systems.

Contribution

It demonstrates the emergence of quantum chaos in NEMS through spectral analysis, highlighting the role of geometry and boundary conditions in spectral statistics.

Findings

Spectral fluctuations follow GOE or GUE distributions.

GUE statistics occur only with a circular quantum dot.

Quantum chaos is observed across various material and geometric parameters.

Abstract

We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems (NEMS) and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian Orthogonal Ensemble (GOE) or the Gaussian Unitary Ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.