Manifestation of Quantum Chaos in Electronic Band Structures

TL;DR

This paper demonstrates that quantum chaos influences the energy spectra of semiconductors, showing universal statistical properties consistent with random matrix theory, and interprets Bloch momenta as tunable parameters affecting quantum chaos signatures.

Contribution

It provides the first analysis of quantum chaos manifestations in real semiconductor band structures using ab initio and tight-binding models, linking them to universal random matrix predictions.

Findings

Energy spectra exhibit statistical properties consistent with quantum chaos.

Bloch momenta act as external parameters influencing spectral correlations.

Results align with universal curves from quantum chaos theory.

Abstract

We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and show that some of their statistical properties obey the universal predictions of quantum chaos derived from the theory of random matrices. Also, the Bloch momenta are interpreted as external, tunable, parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to Aharonov-Bohm fluxes threading a torus. They are used in the investigation of the parametric autocorrelator of crystal velocities. We find that our results are in good agreement with the universal curves recently proposed by Simons and coworkers.