Manifestation of Quantum Chaos in Electronic Band Structures

Details Manifestation of Quantum Chaos in Electronic Band Structures Manifestation of Quantum Chaos in Electronic Band Structures

1994-04-05

arxiv.org/abs/cond-mat/9404005v1

Physics

Condensed Matter

15 pages with 6 Postscript figures included, RevTex-3, CMT-ERM/9401

Scientific paper

10.1103/PhysRevB.50.8245

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.

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