GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons

Abstract

Recent investigations on the Hamiltonian of excitons by F. Schweiner et al. [Phys. Rev. Lett. 118, 046401 (2017)] revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE) or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulae for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.

References in corpus (9)

• Chaotic Dirac billiard in graphene quantum dots
• Giant Rydberg Excitons in Cuprous Oxide
• Observation of high angular momentum excitons in cuprous oxide
• Coulomb-Sturmian basis for the nuclear many-body problem
• High resolution study of the yellow excitons in Cu${}_2$O subject to an electric field
• Magnetoexcitons in cuprous oxide
• Magnetooptical Properties of Rydberg Excitons - Center-of-Mass Quantization Approach
• Magnetoexcitons break antiunitary symmetries
• $K$ dependent exchange interaction of the $1S$ ortho exciton in Cu${}_2$O

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