Magnetoexcitons Break Antiunitary Symmetries

We show analytically and numerically that the application of an external magnetic field to highly excited Rydberg excitons breaks all antiunitary symmetries in the system. Only by considering the complete valence band structure of a direct-band-gap cubic semiconductor, the Hamiltonian of excitons leads to the statistics of a Gaussian unitary ensemble without the need for interactions with other quasiparticles like phonons. Hence, we give theoretical evidence for a spatially homogeneous system breaking all antiunitary symmetries.

Figure 1

Cumulative distribution function $F(s)$ for increasing values of ${\delta }^{\prime }$, with $\mathit{B}(\phi ,\vartheta )=\mathit{B}(\pi /6,\pi /6)$ and $B=3\text{T}$. Besides the numerical data (red dots), we also show the corresponding functions of a Poissonian ensemble (black dash-dotted line), GOE (blue dashed line), and GUE (green solid line). For increasing values of ${\delta }^{\prime }$, the statistics rapidly change to the one of a Gaussian unitary ensemble (d). Note that we do not show the hydrogenlike case ${\delta }^{\prime }=0$ since we simply obtain the transitional form between Poissonian and GOE statistics and since this system is sufficiently well known from literature (see, e.g., Refs. [1, 22, 23] and further references therein).

Figure 2

Cumulative distribution function $F(s)$ for ${\delta }^{\prime }=-0.15$, with $\mathit{B}(\phi ,\vartheta )=\mathit{B}(0,\pi /6)$ and $B=3\text{T}$. Since $\mathit{B}$ is oriented in one of the symmetry planes of the lattice, only GOE statistics can be observed when neglecting phonons.