Regular and irregular dynamics of Dirac-Weyl wavepackets in a mesoscopic quantum dot at the edge of topological insulator

The dynamics of Dirac-Weyl spin-polarized wavepackets driven by periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It was observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics both in coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince-Strutt diagram for Mathieu equation, and is supported by full quantum mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We found that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in a fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spin-dependent phenomena in nanostructures based on topological insulators.