  When a static electrical field is applied to a two-dimensional (2D) Dirac
material, Landau-Zener transition (LZT) and Bloch-Zener oscillations can occur.
Employing alpha-T3 lattices as a paradigm for a broad class of 2D Dirac
materials, we uncover two phenomena. First, due to the arbitrarily small energy
gaps near a Dirac point that make it more likely for LZTs to occur than in
other regions of the Brillouin zone, the distribution of differential LZT
probability in the momentum space can form a complicated morphological pattern.
Second, a change in the LZT morphology as induced by a mutual switching of the
two distinct Dirac points can lead to irregular Bloch-Zener oscillations
characterized by a non-smooth behavior in the time evolution of the electrical
current density associated with the oscillation. These phenomena are due to
mixed interference of quantum states in multiple bands modulated by the
geometric and dynamic phases. We demonstrate that the adiabatic-impulse model
describing Landau-Zener-Stuckelberg interferometry can be exploited to
calculate the phases, due to the equivalence between the alpha-T3 lattice
subject to a constant electrical field and strongly periodically driven two- or
three-level systems. The degree of irregularity of Bloch-Zener oscillations can
be harnessed by selecting the morphology pattern, which is potentially
experimentally realizable.
