Unconventional dynamics of electrons in topological insulators in a magnetic field: Berry phase effects

The semiclassical dynamics of charge carriers moving over the surface of a Bi$_2$Te$_3$-type 3D topological insulator in a static magnetic field is studied. The effects related to the changes in the symmetry of constant energy surfaces (contours), as well as to the nonzero Berry curvature, are taken into account. It is shown that effects related both to the anomalous velocity proportional to the Berry curvature and to the distortions of the trajectories stemming from the additional contribution to the energy proportional the orbital magnetic moment of a wave packet appear in contrast to the conventional dynamics of electrons moving in a uniform static magnetic field along trajectories determined by the conditions $E(k)=\text{const}$ and $p_z=\text{const}$. This should lead to changes in the cyclotron resonance conditions for surface electrons. Although the magnetic field breaks the time-reversal symmetry and the topological order, the studies of the cyclotron resonance allow finding out whether a given insulator is a trivial one or not in zero magnetic field.