Cyclotron resonance in topological insulators: non-relativistic effects
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The low-energy Hamiltonian used to describe the dynamics of the helical Dirac
fermions on the surface of a topological insulator contains a subdominant
non-relativistic (Schr\"odinger) contribution. This term can have an important
effect on some properties while having no effect on others. The Hall plateaus
retain the same relativistic quantization as the pure Dirac case. The height of
the universal interband background conductivity is unaltered, but its onset is
changed. However, the non-relativistic term leads directly to particle-hole
asymmetry. It also splits the interband magneto-optical lines into doublets.
Here, we find that, while the shape of the semiclassical cyclotron resonance
line is unaltered, the cyclotron frequency and its optical spectral weight are
changed. There are significant differences in both of these quantities for a
fixed value of chemical potential or fixed doping away from charge neutrality
depending on whether the Fermi energy lies in the valence or conduction band.