  Adding a small subdominant quadratic in momentum term to a dominant linear
Dirac dispersion curve affects conduction and valence band differently and
leads to an hourglass-like structure for energy as a function of momentum. This
applies to the protected surface states in topological insulators. The energies
of the conduction and valence band Landau levels are also different and this
leads to the splitting of optical absorption lines produced by the magnetic
field, which acquire a two peak structure. It also changes the peaks in the
imaginary part of the Hall conductivity into two distinct contributions of
opposite signs. The real part of the circularly polarized optical conductivity
however retains its single peak structure but the peaks in right and left
handedness case are shifted in energy with respect to each other in contrast to
the pure Dirac case. The magnitude of the semiclassical cyclotron frequency is
significantly modified by the presence of a mass term as is its variation with
value of the chemical potential $\mu$. Its optical spectral weight is found to
decrease with increasing $\mu$ rather than increase as it does in the pure
Dirac limit.

Mesoscale and Nanoscale Physics;Materials Science;Optics