Mass acquisition of Dirac fermions in the presence of magnetic doping in the topological insulator Sb$_{2}$Te$_{3}$

The nontrivial bulk band topology and time reversal symmetry yield gapless surface states in three dimensional topological insulators. The gapless nature of surface states in strong topological insulator is predicted to be violated by time-reversal-symmetry breaking perturbations, which opens back-scattering channels between Kramers pairs and induces a massive gap near the Dirac point of surface states. Such a massive Dirac fermion system gives rise to an unconventional magnetoelectric response relating to many exotic phenomena such as half-quantized anomalous Hall effect, topological quantized magnetoelectric effect and even the magnetic monopole. Here we introduce time-reversal-symmetry breaking by doping Cr atoms into the topmost quintuple layer or into the bulk of Sb$_{2}$Te$_{3}$ thin films. We demonstrate for the first time by Landau level spectroscopy the deviation of zero modes, which indicates the acquirement of a mass term in the presence of surface or bulk magnetic doping. We also show that the magnitude of the mass term in the surface states depends on both the Cr doping level and the magnetic field, offering a new way of measuring the doping- and field-dependence of local magnetization of dopants. Our observation suggests Cr-doped Sb$_{2}$Te$_{3}$ is a promising candidate for realization of proposed novel magnetoelectric effects.