The field dependence of quantized Landau levels on Bi$_{2}$Te$_{3+d}$ via scanning tunneling spectroscopy

Measurements of Landau level (LL) spectra by scanning tunneling spectroscopy can provide important information on quasi-particle lifetime, effective g-factor as well as the dispersion of surface state bands. We have studied the effect of magnetic fields on spatially inhomogeneous samples of the topological insulator Bi$_{2}$Te$_{3+d}$. Using spatial maps of Landau levels as a function of magnetic field, we show that the surface state electrons near the Dirac point are surprisingly sensitive to perturbations. The magnetic field dependence also allows us to obtain an upper limit to the effective g-factor for the surface state electrons.