Quantized Landau level spectrum and its density dependence in graphene supported by SiO$_{2}$*

Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a chlorinated thermal SiO$_{2}$ which allowed observing the Landau level sequence characteristic of single layer graphene while tuning the carrier density through the Si back-gate. Upon changing the carrier density we find abrupt jumps in the Fermi level after each Landau level is filled. Moreover, at low doping levels a marked increase in the Fermi velocity is observed which is consistent with the logarithmic divergence expected due to the onset of many body effects close to the Dirac point.