  An experimental study of Landau levels (LLs) in a system of two-dimensional
massless Dirac fermions based on a critical thickness HgTe quantum well has
been carried out. The magnetotransport and the capacitive response have been
investigated simultaneously. It is shown that the formation of Shubnikov-de
Haas (SdH) oscillations associated with odd v filling factors occurs in a
magnetic field whose strength grows monotonically with v. This behavior is
consistent with calculations of the electron spectrum, which predicts a
decrease in cyclotron gaps with increasing v. Oscillations with even filling
factors, corresponding to spin gaps, behave less trivially. First, the SdH
oscillations with filling factors of 4 and higher are resolved in a magnetic
field that is 2-2.5 times smaller than the field required to resolve
neighboring SdH oscillations with odd filling factors of 3 and higher. This
indicates a significant increase in the size of the spin gap caused by an
interface inversion asymmetry (IIA) leading to Dirac cone splitting in a zero
magnetic field. Using the spin splitting value gamma as a fitting parameter, we
obtained the best agreement between experimental data and calculations at
gamma=1.5 meV. Next, spin splitting for the zeroth and first LLs is observed in
2-3 times stronger magnetic fields than for the other levels, indicating an
increase in disorder near the Dirac point, due to the lack of screening.
