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An experimental study of Landau levels (LLs) in a system of two-dimensionalmassless Dirac fermions based on a critical thickness HgTe quantum well hasbeen carried out. The magnetotransport and the capacitive response have beeninvestigated simultaneously. It is shown that the formation of Shubnikov-deHaas (SdH) oscillations associated with odd v filling factors occurs in amagnetic field whose strength grows monotonically with v. This behavior isconsistent with calculations of the electron spectrum, which predicts adecrease in cyclotron gaps with increasing v. Oscillations with even fillingfactors, corresponding to spin gaps, behave less trivially. First, the SdHoscillations with filling factors of 4 and higher are resolved in a magneticfield that is 2-2.5 times smaller than the field required to resolveneighboring SdH oscillations with odd filling factors of 3 and higher. Thisindicates a significant increase in the size of the spin gap caused by aninterface inversion asymmetry (IIA) leading to Dirac cone splitting in a zeromagnetic field. Using the spin splitting value gamma as a fitting parameter, weobtained the best agreement between experimental data and calculations atgamma=1.5 meV. Next, spin splitting for the zeroth and first LLs is observed in2-3 times stronger magnetic fields than for the other levels, indicating anincrease in disorder near the Dirac point, due to the lack of screening.

Spin Splitting and Disorder in HgTe-Based Massless Dirac Fermion Landau Levels