Capacitance spectroscopy of a system of gapless Dirac fermions in a HgTe quantum well

Information on the density of states of two-dimensional Dirac fermions in a $6.6$-nm-thick HgTe quantum well that corresponds to a transition from the direct to inverted spectrum is obtained for the first time by means of capacitance measurements. It is found that the density of states of Dirac electrons is a linear function of the Fermi energy at $E_{\mathrm{F}}>30$ meV with the corresponding velocity $\mathrm{vDF} = 8.2 \times 10^5$ m/s. At lower energies, this dependence deviates from the linear law, indicating a strong effect of disorder, which is associated with fluctuations of a built-in charge, on the density of states of the studied system near the Dirac point. At negative energies, a sharp increase in the density of states is observed, which is associated with the tail of the density of states of valleys of heavy holes. The described behavior is in agreement with the proposed model, which includes both the features of the real spectrum of Dirac fermions and the effect of the fluctuation potential.