  Valence band in narrow HgTe quantum wells contains well-conductive Dirac-like
light holes at the $\Gamma$ point and poorly conductive heavy hole subband
located in the local valleys. Here we propose and employ two methods to measure
the density of states for these heavy holes. The first method uses a
gate-recharging technique to measure thermodynamical entropy per particle. As
the Fermi level is tuned with gate voltage from light to heavy subband, the
entropy increases dramatically, and the value of this increase gives an
estimate for the density of states. The second method determines the density of
states for heavy holes indirectly from the gate voltage dependence of the
period of the Shubnikov-de Haas oscillations for light holes. The results
obtained by both methods are in the reasonable agreement with each other. Our
approaches can be applied to measure large effective carrier masses in other
two-dimensional gated systems.
