  We propose a characterization tool for studies of the band structure of new
materials promising for the observation of topological phase transitions. We
show that a specific resonant feature in the entropy per electron dependence on
the chemical potential may be considered as a fingerprint of the transition
between topological and trivial insulator phases. The entropy per electron in a
honeycomb two-dimensional crystal of germanene subjected to the external
electric field is obtained from the first principle calculation of the density
of electronic states and the Maxwell relation. We demonstrate that, in
agreement to the recent prediction of the analytical model, strong spikes in
the entropy per particle dependence on the chemical potential appear at low
temperatures. They are observed at the values of the applied bias both below
and above the critical value that corresponds to the transition between the
topological insulator and trivial insulator phases, while the giant resonant
feature in the vicinity of zero chemical potential is strongly suppressed at
the topological transition point, in the low temperature limit. In a wide
energy range, the van Hove singularities in the electronic density of states
manifest themselves as zeros in the entropy per particle dependence on the
chemical potential.
