  We address the problem of hybridization between topological surface states
and a non-topological flat bulk band. Our model, being a mixture of
three-dimensional Bernevig-Hughes-Zhang and two-dimensional pseudospin-1
Hamiltonian, allows explicit treatment of the topological surface state
evolution by continuously changing the hybridization between the inverted bands
and an additional "parasitic" flat band in the bulk. We show that the
hybridization with a flat band lying below the edge of conduction band converts
the initial Dirac-like surface states into a branch below and one above the
flat band. Our results univocally demonstrate that the upper branch of the
topological surface states is formed by Dyakonov-Khaetskii surface states known
for HgTe since the 1980s. Additionally we explore an evolution of the surface
states and the arising of Fermi arcs in Dirac semimetals when the flat band
crosses the conduction band.
