The transverse Nernst Ettingshausen (N-E) effect and electron mobility in Pb$_{1-x}$Sn$_x$Se alloys are studied experimentally and theoretically as functions of temperature and chemical composition in the vicinity of vanishing energy gap $E_g$. The study is motivated by the recent discovery that, by lowering the temperature, one can change the band ordering from trivial to nontrivial one in which the topological crystalline insulator states appear at the surface. Our work presents several new aspects. It is shown experimentally and theoretically that the bulk N-E effect has a maximum when the energy gap $E_g$ of the mixed crystal goes through zero value. This result contradicts the claim made in the literature that the N-E effect changes sign when the gap vanishes. We successfully describe $dc$ transport effects in the situation of extreme bands nonparabolicity which, to the best of our knowledge, has never been tried before. A situation is reached in which both two-dimensional bands (topological surface states) and three-dimensional bands are linear in electron textbf{k} vector. Various scattering modes and their contribution to transport phenomena in Pb$_{1-x}$Sn$_x$Se are analyzed. As the energy gap goes through zero, some transport integrals have a singular (nonphysical) behaviour and we demonstrate how to deal with this problem by introducing damping.
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