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Evidence for massive bulk Dirac Fermions in Pb$_{1-x}$Sn$_x$Se from Nernst and thermopower experiments

The lead chalcogenides (Pb,Sn)Te and (Pb,Sn)Se are the first examples of topological crystalline insulators (TCI) predicted \cite{Fu,Hsieh} (and confirmed \cite{Hasan,Story,Takahashi}) to display topological surface Dirac states (SDS) that are protected by mirror symmetry. A starting premise \cite{Hsieh} is that the SDS arise from bulk states describable as massive Dirac states \cite{Wallis,Svane}, but this assumption is untested. Here we show that the thermoelectric response of the bulk states display features specific to the Dirac spectrum. We show that, in the quantum limit, the lowest Landau Level (LL) is singly spin-degenerate, whereas higher levels are doubly degenerate. The abrupt change in spin degeneracy leads to a large step-decrease in the thermopower $S_{xx}$. In the lowest LL, $S_{xx}$ displays a striking linear increase vs. magnetic field. In addition, the Nernst signal undergoes an anomalous sign change when the bulk gap inverts at 180 K.