Origin of anomalous temperature dependence of the Nernst effect in narrow-gap semiconductors

Based on the Boltzmann transport theory, we study the origin of the anomalous temperature dependence of the Nernst coefficient ($\nu$) due to the phonon-drag mechanism. For narrow-gap semiconductors, we find that there are two characteristic temperatures at which a noticeable peak structure appears in $\nu$. Contrarily, the Seebeck coefficient ($S$) always has only one peak. While the breakdown of the Sondheimer cancellation due to the momentum-dependence of the electron relaxation time is essential for the peak in $\nu$ at low $T$, the contribution of the valence band to the phonon-drag current is essential for the peak at higher $T$. By considering this mechanism, we successfully reproduce $\nu$ and $S$ of FeSb$_2$ for which a gigantic phonon-drag effect is observed experimentally.