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Origin of anomalous temperature dependence of 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 ($ν$) 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 $ν$. 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 $ν$ 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 $ν$ and $S$ of FeSb$_2$ for which a gigantic phonon-drag effect is observed experimentally.