Nernst Effect in Semimetals: The Effective Mass and the Figure of Merit

We present a study of electric, thermal, and thermoelectric transport in elemental bismuth, which presents a Nernst coefficient much larger than what was found in correlated metals. We argue that this is due to the combination of an exceptionally low carrier density with a very long electronic mean-free path. The low thermomagnetic figure of merit is traced to the lightness of electrons. Heavy-electron semimetals, which keep a metallic behavior in the presence of a magnetic field, emerge as promising candidates for thermomagnetic cooling at low temperatures.

Figure 1

(a) Thermal conductivity, $\kappa$ of the Bi single crystal. Solid line represents a $aT+b{T}^3$ fit (see text). Inset compares the magnitude of $\kappa (3K)$ of the sample of this study (solid circle) with those reported in Ref. 15 (open circles) as a function of mean diameter. (b) Resistivity of the same sample at zero field and in presence of a field of 0.1 T.

Figure 2

The temperature dependence of the absolute value of the Nernst coefficient of the bismuth single crystal for two different orientations of the magnetic field. The solid line represents a linear function $\alpha \mathrm{T}$ with $\alpha =283\frac{{\omega }_c\tau }{{ϵ}_{F}B}=0.38\mathrm{mV}{\mathrm{K}}^{-2}{\mathrm{T}}^{-1}$ (see text and Table ). Both this function and the low-temperature data are displayed in the inset as a $\nu /T$ vs $T$ plot.

Figure 3

The magnitude of the Nernst coefficient in bismuth compared to what is found in some other metals [4, 5, 7, 8, 12].

Figure 4

The Nernst signal (a) and the thermomagnetic figure of merit (b) in Bi and in ${\mathrm{PrFe}}_4{\mathrm{P}}_{12}$ as a function of magnetic field at $T=1.2\mathrm{K}$.