Crystal size effects on giant thermopower in ${\mathrm{CrSb}}_2$

We have examined size effect on thermal, transport, and thermodynamic properties of a ${\mathrm{CrSb}}_2$ single crystal. We demonstrate highly anisotropic quasi-one-dimensional electrical conductivity, quasiballistic phonons, and giant thermopower of $-6$ mV/K at 15 K. A thermopower peak is suppressed to $-1.6$ mV/K by changing crystal dimensions and shows linear dependence on the phonon mean-free path. Whereas electronic diffusion thermopower is significant, the bulk of the giant thermopower in ${\mathrm{CrSb}}_2$ stems from the coupling of the very long mean-free path phonons with the in-gap states.

Figure 1

Size dependence of the thermal transport properties: (a) thermal conductivity $\kappa$ and (b) thermopower $S$ for thermal gradient along the $b$ axis. Both $S$ and $\kappa$ show strong size dependence. (c) and (d) $\kappa$ and $S$ along different crystal axes in 0 and 9 T magnetic field. Note that anisotropy in $S\left(T\right)$ and $\kappa \left(T\right)$ are similar.

Figure 2

(a) and (b) Temperature dependence of the electrical resistivity for S1 with current along all three principal crystallographic axes. Note the two orders of magnitude higher conductivity when $I//c$ axis. Different regions of activated transport are noted in (b). (c) Hall effect measured at several different temperatures. The open symbols show the data and the black lines show the linear fit. (d) Heat capacity of ${\mathrm{CrSb}}_2$ crystal and (e) Debye model fits in the low temperature range. (f) Phonon mean-free paths vs temperature below 20 K. When compared to about 1 nm at 15 K and 7 nm at 40 and 80 K electron mean-free path, the phonon MFPs are much longer. Dotted lines represent the crystal surface-dominated mean-free path $l_b$ for each sample. Inset shows sample shape.

Figure 3

Temperature dependence of the thermal conductivity in low temperature. (a) and (b) The fitting of $\kappa /T$ vs $T^2$ and $\kappa$ vs $T$. The solid lines are fitting results. (a) and (b) share the same legend. (c) Thermal conductivity below 50 K. The solid lines are fitting of Callaway model.

Figure 4

(a) Density of states (red) and electron density (blue) as a function of energy. The inset shows the energy range corresponding to the measured carrier densities. (b) Electronic band dispersion showing the chemical potential corresponding to the measured carrier densities. The Fermi energy has been set to zero. The red and green spots represent the minimum of conduction band and maximum of valence band, respectively.

Figure 5

(a) and (b) Phonon thermopower values for crystals S1–S6 as a function of the phonon mean-free paths at the corresponding temperatures. The solid line is the linear fitting of the data revealing the linear dependence of $S$ on the phonon MFPs. (c) Magnetoresistance and Hall coefficient ${\mathrm{R}}_H$ vs temperature below 60 K.