Ingredients for enhanced thermoelectric power at cryotemperatures in the correlated semiconductor CoSbS revealed by its optical response

Semiconducting CoSbS is well known for its thermoelectric performance at high temperatures but it is also of interest because of its colossal low-temperature thermopower. Here, we address the temperature dependence of its optical response over a broad spectral range, from which we reveal several ingredients determining the thermoelectric properties at cryotemperatures. We discover coherent phonon modes and with the additional support of scanning transmission electron microscopy investigations we provide evidence for in-gap impurity states driving the formation of correlated electrons in the valence band. Their implications, with respect to the high thermoelectric power at low temperatures, are discussed within the framework of the phonon-drag transport of low-mobility heavy quasiparticles.

Figure 1

Real part ${\sigma }_1\left(\omega \right)$ of the optical conductivity at FIR energy scales ($1\text{eV}=8.06548\times {10}^3{\mathrm{cm}}^{-1}$) at four selected $T$ [21]. The insets show the complete spectrum at 300 K (please note the logarithmic energy scale) and the crystal structure of CoSbS [25].

Figure 2

Enlargement of ${\sigma }_1\left(\omega \right)$ at energies where the sharp absorption onset at about 5000 ${\mathrm{cm}}^{-1}$ takes place for three selected $T$. The intercept of the linear extrapolation (thick dashed lines) of its leading edge with the energy axis defines $E_g$. The inset shows its $T$ dependence. The four harmonic oscillators (HOs), describing the gap edge, are shown at 10 and 300 K [21], thus highlighting the spectral weight [30] reshuffling between and the line-shape narrowing of the Lorentz HOs (L1–L4), pointed out in the text. Reddish and bluish colors refer to 300 and 10 K, respectively. The dotted lines are the total fits at 10 and 300 K [Eq. (S1) in the Supplemental Material (SM) 21], while the gray dashed-dotted line is the $T$-independent contribution given by the additional HOs at high frequencies (Fig. S3 in SM [21]).

Figure 3

(a) Proposal for the DOS evolution when crossing 200 K, with the relevant excitations (arrows) either across $E_g$ or involving the impurity states (see text). The same color code as in (b) allows relating the excitations to their spectral weight (SW) evolution. The thickness of the arrows indeed mimics the $T$ dependence of their relative SW changes (increasing with thickness). (b) $T$ dependence of (total) SW, normalized at 300 K, encountered in selected components of the Lorentz phenomenological fit [30]: Electronic background at FIR energy scales (inset of Fig. S4 in SM [21]), and HOs L1 and L2 as well as L3 and L4 (Fig. 2 and Fig. S3 in SM [21]).

Figure 4

(a) High-resolution STEM image recorded on a HAADF detector with the incident beam along the $\left[001\right]$ direction of the CoSbS single crystal. The image is filtered in frequency space by applying a periodic mask to remove the noise. Scale bar: 1 nm. (b), (c) Magnified images from areas I and II marked by rectangles in (a) are shown in (b) and (c), respectively. Scale bar: 0.5 nm. The $\left[001\right]$ projection of the structure model (right inset of Fig. 1) is embedded in (b) with wine, red, and yellow spheres representing Sb, Co, and S, respectively. Overall, the image intensity of Sb columns in (c) is weaker than that in (b), especially at the atomic positions marked by the white and orange arrows, implying relative changes in the Sb occupancy. The color scale, shown on the right, is used for the intensity of the image in all panels.