Anisotropic optical conductivity of the putative Kondo insulator CeRu${}_4$Sn${}_6$

Kondo insulators and in particular their noncubic representatives have remained poorly understood. Here we report on the development of an anisotropic energy pseudogap in the tetragonal compound CeRu${}_4$Sn${}_6$ employing optical reflectivity measurements in broad frequency and temperature ranges. The low-energy optical conductivity shows semiconductor-like features within the $a$-$a$ plane but a Drude-like response along the $c$ axis, signaling weak metallicity. Local density approximation plus dynamical mean-field theory calculations reproduce these observations qualitatively and help to identify their origin. For large parts of the Brillouin zone, the strongly correlated band structure presents a narrow direct gap within the Kondo resonance. Only for the $c$ direction, due to anisotropy in the hybridization, there is a pronounced band crossing at the Fermi level.

Figure 1

Temperature-dependent electrical resistivity, $\rho \left(T\right)$ (left), and fitted energy gap in units of temperature, $\Delta /k_B$ (right, see text), for single-crystalline CeRu${}_4$Sn${}_6$, with the current density $j$ along the $a$ and $c$ axes. $c^{\prime }$ axis (diagonal of $a$-$a$ plane) data were previously published.[21]

Figure 2

(a,b) Normal-incidence reflectivity spectra of single-crystalline CeRu${}_4$Sn${}_6$ at various temperatures for $E\parallel a$ and $E\parallel c$, respectively. (c,d) Real parts of the optical conductivity, ${\sigma }_1\left(\omega \right)$, for $E\parallel a$ and $E\parallel c$, respectively. The filled circles on the vertical axis represent the independently measured dc conductivity data at the corresponding temperatures. (e,f) Low-energy part of ${\sigma }_1\left(\omega \right)$, with the inset showing semiconductor-like behavior and weak metallicity for $E\parallel a$ and $E\parallel c$, respectively. The sharp features in (c-f) (at 8.9, 15.5, 18.6, 28, and 31.6 meV along the $a$ axis, and at 8.7, 14.4, and 30.9 meV along the $c$ axis) are phonon modes. They are temperature-independent within our resolution ($2{\mathrm{cm}}^{-1}\equiv 0.25\mathrm{meV}$).

Figure 3

Integrated spectral weight of single-crystalline CeRu${}_4$Sn${}_6$ at 6, 100, and 200 K for $E\parallel a$ (a) and $E\parallel c$ (b).

Figure 4

DOS and corresponding $a$ axis ${\sigma }_1\left(\omega \right)$ obtained by LDA (a,b) and LDA+U (c,d). The calculated $c$-axis conductivities are similar (not shown).

Figure 5

LDA+DMFT results: DOS at 290 K (a) and in the low-temperature limit (c), and the corresponding optical conductivities [(b,d) $c$-axis conductivities shifted by $+{10}^3$ ${\Omega }^{-1}$cm${}^{-1}$ for clarity] and $k$-resolved spectra [(e,f) LDA band structure displayed as thin lines], showing a band crossing at the Fermi level for $\Gamma \to X$ ($c$ axis) and a gap in the $a$-$a$ plane.