Pressure suppression of unconventional charge-density-wave state in PrRu${}_4$P${}_{12}$ studied by optical conductivity

Optical conductivity [$\sigma \left(\omega \right)$] of PrRu${}_4$P${}_{12}$ has been studied under high pressure to 14 GPa, at low temperatures to 8 K, and at photon energies 12 meV–1.1 eV. The energy gap in $\sigma \left(\omega \right)$ at ambient pressure, caused by a metal-insulator transition due to an unconventional charge-density-wave formation at 63 K, is gradually filled in with increasing pressure to 10 GPa. At 14 GPa and below 30 K, $\sigma \left(\omega \right)$ exhibits a pronounced Drude-type component due to free carriers. This indicates that the initial insulating ground state at zero pressure has been turned into a metallic one at 14 GPa. This is consistent with a previous resistivity study under pressure, where the resistivity rapidly decreased with cooling below 30 K at 14 GPa. The evolution of electronic structure with pressure is discussed in terms of the hybridization between the 4$f$ and conduction electrons.

Figure 1

Optical reflectance relative to diamond [$R_{\mathrm{d}}\left(\omega \right)$] of PrRu${}_4$P${}_{12}$ at several pressures and temperatures. The broken curves indicate the extrapolations discussed in the text. The spectra in (a) were derived from previous data measured at zero external pressure,[3] and those in (b)–(d) were obtained in this work. For the spectra in (b)–(d), the range between 0.235 eV and 0.284 eV has been interpolated with a straight line, as discussed in the text.

Figure 2

Optical conductivity ($\sigma$) of PrRu${}_4$P${}_{12}$ at different pressures and temperatures. For clarity, each spectrum is vertically offset by 500 ${\Omega }^{-1}$ cm${}^{-1}$. The thin curves correspond to the extrapolated portion of $R_{\mathrm{d}}\left(\omega \right)$. The broken curves indicate the results of Drude-Lorentz spectral fitting for the 8 K data discussed in the text.

Figure 3

Optical conductivity ($\sigma$) of PrRu${}_4$P${}_{12}$ at 8 K and at different pressures. The broken portion of the spectra indicates the extrapolated range.

Figure 4

(a) The peak position (${\omega }_0$) and (b) the spectral weight ($S$) of the Lorentz and Drude oscillators, which were obtained from the spectral fitting indicated in Fig. 2, plotted as a function of pressure. L1, L2, and L3 denote the three Lorentz oscillators in Fig. 2.

Figure 5

Effective carrier density $N^{*}\left(\omega \right)$ of PrRu${}_4$P${}_{12}$. Graphs (a)–(d) show the $T$ dependencies at a fixed pressure, while (e) shows the pressure dependence at 8 K. The circles indicate the energy ranges where the $N^{*}\left(\omega \right)$ spectra at different temperatures merge, as discussed in the text. In (d), the 50 K spectrum is not shown since it almost overlaps with the 60 K spectrum.

Figure 6

Schematic illustrations of theoretical predictions in Ref. 12. (a) Phase diagram of PrRu${}_4$P${}_{12}$ in terms of $T$ and the effective crystal field, $\Delta ={\Delta }_0-J+\frac{3}{4}K$. The three horizontal lines indicate the suggested positions of 0, 10, and 14 GPa. (b) Density of states as a function of energy [$D\left(E\right)$] around the Fermi level ($E_{\mathrm{F}}$) at $T=0$ (given by MF theory), at a low but finite $T$ ($0<T<T_{\mathrm{C}}$), and just below $T_{\mathrm{C}}$ ($T⩽T_{\mathrm{C}}$). The horizontal (red) arrow indicates an optical transition for the gap excitation peak in $\sigma \left(\omega \right)$. The original $D\left(E\right)$ in Ref. 12 is asymmetric about $E_{\mathrm{F}}$, but here it is drawn symmetrically for simplicity.