Pressure suppression of the excitonic insulator state in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ observed by optical conductivity

The layered chalcogenide ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ has recently attracted much interest as a strong candidate for a long-sought excitonic insulator (EI). Since the physical properties of an EI are expected to depend sensitively on the external pressure ($P$), it is important to clarify the $P$ evolution of a microscopic electronic state in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$. Here we report the optical conductivity $\left[\sigma \right(\omega )$] of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ measured at high $P$ to 10 GPa and at low temperatures to 8 K. With cooling at $P=0$, $\sigma \left(\omega \right)$ develops an energy gap of about 0.17 eV and a pronounced excitonic peak at 0.38 eV as reported previously. With increasing $P$, the energy gap becomes narrower and the excitonic peak is diminished. Above a structural transition at $P_s\simeq 3$ GPa, the energy gap becomes partially filled, indicating that ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ is a semimetal after the EI state is suppressed by $P$. At higher $P$, $\sigma \left(\omega \right)$ exhibits metallic characteristics with no energy gap. The detailed $P$ evolution of the energy gap and $\sigma \left(\omega \right)$ is presented, and discussed mainly in terms of a weakening of excitonic correlation with $P$.

Figure 1

Schematic phase diagram of EI in terms of the temperature ($T$) and the one-particle band gap in the absence of $e\text{−}h$ correlation ($E_g$). Positive and negative values of $E_g$ correspond to semiconducting and semimetallic states, respectively. An EI state is expected in the vicinity of $E_g=0$ below the transition temperature ($T_c$), with a characteristic flattening of the band edges as indicated.

Figure 2

Temperature-pressure ($T\text{−}P$) phase diagram of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ after Matsubayashi et al. [23]. $T_c$, $T^{*}$, and $P_s$ indicate the structural transition temperatures and pressure, and $T_{sc}$ the superconducting transition temperature. The green arrows and dots indicate the ($P,T$) paths and points where $\sigma \left(\omega \right)$ was measured in this work.

Figure 3

(a) Optical reflectance $[R_d\left(\omega \right)$] and (b),(c) conductivity $\left[\sigma \right(\omega )$] of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ at 295 K under high pressure ($P$). $R_d\left(\omega \right)$ in the 0.235–0.285 eV range has been interpolated by a straight line since it could not be measured well due to strong absorption by diamond [39]. The arrow in (b) indicates the excitonic peak discussed in the text. In (c), the same spectra as those in (b) are vertically offset, and the broken line emphasizes the shifts and strong suppression of the excitonic peak observed near $P_s=3$ GPa. (d)–(f) $R_d\left(\omega \right)$ of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ measured at $P=2.5$, 3.5, and 6.5 GPa and at different temperatures. (g)–(j) $\sigma \left(\omega \right)$ of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ at $P=0$, 2.5, 3.5, and 6.5 GPa and at low temperatures. The red vertical arrows in (g) and (h) indicate the onset of $\sigma \left(\omega \right)$, and the blue vertical arrow in (i) indicates the Drude component remaining at 8 K. The same temperature labels (the colors of the curves) apply in (d)–(f) and (g)–(j).

Figure 4

Low-energy portion of $\sigma \left(\omega \right)$ in $E\parallel a$ polarization at (a) $P=0$ and (b) $P=2.5$ GPa. The broken lines indicate extrapolations to the linear-in-energy portion of the spectra, and the vertical arrows indicate the onset given by the crossing of the extrapolations with $\sigma \left(\omega \right)=0$. (c) The onset energy in (a) and (b) plotted as a function of temperature ($T$). The curves indicate $\mathrm{\Delta }\left(T\right)=\mathrm{\Delta }\left(0\right)\{1-{(T/T_c)}^{\alpha }\}$ with the indicated values of $\alpha$. $\mathrm{\Delta }\left(0\right)=0.175$ eV and $T_c=328$ K are used for $P=0$, and $\mathrm{\Delta }\left(0\right)=0.062$ eV and $T_c=170$ K for $P=2.5$ GPa. The error bars indicate variations arising from how the extrapolations (straight lines) are drawn to the linear-in-energy portions of $\sigma \left(\omega \right)$ in (a) and (b).

Figure 5

Effective electron number $N^{*}\left(\omega \right)$ per formula unit (f.u.) of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$, calculated with Eq. (1) and the measured $\sigma \left(\omega \right)$ spectra at different pressures and temperatures.