Optical Conductivity Measurements of ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$ Under High Pressure: Evidence of a Bandwidth-Controlled Insulator-to-Metal Mott Transition

The optical properties of a ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$ single crystal are investigated under high pressure. At ambient pressure, the optical conductivity exhibits a charge gap of $\approx 0.12\mathrm{eV}$ and a broad midinfrared band at $\approx 0.55\mathrm{eV}$. As pressure is increased, the low energy spectral weight is strongly enhanced and the optical gap is rapidly filled, pointing to an insulator to metal transition around 6 GPa. The overall evolution of the optical conductivity demonstrates that ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$ is a Mott insulator which undergoes a bandwidth-controlled Mott metal-insulator transition under pressure, in remarkably good agreement with theory. With the use of our optical data and ab initio band structure calculations, our results were successfully compared to the ($U/D$, $T/D$) phase diagram predicted by dynamical mean field theory for strongly correlated systems.

Figure 1

(a) Renormalized $R_{\mathrm{sd}}(\omega )$ reflectivity at the sample-diamond interface from 1.6 GPa (lowest) to 10.7 GPa (highest curve), compared to $R_{\mathrm{sd}}^{\mathrm{cal}}(\omega )$ (see text). (b) Pressure-dependent optical conductivity $\sigma (\omega )$ from 1.6 GPa (lowest) to 10.7 GPa (highest curve). The dashed area corresponds to ambient pressure optical conductivity. (c) Spectral weight ${\mathrm{SW}}_{{\Omega }_0}^{\Omega }(P)={\int }_{{\Omega }_0}^{\Omega }\sigma (\omega ,P)d\omega$, integrated between ${\Omega }_0=400{\mathrm{cm}}^{-1}$ and $\Omega$ for various pressures from 0 GPa (lowest) to 10.7 GPa (highest curve). (d) Relative spectral weight $\frac{{\mathrm{SW}}_{{\Omega }_1}^{{\Omega }_2}(P)-{\mathrm{SW}}_{{\Omega }_1}^{{\Omega }_2}(0)}{{\mathrm{SW}}_{{\Omega }_1}^{{\Omega }_2}(0)}$ as a function of pressure, integrated at low energy (${\Omega }_1$, ${\Omega }_2=400$, $1000{\mathrm{cm}}^{-1}$) and high energy (${\Omega }_1$, ${\Omega }_2=2700$, $10000{\mathrm{cm}}^{-1}$). Solid lines are a guide for the eye.

Figure 2

(a) Schematic view of the evolution of the spectral function and of the optical conductivity in a Mott insulator and in a correlated metal on each side of a bandwidth-controlled metal-insulator transition (from Ref. 29). (b) Usual Drude-Lorentz fit of the optical conductivity at 0 and 10.7 GPa. The dashed line corresponds to the pressure-independent high-frequencies contributions. The red area represents the broad midinfrared band at 0 GPa. The Drude peak and the two midinfrared features at $\approx U/2$ and $\approx U$ at 10.7 GPa are shown by green, blue, and red areas, respectively. The thick (gray) solid lines correspond to the fit of the optical conductivity spectra. Fit parameters are listed in Ref. 44.

Figure 3

(a) Calculated band structure around the Fermi level for 0, 5, 7.5, and 10 GPa. For these four pressure values, the half-bandwidth $D$ of the lowest band (band 1) is equal to 0.23, 0.26, 0.29, and 0.335 eV, respectively. (b) Density of states at ambient pressure and 10 GPa.

Figure 4

Theoretical $T/D$, $U/D$ phase diagram for a one-band Mott insulator predicted by the DMFT. Our data points (white circles) on ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$ are positioned using $U=0.55\mathrm{eV}$ (see text) and the half-bandwidth $D$ mentioned in Fig. 3. The colored line below the white circles recalls the behavior revealed by our optical conductivity data: Mott insulator regime (red part) below 6 GPa, followed by a progressive growth of low energy SW (blue part) at higher pressure.