$J_{\mathrm{eff}}=\frac{3}{2}$ metallic phase and unconventional superconductivity in ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$

By means of density functional theory plus dynamical mean-field theory (DFT $+$ DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled $J_{\mathrm{eff}}=3/2$ insulator ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry $J_{\mathrm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of $J_{\mathrm{eff}}$ at the Ta $L_2$ edge up to 10.4 GPa. Our exact diagonalization-based DFT $+$ DMFT calculations including spin-orbit coupling also reveal that the $J_{\mathrm{eff}}=3/2$ character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of $J_{\mathrm{eff}}=3/2$ moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these $J_{\mathrm{eff}}=3/2$ moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.

Figure 1

(a) Crystal structure of ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$. Red, black, and green spheres represent the Ga, Ta, and Se atoms, respectively. (b) A schematic pressure-temperature phase diagram of ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$. The cyan, green, and red colored regions represent the $J_{\mathrm{eff}}=3/2$ Mott-insulating, metallic, and superconducting phases, respectively. It should be noted that the phase boundary lines have not yet been well identified due to the lack of experimental information. (c) Schematic electronic structure near $E_F$ which is dominated by molecular orbital states of the higher-lying $t_2$ type and the lower-lying $e$ and $a_1$ types. The $t_2$ levels are further split into $J_{\mathrm{eff}}=1/2$ and $3/2$ by SOC. At ambient pressure, the Mott gap is stabilized by the on-site Coulomb interaction $U$.

Figure 2

Calculated phase diagram for ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$ as a function of $U$ and pressure within DFT $+$ DMFT $+$ SOC (at zero temperature). Blue circles, red diamonds, and green triangles represent the calculated points corresponding to the metallic, insulating, and coexistence phases, respectively. The realistic value of $U\approx 0.8$ eV is depicted by a gray arrow.

Figure 3

[(a),(b)] Pressure-dependent RIXS data at the (a) $L_3$ and (b) $L_2$ edges. The different symbols and colors represent different pressure values.

Figure 4

(a)–(c) Calculated spectral functions at (a) $P=0$, (b) 5, and (c) 14.5 GPa. The filled blue and red solid lines represent the molecular $J_{\mathrm{eff}}=3/2$ and $J_{\mathrm{eff}}=1/2$ states, respectively. The dashed magenta and green lines present the $a_1$ and $e$ states, respectively. The arrows connect the center-of-mass positions of the $J_{\mathrm{eff}}=1/2$ and $e$ states.

Figure 5

(a) Calculated renormalization factor $Z$ as a function of pressure. Blue circles (red triangles) show the $Z$ values of the $J_{\mathrm{eff}}=3/2$ ($J_{\mathrm{eff}}=1/2$) bands. [(b),(c)] The calculated exponent $\alpha$ as a function of (b) pressure and (c) electron number. The horizontal red dashed lines show $\alpha =0.5$, namely, the exponent value typically associated with a spin-freezing crossover [37]. The density of electrons $\delta =1$ corresponds to pristine ${\mathrm{GaTa}}_4{\mathrm{Se}}_8$. For the exponent fitting, $J_{\mathrm{H}}/U=0.1$ is used with $U=0.8$ eV.