Guest metal-driven quantum anharmonic effects on stability and two-gap superconductivity in carbon-boron clathrates

Abstract

Traditionally, strong quantum anharmonic effects have been considered a characteristic of hydrogen-rich compounds. Here we propose that these effects also play a decisive role in boron-carbon clathrates. The stability and superconducting transition temperature (Tc) of carbon-boron clathrates XYB6C6, whose metal atoms have an average oxidation state of +1.5, have long remained under debate. At this oxidation state, some combinations (e.g., RbSrB6C6) are dynamically stable, whereas others (e.g., RbPbB6C6) are not. Using the stochastic self-consistent harmonic approximation combined with machine learning, we find that the anharmonicity originates primarily from guest metal atoms. For comparison, we find that quantum fluctuations have negligible influence on SrB3C3, but remove the lattice instability of RbPbB6C6. The predicted Tc of RbPbB6C6 (88 K) is nearly twice that of SrB3C3. Moreover, RbPbB6C6 exhibits two-gap superconductivity due to the higher C/B ratio in the density of states at the Fermi level compared to SrB3C3, weakening the sp3 hybridization. These findings demonstrate that quantum anharmonicity crucially governs the stability and superconductivity of XYB6C6 clathrates.

Figures (5)

• Figure 1: Crystal structures for (a) SrB$_3$C$_3$ and (b) RbPbB$_6$C$_6$. The atoms are represented by silver, orange, red, green, and brown spheres, corresponding to Sr, Rb, Pb, B, and C, respectively.
• Figure 2: The band structure and projected density of states for (a) SrB$_3$C$_3$ and (b) RbPbB$_6$C$_6$. In band structures, multiple bands dominated by nonmetal atoms that intersect with the Fermi level ($E_\text{F}$ = 0 eV) are marked with different colors.
• Figure 3: Harmonic and anharmonic phonon properties and EPC of SrB$_3$C$_3$. (a) Harmonic phonon spectrum with $\lambda_{q\nu}$. (b) Anharmonic phonon spectrum with $\lambda_{q\nu}$. The color mapping from blue to red in panels (a) and (b) represents the magnitude of $\lambda_{q\nu}$ for each phonon mode, with red indicating the highest values. (c) Harmonic and anharmonic phonon density of states (PHDOS). (d) Projected PHDOS on Sr, B, and C atoms in the anharmonic framework. (e) Eliashberg spectral function $\alpha^2F(\omega)$ and cumulative EPC constant $\lambda(\omega)$. Double-degenerate $E_g$ modes at the $\Gamma$ point in (f) harmonic and (g) anharmonic frameworks. Displacements are shown by red and light blue arrows for the harmonic and anharmonic frameworks, respectively. (h) Momentum-resolved EPC strength $\lambda_{nk}$ on the Fermi surface. (i) Superconducting gap $\Delta_{nk}$ on the Fermi surface at 10 K. (j) Temperature dependence of the superconducting gap $\Delta$. (k) Superconducting density of states (SDOS) at 10 K.
• Figure 4: Anharmonic phonon properties and EPC of RbPbB$_6$C$_6$. (a) Phonon spectrum. The color map from blue to red represents the magnitude of $\lambda_{q\nu}$ for each phonon mode, with red denoting the highest coupling strengths. (b) Phonon density of states projected on Rb, Pb and the combined B+C atoms, Eliashberg spectral function $\alpha^2F(\omega)$, and integrated EPC strength $\lambda(\omega)$ in the anharmonic framework.
• Figure 5: Temperature dependence of the superconducting gap $\Delta$ for RbPbB6C6, obtained by solving the anisotropic Migdal-Eliashberg equation at $\mu^* = 0.1$. The inset shows the band- and momentum-resolved superconducting gap $\Delta_{nk}$ on the Fermi surface at 10 K, with the color scale indicating $\Delta_{nk}$ values ranging from 15.72 meV (blue) to 20.45 meV (red).