The Impact of Ionic Anharmonicity on Superconductivity in Metal-Stuffed B-C Clathrates

TL;DR

Problem: identify high-$T_c$ superconductors among lightweight metal-stuffed B$-$C clathrates at near-ambient pressure. Approach: incorporate ionic quantum and anharmonic lattice dynamics via stochastic self-consistent harmonic approximation (SSCHA) with attention-centered neural-network potentials, followed by anisotropic Migdal-Eliashberg calculations. Findings: 15 dynamically stable XY$B_6C_6$ compounds are identified; Tc reaches $\approx 102$ K for KRbB$_6$C$_6$ at ambient pressure and $\approx 115$ K for RbB$_3$C$_3$ at 15 GPa, surpassing the anharmonic $T_c$ of KPbB$_6$C$_6$ ($\approx 92$ K). Significance: demonstrates the essential role of anharmonic lattice dynamics in stabilizing lightweight B$-$C clathrates with strong EPC and guides design of high-$T_c$ superconductors under accessible pressures.

Abstract

Metal-stuffed B$-$C compounds with sodalite clathrate structure have captured increasing attention due to their predicted exceptional superconductivity above liquid nitrogen temperature at ambient pressure. However, by neglecting the quantum lattice anharmonicity, the existing studies may result in an incomplete understanding of such a lightweight system. Here, using state-of-the-art ab initio methods incorporating quantum effects and machine learning potentials, we revisit the properties of a series of $XY$$\text{B}_{6}\text{C}_{6}$ clathrates where $X$ and $Y$ are metals. Our findings show that ionic quantum and anharmonic effects can harden the $E_g$ and $E_u$ vibrational modes, enabling the dynamical stability of 15 materials previously considered unstable in the harmonic approximation, including materials with previously unreported ($XY$)$^{1+}$ state, which is demonstrated here to be crucial to reach high critical temperatures. Further calculations based on the anisotropic Migdal-Eliashberg equation demonstrate that the $T_\text{c}$ values for KRb$\text{B}_{6}\text{C}_{6}$ and Rb$\text{B}_{3}\text{C}_{3}$ among these stabilized compounds are 102 and 115 K at 0 and 15 GPa, respectively, both being higher than $T_\text{c}$ of 92 K of KPb$\text{B}_{6}\text{C}_{6}$ at the anharmonic level. These record-high $T_\text{c}$ values, surpassing liquid nitrogen temperatures, emphasize the importance of anharmonic effects in stabilizing B-C clathrates with large electron-phonon coupling strength and advancing the search for high-$T_\text{c}$ superconductivity at (near) ambient pressure.

Figures (4)

• Figure 1: (a) Crystal structure of $XY$$\text{B}_{6}\text{C}_{6}$, where light blue and green spheres represent metal atoms ($X$ and $Y$), and pink and dark blue spheres represent B and C atoms, respectively. (b) Projected electronic density of states (PDOS) for the Cs0_.5Rb0_.5B3C3, K0_.5Pb0_.5B3C3 and Sr0_.75La0_.25B3C3Rb0.4. Vertical lines indicate the Fermi level. (c) The heat map in lower triangle shows the density of states at the Fermi level, $N$($E_{f}$), in units of states$\cdot$eV$^{-1}$$\cdot$$\text{B}_{6}\text{C}_{6}$$^{-1}$ for various $XY$$\text{B}_{6}\text{C}_{6}$ combinations at ambient pressure. Metals $X$ and $Y$ are on the x- and y-axes. The color scale is centered on KPb$\text{B}{_6}\text{C}{_6}$ (yellow star), shown in white. Combinations with higher $N$($E_{f}$) are red, and those with lower values are blue. Black crosses indicate dynamically stable combinations at ambient pressure considering anharmonic effects, and pink hexagons show stability under mild pressure (20 GPa). Black dashed lines separate combinations based on the average valence state of the metals.
• Figure 2: The gray dashed line represents the harmonic spectrum, and the black solid line represents the anharmonic spectrum obtained from the 4-order Hessian matrix, where pink solid circles indicate the electron-phonon coupling strength, with the radius proportional to its strength for (a) RbB$_3$C$_3$ and (b) KRbB$_6$C$_6$. (c) and (d) show the visualized vibrational eigenmodes of the $E_g$ and $E_u$ phonon modes, respectively.
• Figure 3: Projected phonon density of states (PHDOS), Eliashberg spectral function $\alpha^2F(\omega)/\omega$ and integral $\lambda(\omega)$ for (a) KRb$\text{B}_{6}\text{C}_{6}$, (b) CsBa$\text{B}_{6}\text{C}_{6}$, (c) Rb$\text{B}_{3}\text{C}_{3}$, (d) CsPb$\text{B}_{6}\text{C}_{6}$.
• Figure 4: The average valence state of metal atoms, density of states at the Fermi level $N$($E_{f}$), EPC constant $\lambda$, phonon frequency logarithmic average $\omega_{\text{log}}$, and superconducting critical temperature $T_\text{c}$ for $XY$$\text{B}_{6}\text{C}_{6}$ compounds.