Single layer clathrane: A potential superconducting two-dimensional (2D) hydrogenated metal borocarbide

Abstract

We propose a new family of two-dimensional (2D) metal-borocarbide clathrane superconductors, derived from three-dimensional (3D) MM$^\prime$B$_6$C$_6$ clathrates. First-principles calculations reveal that hydrogen passivation and surface metal decoration stabilize the M$_2$M$^\prime$B$_8$C$_8$H$_8$ monolayers. These 2D systems exhibit tunable superconductivity governed by hole concentration, structural anisotropy, and electron-phonon coupling. We find that in-plane anisotropy competes with superconductivity, reducing \tc\ despite favorable doping. Biaxial strain mitigates this anisotropy, enhances Fermi surface nesting, and increases \tc\ by an average of 15.5~K. For example, the \tc\ of Sr$_3$B$_8$C$_8$H$_8$ is predicted to increase from 11.3~K to 22.2~K with strain engineering. These findings identify 2D clathranes as promising, strain-tunable superconductors and highlight design principles for optimizing low-dimensional superconducting materials.

Figures (4)

• Figure 1: (A) Supercell of the 2D hydrogenated metal borocarbides (M$_2$M$^\prime$B$_8$C$_8$H$_8$). The color of the surface metals is red, cage metals are gray, boron is green, carbon is black, and hydrogen is white. (B) Top view of the structure; the equatorial boron/carbon atoms are marked with green/black arrows. (C) The energy ($\Delta E_\textsc{EXF}$) associated with the formation of the 2D structures along with solid M$^\prime$, $\alpha$-boron, and graphite via hydrogenation of the 3D structure. The green color shows regions where 3D structures are thermodynamically preferred (Ca$_2$Y, Ca$_2$La, Y$_2$Ca, Y$_3$, Y$_2$La, La$_2$Y, and La$_3$), otherwise the color is scaled to the energy difference. Dynamically unstable structures are enclosed with blue squares.
• Figure 2: Electronic structure of Sr$_3$B$_8$C$_8$H$_8$. (a) Electronic band structure and atom-projected density of states (PDOS) of Sr$_3$B$_8$C$_8$H$_8$. The Fermi level ($E_\mathrm{F}$) is set to 0 eV. (b) Partial charge density integrated around $E_\mathrm{F}$+1 eV within an energy window of $\pm$0.1 eV, corresponding to the green-shaded region in (a). (c) Partial charge density integrated around $E_\mathrm{F}$ within an energy window of $\pm$0.1 eV, corresponding to the blue-shaded region in (a). The isosurfaces in (b) and (c) enclose 50% of the total charge within the selected energy windows. Atom color coding is consistent with Figure \ref{['fig:1']}. (d) Fermi surface of the 2D Sr3B8C8H8 clathrane. The black dashed arrow illustrates an example of a $\mathbf{q}$-vector at the M point ($q_x = 0.5$, $q_y = 0.5$) that connects nested electronic states on the steepest band. (e) Phonon dispersion, Eliashberg spectral function, $\alpha^2\mathrm{F}(\omega)$, and the integrated electron-phonon coupling constant, $\lambda(\omega)$, within the frequency range of 0-800 cm$^{-1}$. The width of the red lines in the phonon dispersion corresponds to the mode-resolved electron-phonon coupling strength, proportional to $\lambda_{\mathbf{q}\nu} \omega_{\mathbf{q}\nu}$ for each phonon mode $\nu$ at wavevector $\mathbf{q}$. The plot in the full frequency range is available in the SI.
• Figure 3: (a) Summary of the superconducting transition temperatures ($T_c$s) for various M$_2$M$^\prime$B$_8$C$_8$H$_8$ compositions under zero external stress, i.e., fully relaxed in-plane lattice constants. The $T_c$s are calculated using Eliashberg theory with a $\mu^\star$ of 0.1; for systems with $T_c < 10$ K, values are estimated using the Allen-Dynes modified McMillan formula. (b) Correlation between $T_c$, the density of states at the Fermi level, $g(E_\textsc{F})$, and the in-plane structural anisotropy in Å (quantified by the lattice constant difference $b - a$). The inset shows the symbols employed for systems with the listed number of holes, or with an excess electron (denoted by -1).
• Figure 4: (a) Comparative summary of $T_c$ in 3D bulk MM$^\prime$B$_6$C$_6$, unstrained 2D M$_2$M$^\prime$B$_8$C$_8$H$_8$, and biaxial strained 2D M$_2$M$^\prime$B$_8$C$_8$H$_8$. The $T_c$s are calculated using Eliashberg theory with a $\mu^\star$ of 0.1; for systems with $T_c < 10$ K, values are estimated using the Allen-Dynes modified McMillan formula. Ca$_2$Pb, Ca$_2$Sn, Ca$_2$Sr, Ca$_3$, Pb$_2$Ca, Sr$_2$Ca, Sr$_2$Sn, Ba$_2$Rb, and Ca$_2$Rb are dynamically unstable in 3D but stable in the 2D analogues. (b) Fermi surface of biaxially strained 2D Sr3B8C8H8. (c) Phonon dispersion, Eliashberg spectral function, $\alpha^2\mathrm{F}(\omega)$, and the integrated electron-phonon coupling constant, $\lambda(\omega)$, within the frequency range of 0-900 cm$^{-1}$. The width of the red lines in the phonon dispersion corresponds to the mode-resolved electron-phonon coupling strength, proportional to $\lambda_{\mathbf{q}\nu} \omega_{\mathbf{q}\nu}$ for each phonon mode $\nu$ at wavevector $\mathbf{q}$. The plot in the full frequency range is available in the SI. (d) Two-dimensional nesting function, $\chi(\mathbf{q})$, of unstrained Sr3B8C8H8. (e) Nesting function of biaxially strained Sr3B8C8H8.