Electron-phonon coupling and superconductivity in Li-intercalated layered borocarbide compounds

We explore the electron-phonon coupling and possible superconductivity in Li-intercalated borocarbide materials using precise Wannier interpolation-based first-principles technique. We find a $T_c$ of 36.8 K for the previously suggested superconductor Li${}_2$B${}_3$C, however, we also propose another material Li${}_4$B${}_5$C${}_3$ with an estimated $T_c$ of 16.8 K. Replacing BC layers with BC${}_3$ in Li${}_2$B${}_3$C allows the $\pi$ electronic states to be dominant at the Fermi level for Li${}_4$B${}_5$C${}_3$. We analyze wave-vector-resolved electron-phonon coupling parameters and suggest that Li${}_4$B${}_5$C${}_3$ may be more suitable for experimental fabrication than Li${}_2$B${}_3$C.

Figure 1

Crystal structures of Li${}_2$B${}_3$C [(a) and (b)] and Li${}_4$B${}_5$C [(c) and (d)]. Lithium, boron, and carbon atoms are represented by purple, gray, and peach color spheres, respectively. The arrows show displacement vectors of the vibrational modes, which strongly couple with electrons: (a) the $E^{\prime }$ mode at the $\Gamma$ point in the first Brillouin zone, (b) the $B_2$ mode at the $M$ point, (c) the $E_{2g}$ B–B stretching mode at the $\Gamma$ point, and (d) the $E_{2g}$ B–C and C–C stretching mode at the $\Gamma$ point.

Figure 2

Band structures and projected densities of states of Li${}_2$B${}_3$C (top) and Li${}_4$B${}_5$C${}_3$ (bottom) near the Fermi energy (the Fermi energy is set to 0 eV). The band structure of Li${}_2$B${}_3$C is computed in a small Brillouin zone corresponding to a $2\times 2$ supercell so that one can compare the two band structures easily. The band structures are plotted in red (blue) when the projected density of $\pi$ electronic states of the BC layer ($\sigma$ electronic states of the boron layer) exceeds 0.15. Here the maximum value among all of the wave-vector-resolved projected densities of states is normalized to 1. The band structures are plotted in yellow when the projected densities of both $\pi$ electronic states of the BC layer and $\sigma$ electronic states of the boron layer exceed 0.15. The black thick solid lines in the right panels show the total densities of states. The green chain, red solid, blue dotted, and magenta dashed lines represent the contributions from the $\sigma$ state in the BC layer, the $\pi$ state in the BC layer, the $\sigma$ state in the boron layer, and the $\pi$ state in the boron layer, respectively. The contributions from lithium atoms are small near the Fermi energy.

Figure 3

Phonon densities of states $F\left(\omega \right)$ (black solid line and the grey-shaded area below) and the Eliashberg spectral functions ${\alpha }^{2}F\left(\omega \right)$ (blue line) for Li${}_2$B${}_3$C and Li${}_4$B${}_5$C${}_3$ calculated in this work. The $F\left(\omega \right)$ is given in arbitrary units.

Figure 4

Wave-vector-resolved electron-phonon coupling ${\lambda }_{\vec{Q}}$ (solid black) and the Fermi surface nesting (red) function (as explained in Refs. [45] and [44], for instance) for a path inside the corresponding Brillouin zone for Li${}_2$B${}_3$C and Li${}_4$B${}_5$C${}_3$. The nesting is given in arbitrary units.