Simulating the effect of boron doping in superconducting carbon

We examine the effect of boron doping in superconducting forms of amorphous carbon. By judiciously optimizing boron substitutional sites in simulated amorphous carbon, we predict a superconducting transition temperature near 37 K at 14% boron concentration. Our findings have direct implications for understanding the recently discovered high-$T_c$ superconductivity in Q-carbon.

Figure 1

(a) Ball-and-stick model of amorphous carbon. Orange and gray spheres represent threefold- and fourfold-coordinated carbon atoms, respectively. (b) Radial distribution function of amorphous carbon. (c) Density of states (in states/spin/Ry/cell) of undoped amorphous carbon (red solid line) and its projection onto the $p$-orbital of threefold-coordinated carbon atoms (blue dashed line). The vertical dashed line at 0 eV indicates the Fermi level. A Gaussian broadening width and energy grid of 0.05 eV is used.

Figure 2

Site dependence of relative Kohn-Sham eigenvalue energies of the ${\mathrm{C}}_{64}$ to ${\mathrm{BC}}_{63}$ case (top panel) and the ${\mathrm{B}}_5\text{−}\mathrm{S}1$ to ${\mathrm{B}}_6$ case (bottom panel). Black triangles, blue squares, red circles, and green pentagons represent twofold, threefold, fourfold, and fivefold coordination, respectively (twofold is almost fourfold since it has two nearest-neighbor atoms at a slightly longer distance than 1.8 Å). Here the energy difference between the 128th and 123rd states is plotted. The horizontal dashed line shows the corresponding value in the undoped case. Here the eigenvalues are computed using an LDA exchange-correlation functional, and they could be altered when one uses a different functional (see the Supplemental Material) [27].

Figure 3

Densities of states (DOS, in states/spin/Ry/cell) of ${\mathrm{B}}_4\text{−}\mathrm{S}1$ (blue solid), ${\mathrm{B}}_5\text{−}\mathrm{S}1$ (green dashed), ${\mathrm{B}}_6\text{−}\mathrm{S}1$ (black dash-dotted), ${\mathrm{B}}_7\text{−}\mathrm{S}1$ (magenta dash-dotted), ${\mathrm{B}}_8\text{−}\mathrm{S}1$ (cyan dashed), and ${\mathrm{B}}_9\text{−}\mathrm{S}1$ (red solid) structures.

Figure 4

Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ of ${\mathrm{B}}_4\text{−}\mathrm{S}1$ (blue line) and ${\mathrm{B}}_9\text{−}\mathrm{S}{1}_a$ (red line) structures. The inset shows the magnified view of the low-frequency region.