Theoretical prediction of superconductivity in monolayer ${\mathrm{B}}_3\mathrm{N}$

Using first-principles calculations, we predict the two-dimensional (2D) monolayer boron-nitrogen compound ${\mathrm{B}}_3\mathrm{N}$, which shows a honeycomb lattice similar to graphene. Its stability is proved by phonon spectra and ab initio molecular dynamics simulations. Since pristine ${\mathrm{B}}_3\mathrm{N}$ is a metal by band structure calculation, we investigate the electron-phonon coupling and possible phonon-mediated superconductivity. Based on the Eliashberg equation, the calculated electron-phonon coupling strength is about 0.66, and the superconducting transition temperature $T_c$ is 14.1 K, which is comparable to that of borophene. Furthermore, when 0.04 electron/cell doping and 10% biaxial tensile strain are applied, $T_c$ can be increased to 17.4 K. Thus, the predicted ${\mathrm{B}}_3\mathrm{N}$ provides a platform for 2D superconductivity.

Figure 1

(a) Periodic structure of ${\mathrm{B}}_3\mathrm{N}$. Green (gray) spheres represent B (N) atoms, and the unit cell is shown. (b) Side view of the ${\mathrm{B}}_3\mathrm{N}$ unit cell. $\mathit{h}$ is the perpendicular distance between the ${\mathrm{N}}_1$ and ${\mathrm{N}}_2$ atoms.

Figure 2

(a) Phonon dispersion of pristine ${\mathrm{B}}_3\mathrm{N}$. The phonon linewidth is also shown by red shading, and the area of shading is proportional to the magnitude of phonon linewidth ${\gamma }_{\mathbf{q}\nu }$. (b) Atom-projected phonon DOS and (c) direction-projected phonon DOS for B and N atoms for pristine ${\mathrm{B}}_3\mathrm{N}$. (d) The variation of the free energy in the AIMD simulations over a timescale of 6 ps and the image of the pristine ${\mathrm{B}}_3\mathrm{N}$ structure at the end of 6 ps AIMD simulations at 700 K.

Figure 3

(a) Orbital-projected electronic band structure of pristine ${\mathrm{B}}_3\mathrm{N}$ along high-symmetry line $\mathrm{\Gamma }-M-K-\mathrm{\Gamma }$. The inset shows the band structure in the range of energy from $-0.2$ to 0.2 eV. (b) The total DOS and the DOSs of B and N. (c) Orbital-projected DOSs for B and N. (d) The top and (e) side views of the FS of pristine ${\mathrm{B}}_3\mathrm{N}$.

Figure 4

The 24 vibration modes of pristine ${\mathrm{B}}_3\mathrm{N}$ at the $\mathrm{\Gamma }$ point in the Brillouin zone. The vibration frequencies are shown below each graph. The dark green spheres and gray spheres represent B and N, respectively, and the light green arrows represent the direction of the atomic vibration.

Figure 5

Eliashberg spectral function ${\alpha }^{2}F(\omega$) and electron-phonon coupling $\lambda \left(\omega \right)$ for (a) pristine ${\mathrm{B}}_3\mathrm{N}$ and (b) ${\mathrm{B}}_3\mathrm{N}$ with 0.04 electron/cell doping and 10% tensile strain.

Figure 6

(a) Phonon spectra (solid red lines) and (b) atom-projected phonon DOS for ${\mathrm{B}}_3\mathrm{N}$ with 0.04 electron/cell doping and 10% tensile strain. For comparison, the phonon spectra for pristine ${\mathrm{B}}_3\mathrm{N}$ are also included as solid black lines in (a).

Figure 7

$\lambda$ and $T_c$ as a function of degauss for different $k$ meshes and $q$ meshes for pristine ${\mathrm{B}}_3\mathrm{N}$.

Figure 8

Phonon spectra for ${\mathrm{B}}_3\mathrm{N}$ with 0.04 electron/cell doping under biaxial tensile strains of $18\%$ (black line) and $19\%$ (red line).

Figure 9

Comparison of band structures of the pristine ${\mathrm{B}}_3\mathrm{N}$ calculated from the DFT calculation (solid black lines) and (a) MLWF fitting with the $p_x, p_y$, and $p_z$ orbitals of B atoms, (b) MLWF fitting with the $p_z$ orbital of B atoms, and (c) the hybridized two-orbital model (dashed red lines).