Type-II Dirac cones and electron-phonon interaction in monolayer biphenylene from first-principles calculations

We report a first-principles investigation of electronic structure, topological bands, and electron-phonon interactions in metallic biphenylene sheets. Biphenylene is a recently synthesized $s{p}^{2}$-bonded carbon allotrope. We find coupling of electrons at the Fermi surface to very high frequency carbon-derived phonons, analogous to superconducting ${\mathrm{MgB}}_{2}$. This leads to low-temperature weak coupling superconductivity due to an unusual combination of exceptionally large logarithmically averaged phonon frequency ${\ensuremath{\omega}}_{\text{log}}$=1369 K and moderate electron-phonon coupling. The electronic structure shows a two-band Fermi surface dominated by C ${p}_{z}$ orbitals and a pair of type-II tilted Dirac cones along the $\mathrm{\ensuremath{\Gamma}}$-Y line at the Brillouin zone boundary. Berry curvature and edge-state calculations show that monolayer biphenylene is a two-dimensional ${\mathbb{Z}}_{2}$ topological material. Thus, monolayer biphenylene is predicted to be a topological superconductor based on C $p$ orbitals and high-frequency phonons.