Prediction of phonon-mediated superconductivity in hole-doped black phosphorus

We study the conventional electron-phonon mediated superconducting properties of hole-doped black phosphorus by density functional calculations and get quite a large electron-phonon coupling (EPC) constant lambda similar to 1.0 with transition temperature T-C similar to 10 K, which is comparable to MgB2 when holes are doped into the degenerate and nearly flat energy bands around the Fermi level. We predict that the softening of low-frequency B-3g(1) optical mode and its phonon displacement, which breaks the lattice nonsymmorphic symmetry of gliding plane and lifts the band double degeneracy, lead to a large EPC. These factors are favorable for BCS superconductivity.