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We theoretically explore the superconducting critical temperature of hole doped blue phosphorene within the density functional theory simulations. We show that for the hole doped blue phosphorene, owing to the quite
strong electron-phonon coupling, the isotropic superconducting state is induced. The theory is based on the Migdal-Eliashberg formalism and the critical temperature is obtained through set-of-equations, self-consistency. In addition, we include a vertex correction diagram to the Migdal-Eliashberg formalism. Although the inclusion of the vertex correction beyond the Migdal-Eliashberg formalism reduces the critical temperature of about 40K, our accurate numerical results show that the critical temperature is still quite high.
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