Modulating the vibronic correlation in 2D superconductor by electric field

Superconductivity in the extreme two-dimensional atomic layers has been suffered because of the strong affection dimensionality confinement on electron-phonon binding. Here, using first-principles method, we study the effect of applied perpendicular and parallel electric field on the strength of phonon renormalization and electron-phonon coupling in bi-layer MgB2 as a known 2D superconductor. The changes of phonon frequency and line-width demonstrate that important E2g optical modes are strongly sensitive to the applied parallel electric field which directs to sharp reduction of vibronic coupling. Whereas, we show that perpendicular electric field modulates the system to the strong-coupling superconductor and predict the enhancement of critical temperature Tc. Our study opens up the use of electric filed to probe and measure the variation amount of electron-phonon renormalization as a gauge in 2D superconductivity.