Nonadiabatic electron-phonon coupling and its effects on superconductivity

As one of the most striking phenomena in many-body systems, the breakdown of the adiabatic Born-Oppenheimer (ABO) approximation is essential for understanding and predicting the dynamics of quantum materials. Here, we demonstrate that strong nonadiabatic (NA) effects can emerge in electron-phonon coupling (EPC) and resultant superconductivity, yielding a surprisingly large contribution (up to 20%) to the total EPC strength \ensuremath{\lambda} of doped graphene/graphane and modulating the superconductivity transition temperature ${T}_{c}$ by \ensuremath{\sim}20%. The NA EPC, with a detectable isotopic effect, results from the renormalized EPC matrix elements (up to 40%) combined with the Fermi surface modulation, due to electron distributions deviating from the equilibrium. Our results imply that nonadiabaticity plays a wider and more important role than previously conceived, offering new understandings and strategies for dynamic engineering of quantum materials.