Small Fermi energy, zero-point fluctuations, and nonadiabaticity in MgB2

Small Fermi energy effects are induced in MgB(2) by the low hole doping in the sigma bands which are characterized by a Fermi energy E(F)(sigma)similar to0.5 eV. We show that due to the particularly strong deformation potential relative to the E(2g) phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB(2) even if omega(ph)/E(F)similar to0.1-0.2, where omega(ph) are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.