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

Small Fermi energy effects are induced in MgB2 by the low hole doping in the σ bands which are characterized by a Fermi energy EFσ∼0.5 eV. We show that due to the particularly strong deformation potential relative to the E2g 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 MgB2 even if ωph∕EF∼0.1−0.2, where ωph are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.