Ground electronic state of MgB$_{2}$: Intrinsic nonadiabatic state at broken translation symmetry.

Study of the band structure of MgB$_{2}^{ }$has shown that electron coupling to E$_{2g}$ phonon mode induces not only $\sigma $-bands splitting at $\Gamma $ point but also fluctuation of the top of one of $\sigma $ band at the Fermi level, resulting in dramatic decrease of the Fermi energy. As a consequence, the original adiabatic state ($\omega $/E$_{F} \quad <$ 1) corresponding to the equilibrium nuclear geometry has been changed to the intrinsic nonadiabatic state ($\omega $/E$_{F} \quad >>$ 1) at distorted geometry, already at the displacement which is smaller than the rms. displacement of B-B atoms corresponding to zero-point energy of the E$_{2g}$ phonon mode. At these circumstances, not only Migdal theorem but also Born-Oppenheimer approximation has been broken, and standard treatment of EP interactions, including calculation of nonadiabatic corrections to adiabatic ground state by means of perturbation theory, can not be applied. Study of the electron-nuclear Hamiltonian by means of the quasiparticle unitary transformation (Q,P--dependent) which treats electrons and nuclei on the same footing, has revealed that EP interactions in the intrinsic nonadiabatic state stabilize the fermionic ground state of MgB$_{2}$ at broken translation symmetry and corresponding wave function is dependent not only on nuclear coordinates, but it is strongly modulated mainly by nuclear momenta. From the results follow that in this case, instead of Cooper pairs formation, condensation process is represented rather by real-space, T-dependent formation of mobile bipolarons.