A flat/steep band scenario in momentum space

Based on chemical bonding considerations in a crystalline solid, a Hamiltonian was proposed for the flat/steep band scenario. This model has been studied with the first-principles method. With Hg and MgB2 as examples, we have explained the characteristics of this model and observed peak-like structure of the electron-phonon coupling constant lambda(q) in q space. The strong coupling of the flat band electrons with phonons has been corroborated by developing a new functional Psib(Phi), through which we can quantitatively compare different electronic states in coupling to a specific phonon. In the case of MgB2 a multigap structure of the superconducting state results from our model.