Nonadiabatic theory of electron–vibrational coupling: New basis for microscopic interpretation of superconductivity

Abstract

The electron-vibrational problem of the general nonadiabatic molecular systems has been solved by means of the quasi-particle transformations. The SCF ab initio solution of the nonadiabatic fermion Hamiltonian yields stabilization of the electronic ground-state energy due to electron-phonon interaction and it also gives the corrections to the one-and two-particle terms. Two two-particle correction yields effective attractive electron-electron interaction, but in the form different from Frolich's effective electron-electron interaction term. In contrast to the standard electron-phonon Hamiltonian of solid-state physics that does not take into account the possible effects of nonadiabaticity of a system, the presented nonadiabatic theory yields also one-particle corrections. The presence of this term in the Hamiltonian might play a crucial role in the theory of superconductivity since the superconductors are nonadiabatic systems. Since the quasi-particle theory of vibrational energy calculations for nonadiabatic molecules is extremely extensive and will be published elsewhere [lo], we restrict ourselves only to the schematic way of derivation, with the focus being placed on the fermion part of the nonadiabatic e1.-vibr. Hamiltonian.

Nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization—Microscopic mechanism of superconducting state transition: Model study of MgB2

“…We have shown [35] (see also Appendix A16) that in the adiabatic limit (/E F Ͻ Ͻ 1), the solution of the coupled set of electronic and nuclear equations yields the same results as those obtained by Wagner, using the adiabatic bases set with an electronic motion to be dependent only on the instantaneous nuclear coordinates, but independent of the instantaneous nuclear velocities. Under the strict nonadiabatic conditions, the analysis of the solutions of this coupled set of equations offers a new insight on the possibility of the SC state transition.…”

“…[35][36][37][38]. To keep the present study consistent as much as possible, the Appendix outlines only the final equations that are relevant to the study of MgB 2 .…”

“…With respect to the nonadiabatic theory of electron-vibration interactions [35][36][37][38], in the following discussion, instead of the EP coupling constant , we need matrix elements of EP coupling U PQ (r) (Q). Directly available is only the total value of the EP coupling that can be extracted from the dependence of the total "core" energy/unit cell on the deformation displacement of atoms out of the equilibrium positions according to normal mode vibrations.…”

“…Starting Hamiltonian for the study of the nonadiabatic electron-vibration interactions [35] is written in the general form of nonrelativistic "chemical" Hamiltonian of interacting set of atoms:…”

“…In 1992 we published a series of papers on the molecular nonadiabatic theory of electron-vibration interactions elaborated for some aspects of superconductivity [35][36][37][38]. The key point of this treatment is that in an ensemble of interacting electrons and nuclei (a molecular or solid-state system), the motion of the electrons is studied to be explicitly dependent not only on the operators of instantaneous nuclear coordinates, but on the operators of instantaneous nuclear velocity-momenta as well.…”