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

Abstract

ABSTRACT:The theory of the nonadiabatic electron-vibration interactions has been applied to the study of MgB 2 superconducting state transition. It has been shown that at nonadiabatic conditions in which the Born-Oppenheimer approximation is not valid and electronic motion is dependent not only on the nuclear coordinates but also on the nuclear momenta, the fermionic ground-state energy of the studied system can be stabilized by nonadiabatic electron-phonon interactions at broken translation symmetry. Moreover, the new arising state is geometrically degenerate; i.e., there are an infinite number of different nuclear configurations with the same fermionic ground-state energy. The model study of MgB 2 yields results that are in a good agreement with the experimental data. For distorted lattice, with 0.016 Å/atom of in-plane out-of-phase BOB atoms displacements out of the equilibrium (E 2g phonon mode) when the nonadiabatic interactions are most effective, it has been calculated that the new arising state is 87 meV/unit cell more stable than the equilibrium-high symmetry clumped nuclear structure at the level of the Born-Oppenheimer approximation. The calculated T c is 39.5 K. The resulting density of states exhibits two-peak character, in full agreement with the tunneling spectra. The peaks are at Ϯ4 meV, corresponding to the change of the band density of states, and at Ϯ7.6 meV, corresponding to the band. The superconducting state transition can be characterized as a nonadiabatic sudden increase of the cooperative kinetic effect at lattice energy stabilization (NASICKELES).

Toward possibility of high-temperature bipolaronic superconductivity in boron tubular polymorph: Theoretical aspects of transition into anti-adiabatic state

“…Thermodynamic properties of a system in stabilized anti-adiabatic electronic ground state are identical with thermodynamics of a superconducting state. Temperature of adiabatic↔anti-adiabatic state transition corresponds to T c of superconductors with super-carriers in form of mobile bipolarons, as we have shown for different types of superconductors including MgB 2 and high-temperature cuprates [22,26,27]. In what follows, we apply the anti-adiabatic theory [25][26][27][28] in study of SWBNT.…”

“…Expression (22) represents well known energy of standard adiabatic polarons (small, selftrapped) that contributes to the total energy of system. d2/ Electronic specific heat and entropy in anti-adiabatic state At formation of the anti-adiabatic ground state, electronic energy is decreased and for involved band(s) the gap in one-particle spectrum has been opened (shift of orbital energies).…”

“…In what follows, we apply the anti-adiabatic theory [25][26][27][28] in study of SWBNT. Since it is the topology of the BS close to the FL that is crucial, a semiempirical INDO treatment for the BS calculations [29] using valence Slater-type atomic orbitals (STO) basis as in the aforementioned MgB 2 and cuprates studies [22,26,27] is appropriate.…”

“…ω/E F >1. Consequently, the system becomes anti-adiabatic [21][22][23]. Since Eliashberg's treatment [15] is based on a strict adiabatic assumption, transition into the anti-adiabatic state not only invalidates application of the strong coupling theory (BCS-like theories in general) [15][16][17], but at the same time it means breakdown of the crucial Born-Oppenheimer approximation (BOA) which has to be valid not only in equilibrium but also over the relevant configuration space including geometry with corresponding vibration displacements.…”

“…It corresponds to situation at T>T c . For extreme adiabatic limit 0 / Expression (22) represents well known energy of standard adiabatic polarons (small, selftrapped) that contributes to the total energy of system.…”