Ab initio theory of complex electronic ground state of superconductors: I. Nonadiabatic modification of the Born–Oppenheimer approximation

Abstract

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On the mechanism of high-temperature superconductivity in hydrogen sulfide at 200 GPa: Transition into superconducting anti-adiabatic state in coupling to H-vibrations

“…It indicates formation of anti-adiabatic regime with ω H /E F 1.6, or 1.2 depending on particular ω H . According to nonadiabatic theory of electronvibration interactions [10][11][12], whether system can be stabilized in anti-adiabatic state at distorted geometry depends on correction…”

“…In this case, not only Eliashberg approximation does not hold, but Born-Oppenheimer approximation (BOA) is broken. Theory of electronvibration interaction beyond the BOA was elaborated in [10] and it has been shown [11][12][13][14][15][16] for different types of low and high-T c superconductors (e.g. A15 structures, cuprates and MgB 2 ) that transition into superconducting state is directly related to EP coupling-induced transition from metal-like adiabatic state into stabilized and geometrically degenerated anti-adiabatic ground state connected with gap(s) opening in single-particle spectrum.…”

Electronic Structure of Single-Wall Silicon Nanotubes and Silicon Nanoribbons: Helical Symmetry Treatment and Effect of Dimensionality

“…[51][52][53] The mentioned aspect of band structure instability is important for crossing of the system from adiabatic metal-like state into anti-adiabatic state which, if stabilized, is directly related to superconducting state transition. 42,51,[54][55][56] Study of this problem, i.e. aspects of anti-adiabatic state stabilization and superconducting state transition, is out of the scope of the present paper and it will be published elsewhere.…”

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

“…Treatment of this problem is presented in full extension in [25][26][27][28]. In order to make the results of this paper intelligible, we present here the final form of corrections to particular energy terms, which arise as the consequence of non-adiabatic electron-vibration coupling and explicitly accounts for dependence of electronic structure on instantaneous nuclear coordinates (Q) and momenta (P), i.e.…”

“…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. In these circumstances, calculations beyond the BOA are required to allow comparison of theory and experiment in detail [24], such as it enables the anti-adiabatic theory of superconductivity suggested recently [25][26][27]. The latter theory solves the BOA breakdown by introducing an explicit dependence of the electronic structure on nuclear dynamics.…”