Abstract
The nonadiabatic Heisenberg model presents a nonadiabatic mechanism generating Cooper pairs in narrow, roughly half-filled “superconducting bands” of special symmetry. Here, I show that this mechanism may be understood as the outcome of a special spin structure in the reciprocal space, hereinafter referred to as “k-space magnetism”. The presented picture permits a vivid depiction of this new mechanism highlighting the height similarity as well as the essential difference between the new nonadiabatic and the familiar Bardeen–Cooper–Schrieffer mechanism.
Highlights
IntroductionThe nonadiabatic Heisenberg model (NHM) [1] is an extension of the Heisenberg model [2]
The nonadiabatic Heisenberg model (NHM) [1] is an extension of the Heisenberg model [2]going beyond the adiabatic approximation
The energy bands in the band structures of the metals are degenerate at several points and lines of the Brillouin zone
Summary
The nonadiabatic Heisenberg model (NHM) [1] is an extension of the Heisenberg model [2]. Within the NHM, strongly correlated electrons in a narrow, roughly half-filled superconducting band produce a special spin structure at the Fermi level that we call “k-space magnetism”: the electron. In this case, the boson pair created during the first process in Equation (1) is completely reabsorbed during the second process in Equation (2). The only scattering processes within E km conserving the total electron spin are scattering processes between Cooper pairs: since the system is invariant under time-inversion, the spins of the Bloch states labeled by k and by −k lie exactly opposite. We speak of quantum mechanical constraining forces stabilizing the Cooper pairs in E km [6], or, more illustratively, by “spring mounted Cooper pairs” [8]
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