  High Tc superconductivity in FeAs-based multilayers (pnictides), evading
temperature decoherence effects in a quantum condensate, is assigned to a
Feshbach resonance (called also shape resonance) in the exchange-like interband
pairing. The resonance is switched on by tuning the chemical potential at an
electronic topological transition (ETT) near a band edge, where the Fermi
surface topology of one of the subbands changes from 1D to 2D topology. We show
that the tuning is realized by changing i) the misfit strain between the
superconducting planes and the spacers ii) the charge density and iii) the
disorder. The system is at the verge of a catastrophe i.e. near a structural
and magnetic phase transition associated with the stripes (analogous to the 1/8
stripe phase in cuprates) order to disorder phase transition. Fine tuning of
both the chemical potential and the disorder pushes the critical temperature Ts
of this phase transition to zero giving a quantum critical point. Here the
quantum lattice and magnetic fluctuations promote the Feshbach resonance of the
exchange-like anisotropic pairing. This superconducting phase that resists to
the attacks of temperature is shown to be controlled by the interplay of the
hopping energy between stripes and the quantum fluctuations. The
superconducting gaps in the multiple Fermi surface spots reported by the recent
ARPES experiment of D. V. Evtushinsky et al. arXiv:0809.4455 are shown to
support the Feshbach scenario.

Superconductivity