Feshbach resonance and mesoscopic phase separation near a quantum critical point in multiband FeAs-based superconductors

High-T_c superconductivity in FeAs-based (pnictide) multilayers, evading temperature decoherence effects in a quantum condensate, is assigned to a Feshbach resonance (also called 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 one-dimensional (1D) to two-dimensional (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 order-to-disorder phase transition of the stripes (analogous to the 1/8 stripe phase in cuprates). Fine tuning of both the chemical potential and the disorder pushes the critical temperature T_s 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 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 Evtushinsky et al (2008 arXiv: 0809.4455) are shown to support the Feshbach scenario.