Mapping reservoir-enhanced superconductivity to near-long-range magnetic order in the undoped 1D Anderson- and Kondo-lattices

The undoped Kondo necklace in 1D is a paradigmatic and well understood model of a Kondo insulator. This work performs the first large-scale study of the 1D Anderson-lattice underlying the Kondo necklace with quasi-exact numerical methods, comparing this with the perturbative effective 1D Kondo-necklace model derived from the former. This study is based on an exact mapping of the Anderson model to one of a superconducting pairing layer connected to a metallic reservoir which is valid in arbitrary spatial dimensions, thereby linking the previously disparate areas of reservoir-enhanced superconductivity, following Kivelson's pioneering proposals, and that of periodic Kondo-systems. Our work reveals that below the length-scales on which the insulating state sets in, which can be very large, superconducting and density-density correlations are degenerate and may both appear to approach an almost ordered state, to a degree that far exceeds that of any isolated 1D pairing layer with short-range interactions. We trace these effects to the effective extended-range coupling that the metallic layer mediates within the pairing layer. These results translate directly to the appearance of near-long-range magnetic order at intermediate scales in the Kondo-systems, and explain the strong renormalization of the RKKY-coupling that we effectively observe, in terms of the back-action of the pairing layer onto the metallic layer. The effects we predict could be tested either by local probes of quasi-1D heavy fermion compounds such as CeCo$_2$Ga$_8$, in engineered chains of ad-atoms or in ultracold atomic gases.