Possibility of reflectionless tunneling crossed transport at normal metal / superconductor double interfaces

– We investigate one dimensional models (the Blonder, Tinkham, Klapwijk model and a tight-binding model) of non local transport at normal metal / superconductor (NS) double interfaces. We find a negative elastic cotunneling crossed conductance, strongly enhanced by additional scatterers away from the interfaces, suggesting the possibility of reflectionless tunneling non local transport at double NS interfaces with contacts having a sufficiently small extension. Introduction. – Single electron tunneling in a superconductor is prohibited if the applied bias voltage is smaller than the superconducting gap. However, an electron in the spin-up band can be reflected as a hole in the spin-down band, a phenomenon called Andreev reflection [1]. A charge 2e is transmitted in the superconductor at each Andreev reflection, so that the conductance of a highly transparent normal metal / superconductor (NS) contact is doubled compared to the one of the corresponding NN contact. The equilibrium properties of the superconductor (such as the value of the self-consistent superconducting gap) are modified by a normal electrode connected to the superconductor, a phenomenon called the inverse proximity effect. It is expected that most of the inverse proximity effect takes place on a length a if the area of the contact a is much smaller than the superconducting coherence length ξ [2]. The influence of the inverse proximity effect on transport properties can then be neglected, and a single channel, ballistic, one-dimensional model with a step-function variation of the superconducting gap captures the essential physics of localized interfaces, as shown by Blonder, Tinkham, and Klapwijk (BTK) [2]. Moreover, BTK introduce a repulsive potential at the NS interface, characterized by the dimensionless parameter Z, being the strength of the repulsive potential normalized to the Fermi energy. Transparent interfaces correspond to Z = 0 and tunnel interfaces correspond to Z ≫ 1. Disorder in the normal metal modifies strongly subgap transport at a single normal metal / insulator / superconductor (NIS) interface [3,4]. The conductance can be enhanced by orders of magnitude by constructive interferences in which an electron can “try” the tunneling process a huge number of times [3]. This effect due to scattering by disorder is already present in simple double barrier one-dimensional models. Melsen and Beenakker [5] consider a NINIS