Abstract
An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.
Highlights
For two weak links separated on the order of the superconducting coherence length ξ0, this coupling arises from the hybridization of quasiparticles to form a molecular, or multi-weak link, Andreev Bound State (ABS)
In general, arbitrary mesoscopic systems with superconducting regions of size comparable to the coherence length can be effectively modeled with the scattering approach incorporating the partial Andreev reflection and transmission coefficients
We validated this formalism by checking for agreement with the Bogolubiov-de-Gennes results for a single-channel Andreev molecule [5]
Summary
A convenient approach to treat conduction through mesoscopic systems is the LandauerBüttiker scattering formalism [11]. Matrices describe the scattering of propagating electrons or holes on three different types of elements: weak links, semi-infinite superconductors, and a superconductor of finite length, Fig. 1(a). As depicted the CAR process for an electron incident from the left corresponds to first an Andreev reflection and backscattering of the retroreflected hole, which traverses the finite superconductor and exits toward the right. This mechanism can be seen as the formation, in the central slab, of a Cooper pair comprised of electrons from both left and right electrodes. To verify correctness we numerically solved Eq (8) for the spectra in the case of a single channel Andreev molecule with symmetric δ-function barriers, i.e. SL and SR given by Eq (3), and compared for agreement with the Bogolubiov-de-Gennes solution for the same parameters [5]
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