Renormalization effects in spin-polarized metallic wires proximitized by a superconductor: A scattering approach
Thomas Kiendl, Felix von Oppen, Piet W. Brouwer
DOI 10.1103/PhysRevB.99.104510 · Physical Review B
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Abstract
Spin-polarized normal-metal wires coupled to a superconductor can host Majorana states at their ends. These decay into the bulk and are protected by a minigap in the spectrum. Previous studies have found that strong coupling between the superconductor and the normal-metal wire renormalizes the properties of this low-energy phase. Here, we develop a semiclassical scattering approach to explain these renormalization effects. We show that a renormalization of the propagation velocity in the normal wire originates from double Andreev reflection processes at the superconductor interface and that it continues to exist in the absence of a proximity-induced minigap in the normal-metal wire. We also show that the renormalization effects exist for arbitrary transparency of the normal-metal–superconductor interface, provided the superconductor coherence length is sufficiently long in comparison to the thickness of the normal metal.
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