Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associ
ated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of [Breuer-Ryckman-Simon]. These developments parallel those recently obtained for Jacobi matrices.
The electronic transport properties of an SNS junction formed by an InN nanowire (N) and Al contacts (S) with a superconducting transition temperature T_c ~ 0.92 K were investigated. As a function of dc bias, superconducting quasiparticle transport r
esonance peaks at E=2Delta were observed, in agreement with BCS theory with 2Delta(T=0) equiv Delta_0=275mueV. Several additional transport resonances scaling linearly in energy were observed at high-bias above 2Delta, up to Esimeq 15Delta_0, consistent with McMillan-Rowell oscillations. The persistence of McMillan-Rowell oscillations at high-bias and under applied magnetic field were investigated.
