Effect of Zeeman Splitting on Andreev Reflection in Quantum Hall--Superconductor Heterostructures

We study the effect of Zeeman splitting on Andreev processes and non-local transport in heterostructures formed by two-dimensional systems in the superconducting and integer quantum Hall regime. We obtain analytic expressions for the dependence of the Andreev reflection probabilities on the Zeeman splitting in the narrow-contact and long-contact limits using an low-energy effective edge-state Hamiltonian within the Bogoliubov de-Gennes formalism. We find that introducing a higher-order, spin-dependent contribution to the renormalized drift velocity in the effective model is important to obtain accurate results. We then correlate the scattering wave function's penetration into the superconducting region with the observed Andreev reflection probabilities.