Proximity effects and tunneling in an Ising superconductor-magnetic insulator heterostructure.

Hybrid Ising superconductor-ferromagnetic insulator heterostructures provide a unique opportunity to explore the interplay between proximity-induced magnetism, spin-orbit coupling and superconductivity. Here we use a combination of first-principles calculations of NbSe$_{2}$/CrBr$_{3}$ heterostructures and an analytical theory of Ising superconductivity in the presence of defects, and propose a number of nontrivial effects are at play in such junctions. In particular, we address spin and momentum filtering in such junctions and show that tunneling of the states at the K-point are suppressed and the often overlooked states near the $\Gamma$-point in monolayer NbSe$_{2}$ contribute to tunneling. We then show that the interplay of the proximity-induced exchange splitting and scattering off paramagnetic defects leads to the following nontrivial effects; an increase in the magnitude of the superconducting gap, broadening of the tunneling peaks and $C_{2}$ symmetry breaking. Our results provide a unifying microscopic description of tunneling spectroscopy studies performed on two-dimensional Josephson junction heterostructures which form the basis for novel spintronic and superconducting devices.