Irreducible proper 2-knots from exotic open 2-handles

We construct infinite families of irreducible exotic proper knotted surfaces in ${\mathbb{R}}^4$, making progress on a question of Gompf. Here irreducible means these surfaces are not end-sums of standard surfaces with exotic planes. To prove the topological equivalence, we give a highly flexible construction of exotic open 2-handles, which generalizes several similar constructions in the literature. We distinguish exotic surfaces through the genus functions and end Floer homology of their double branched covers. By studying these generalized handles further, we construct a new family of topologically slice links.