Emergent spin quantum Hall edge states at the boundary of two-dimensional electron gas proximitized by an $s$-wave superconductor

Abstract: Hybrid two-dimensional electron gas-superconductor (2DEG-S) structures in a quantized magnetic field offer a promising platform for realizing new topological phases. While recent experiments reveal chiral Andreev edge states, their charge conductance is not integer quantized and is disorder sensitive, raising the question of whether topological protection survives. We argue that it does, but manifests in the spin transport channel. The 2DEG-S system belongs to symmetry class C of the Altland-Zirnbauer classification, which supports an even-integer quantized transverse spin conductivity -- the spin quantum Hall effect, so far unobserved experimentally. We demonstrate that 2DEG-S hybrids host topologically protected edge states carrying a spin current with an even-integer quantized spin conductance robust against disorder. Finally, we propose an experimental setup to probe this protection via electrical measurements, establishing a concrete route to detect the class C origin of the chiral Andreev edge states.