Superconductivity Induced Topological Phase Transition at the Edge of Even Denominator Fractional Quantum Hall States

We show that every even-denominator fractional quantum Hall (FQH) state possesses at least two robust, topologically distinct gapless edge phases if charge conservation is broken at the boundary by coupling to a superconductor. The new edge phase allows for the possibility of a direct coupling between electrons and emergent neutral fermions of the FQH state. This can potentially be experimentally probed through geometric resonances in the tunneling density of states at the edge, providing a probe of fractionalized, yet electrically neutral, bulk quasiparticles. Other measurable consequences include a charge $e$ fractional Josephson effect, a charge $e\mathrm{/}4q$ quasiparticle blocking effect in filling fraction $p\mathrm{/}2q$ FQH states, and modified edge electron tunneling exponents.