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

Abstract

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 $e/4q$ quasiparticle blocking effect in filling fraction $p/2q$ FQH states, and modified edge electron tunneling exponents.

Figures (2)

• Figure 1: (a) Experimental setup for probing quasiparticle backscattering across a QPC. Blue edges indicate the original edge phase and red edges indicate the new, superconductivity-induced edge phase. Dashed lines indicate quasiparticle tunneling. The light red block is a superconductor. (b) Setup for measuring fractional Josephson effect in S-FQH-S junction.
• Figure 2: Possible experimental setup for detecting coherent transmutation of electrons into neutral emergent fermions of the FQH state. Red edge indicates new superconductivity-induced edge phase. Dashed green line indicates the $Z_2$ gauge field that couples to the emergent fermion in the bulk of the FQH state, and which terminates at the new boundary phase.