Distinguishing between non-abelian topological orders in a quantum Hall system

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological Quantum Matter

Background:

• Quantum Hall states exhibit exotic quantum phases with gapless edge modes governed by bulk-edge correspondence.
• The filling factor (ν) = 5/2 state is a prime candidate for non-abelian topological order, with potential for both abelian and non-abelian phases.

Purpose of the Study:

• To develop a novel method for interfacing quantum states to identify the topological order of the ν = 5/2 state.
• To experimentally distinguish between competing topological orders, specifically particle-hole Pfaffian (PH-Pf) and anti-Pfaffian, in the ν = 5/2 quantum Hall state.

Main Methods:

• Interfacing the ν = 5/2 quantum Hall state with an integer ν = 3 state in a half-plane geometry.
• Probing the edge modes at the interface, specifically a fractional ν = 1/2 charge mode and a neutral Majorana mode.
• Measuring the partition noise to analyze the counterpropagating chirality of the Majorana mode.

Main Results:

• The interface supported a fractional ν = 1/2 charge mode and a neutral Majorana mode.
• The measured counterpropagating chirality of the Majorana mode was consistent with the particle-hole Pfaffian (PH-Pf) topological order.
• The experimental results ruled out the anti-Pfaffian topological order for the ν = 5/2 state.

Conclusions:

• The study successfully identified the topological order of the ν = 5/2 quantum Hall state.
• The findings confirm the presence of particle-hole Pfaffian topological order, a crucial step towards realizing non-abelian anyonic states.
• The developed interface method offers a new avenue for characterizing complex topological phases in quantum systems.