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

• Published in: Science (American Association for the Advancement of Science) Vol. 375; no. 6577; pp. 193 - 197
• Main Authors: Dutta, Bivas, Yang, Wenmin, Melcer, Ron, Kundu, Hemanta Kumar, Heiblum, Moty, Umansky, Vladimir, Oreg, Yuval, Stern, Ady, Mross, David
• Format: Journal Article
• Language: English
• Published: United States The American Association for the Advancement of Science 14.01.2022
• Subjects: Chirality; Integers; Interfaces; Low temperature; Magnetic fields; Magnetic properties; Noise measurement; Numbers; Quantum Hall effect; Topology
• ISSN: 0036-8075; 1095-9203; 1095-9203
• DOI: 10.1126/science.abg6116

Quantum Hall states, which form in two-dimensional electron gases at low temperatures and in the presence of strong magnetic fields, have long been known to have nontrivial topological properties. Among the most intriguing is the state that arises at the Landau level filling factor of 5/2. Theoretical calculations suggest several possibilities for the 5/2 ground state and associated topological order but distinguishing among them experimentally is tricky. Dutta et al . developed a method for doing so by interfacing a region in the 5/2 state with a region at an integer filling, and the measurements provided support for the particle-hole Pfaffian order. The technique can be used for the investigation of other exotic states in the quantum Hall setting. —JS Noise measurements lend support for the particle-hole Pfaffian topological order at the 5/2 Landau level filling. Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to “bulk-edge” correspondence. The most studied putative non-abelian state is the spin-polarized filling factor (ν) = 5/2, which permits different topological orders that can be abelian or non-abelian. We developed a method that interfaces the studied quantum state with another state and used it to identify the topological order of ν = 5/2 state. The interface between two half-planes, one hosting the ν = 5/2 state and the other an integer ν = 3 state, supports a fractional ν = 1/2 charge mode and a neutral Majorana mode. The counterpropagating chirality of the Majorana mode, probed by measuring partition noise, is consistent with the particle-hole Pfaffian (PH-Pf) topological order and rules out the anti-Pfaffian order.