Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

TL;DR

This study investigates the fractional quantum Hall effect at filling factor 5/2 in quantum point contacts, revealing a stable plateau and supporting the existence of an incompressible state with chiral Luttinger liquid edge-states in confined geometries.

Contribution

First experimental observation of a 5/2 quantum Hall plateau in quantum point contacts with specific widths, supporting the presence of an incompressible state and chiral edge-state behavior.

Findings

Plateau at filling factor 5/2 observed in QPCs with widths 1.2 and 0.8 microns.

Temperature and bias dependence consistent with chiral Luttinger liquid theory.

Incompressible 5/2 state forms in confined geometries, indicating potential for topological quantum computation.

Abstract

Recent theories suggest that the excitations of certain quantum Hall states may have exotic braiding statistics which could be used to build topological quantum gates. This has prompted an experimental push to study such states using confined geometries where the statistics can be tested. We study the transport properties of quantum point contacts (QPCs) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits well-developed fractional quantum Hall effect, including at bulk filling fraction 5/2. We find that a plateau at effective QPC filling factor 5/2 is identifiable in point contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5 microns. We study the temperature and dc-current-bias dependence of the 5/2 plateau in the QPC, as well as neighboring fractional and integer plateaus in the QPC while keeping the bulk at filling factor 3. Transport near QPC filling factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms in this confined geometry.