Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion

TL;DR

This paper explores the interface between Moore-Read and Halperin 331 fractional quantum Hall states, demonstrating the emergence of a chiral Majorana fermion mode and describing phase transitions involving these states.

Contribution

It introduces a model for the interface between these states, showing how a chiral Majorana mode arises and proposing methods to detect it, advancing understanding of quantum Hall phase transitions.

Findings

Charge modes localize at the interface with a chiral Majorana mode remaining

Quantum phase transition described by a network of Majorana modes

Possible intermediate phase with delocalized Majorana fermions and unique transport properties

Abstract

We consider an interface separating the Moore-Read state and Halperin 331 state in a half filled Landau level, which can be realized in a double quantum well system with varying inter-well tunneling and/or interaction strength. We find in the presence of electron tunneling and strong Coulomb interaction across the interface, all charge modes localize and the only propagating mode left is a chiral Majorana fermion mode. Methods to probe this neutral mode are proposed. Quantum phase transition between the Moore-Read and Halperin 331 states is described by a network of such Majorana fermion modes. In addition to a direct transition, they may also be separated by a phase in which the Majorana fermions are delocalized, realizing an incompressible state which exhibits quantum Hall charge transport and bulk heat conduction.