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

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.

4.5 pages with 3 embedded figures. Published version with added reference

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• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Identifying non-Abelian anyons with upstream noise
• Model wavefunctions for interfaces between lattice Laughlin states
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Fractional quantum Hall interface induced by geometric singularity