Transport in helical Luttinger liquids in the fractional quantum Hall regime

Abstract

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Here we investigate transport properties of hDWs in the $\nu =2/3$ fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

26 pages, 8 figures

References in corpus (6)

• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Fractional topological superconductors with fractionalized Majorana fermions
• A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Transmission of heat modes across a potential barrier

Cited by in corpus (9)

• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Shot noise as a diagnostic in the $\nu =2/3$ fractional quantum Hall edge zoo
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Localization and conductance in fractional quantum Hall edges
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
• Spin responses of a disordered helical superconducting edge under Zeeman field
• Superconductivity of neutral modes in quantum Hall edges
• Phase diagram of an extended parafermion chain