Transport in helical Luttinger liquids in the fractional quantum Hall regime

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naively, 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(1-3). 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 naive 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.

Automated summary

Experimental observation in the fractional quantum Hall regime shows that the current carried by hDWs is significantly smaller than predicted by the naive model. Theoretical analysis using Luttinger liquid theory reveals a redistribution of currents between quasiparticle charge, spin, and neutral modes, leading to the reduction of the hDW current. Including spin-non-conserving tunneling processes reconciles theory with experiment and confirms the emergence of spin modes necessary for the formation of fractional topological superconductivity.