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 excitations1–3. Here we investigate transport properties of hDWs in the ν = 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. Previous work has shown that helical domain walls can form between states of different spin-polarization during a ferromagnetic spin transition in the fractional quantum Hall regime. Here, the authors study the transport through a single helical domain wall and find strong deviations from a simplified theory of weakly interacting edge channels.