Fig. 2: Conduction of helical domain walls.
From: Transport in helical Luttinger liquids in the fractional quantum Hall regime
a A simplified picture of noninteracting chiral edge modes at ν = 2/3. An inner spin-up edge (red) in p state carries current I while a spin-down edge (blue) in u state carries no current. b Charge conservation and chirality of edge states set the potential V4 = ν−1IDWRq to be proportional to the current IDW diverted via the helical domain wall. c Scaling of the domain wall current iDW = IDW/I with hDWs length L. The values are averaged between up and pu states (within red circles in Fig. 1d), error bars are standard deviations. Red line is a fit to an exponential decay with the L = 0 value \({i}_{{{{{{\mathrm{DW}}}}}}}^{0}=0.115\) and the decay length L0 = 47 μm. Arrows indicate \({i}_{{{{{{\mathrm{DW}}}}}}}^{0}\) values expected for naive noninteracting edge model (blue) and Luttinger liquid model in the absence of spin-flip (red) and at spin-flip probability r = 3/4 (green), see text for details. Vertical arrow marks iDW shift when Idc = 1 nA is applied. In the inset iDW dependence on large external dc current is plotted for 7 μm hDW for up and pu gates configuration right after the dc current is applied and before a measurable build-up of nuclear polarization.
