Fig. 3: Behaviour of the kink states for varying magnetic field.

a Conductance as a function of filling factor shown for various magnetic fields at E = 0 (top) and E = 25 mV nm⁻¹ (bottom) measured in device D1-DW. The cross indicates the sharp conductance dip caused by the opening of a minigap. Note, that the state emerging around zero density is the LAF/CAF state, only at E = 25 mV nm⁻¹ the data curve for B = 1.5 T shows the transition between LAF/CAF and LP phase, see also Supplementary Fig. 2. b Conductance of the \(\nu \,=\,0,-1,-2,-4\) quantum Hall states as well as within the minigap as a function of magnetic field. The data for device D1-DW (D2) is shown in black (red). c Schematic band structure around the domain wall shown for the LAF, CAF and FM \(\nu \,=\,0\) phases. The blue (red) lines indicate the chiral states in the \({{{{{\rm{K}}}}}}\)(\({{{{{\rm{K}}}}}}{^\prime}\))-valley. The cross indicates the spectral minigap emerging in the CAF phase. d Schematic band structure for \(\nu \,=\,2\) (orbital index is implicit) in the presence of layer-polarising bias. The domain wall retains only two pairs of valley helical (spin polarised) states, indicated by black circles with in-plane and out-of-plane directions. Their backscattering rate at the chemical potential (thin horizontal line) depends on their spatial separation and width. Both are generally expected to change as a function of magnetic field, leading to a change in DW conductance. The influence of the magnetic field is indicated by grey arrows. A similar effect was observed in artificial domain walls⁷.