Fig. 4

Tight-binding model of the edge and bulk channels. a Simulated two-point conductance as a function of the width of the mobile probe in contact with the ribbon, as shown schematically in the upper inset, capturing the characteristic stepwise features from experiment (see Fig. 2c). Lower inset: Band structure for spin-up (grey) and spin-down (red, dashed) electrons for a 188-ZGNR with edge magnetism and asymmetric potential terms. The dashed horizontal line shows the Fermi energy considered in the other panels, with the band crossings highlighted. b Schematic of the GNR. c Real-space projections of the states contributing to transmission (e.g. those at the corresponding crossing points in a) across the ribbon width. The blue and purple states are spin-degenerate, whereas the red state corresponds to the spin-polarised channel at the lower edge of the ribbon