Extended Data Fig. 5: Reproducibility of the scanning tunneling microscopy data– evidence for a hinge state in a four-layer step edge, acquired using a different sample and tip.

a, Topographic images of two four-layer atomic step edges with opposite geometric orientations. The terraces on both sides of the step edges exhibit an A-type surface. b, Height profiles of the topographic images in panel a, taken perpendicularly to the b axis. The corresponding locations are marked on the topographic images in panel a with color-coded lines, and the directions of the scans are indicated by arrows. c, Differential conductance maps of the two four-layer atomic step edges shown in panel a, taken at the Fermi energy (V = 0 mV). A pronounced edge state is observed on the left edge, while no edge state is visible on the right edge. d, dI/dV spectra taken at the left step edge (orange), right step edge (green), and away from the edge (purple), revealing striking differences between the two step edges. Orange and green dots in panel a denote the respective positions, on the left and right step edges, where the differential spectra were collected. The left step edge exhibits a pronounced in-gap state, whereas on the right edge, the density of states at the bulk gap is notably suppressed. Tunnelling junction set-up for dI/dV maps: V = −600 mV, I = 0.3 nA, and a root mean square oscillation voltage of 10 mV. Tunnelling junction set-up for spectroscopy: V = −600 mV, I = 0.5 nA, and a root mean square oscillation voltage of 1 mV. All data were obtained at T≃4.2 K and are consistent with Extended Data Fig. 4 results.