Extended Data Fig. 4: Scanning tunneling microscopy evidence for a hinge state in a four-layer step edge.
a, Topographic images of two four-layer atomic step edges of opposite geometric orientations. b, Magnified images of the two sides of the four-layer atomic step edges, revealing A type surfaces on both sides. The corresponding regions are marked as 1 and 2 in the large-scale topographic image in panel a. c, Height profiles of the topographic images in panel a, taken perpendicular to the b axis. The corresponding locations are marked on the topographic images in panel a with color-coded lines; the scan directions are indicated with arrows. d, dI/dV spectra shown in color-coding, obtained at the left step edge, right step edge, and regions away from the edge. The positions where these spectra were acquired are marked with matching color-coded dots on the topographic images in panel a. The left step edge exhibits a pronounced in-gap state, while the right step edge shows notable suppression of the density of states at the bulk gap. e, 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 whereas on the right edge, no edge state is visible. Tunnelling junction set-up for spectroscopy: V = −600 mV, I = 0.5 nA, and a root mean square oscillation voltage of 1 mV. 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. All data were obtained at T ≃ 4.2 K. f, Schematic of a four-layer edge showing quantum hybridization of the quantum spin Hall edge states for neighboring layers. The edges of A and B layers with a facing angle smaller than 180° exhibit a stronger hybridization of the monolayer edge states (depicted as purple spheres). The hybridization of quantum spin Hall edge state is destructive, as illustrated by the lighter color of the edge states (purple spheres). As a result, the left four-layer configuration hosts hinge states on the top and bottom hinges, while the right configuration lacks hinge states.
