Figure 3

(a1,b1,c1) Comparison of the bulk band structures calculated with the \(8\times 8\) Kane model (black dashed lines) and the effective 2D 3\(\times\)BHZ model (solid lines) with E-like subbands in purple and H-like subbands in blue. The panels correspond to the phases I, II and III indicated by the cyan stars in Fig. 2b. (a2,b2,c2) Band structures for a nanoribbon geometry of width \(L_y = 1000\) nm shown by the local density of states of the bulk (gray tones) and edges (orange and green tones). The E-k range match the shaded regions from the panels above. The 3\(\times\)BHZ bulk subbands are shown as the solid lines as a guide to the eyes. (a2) For \(d_0=6\) nm the topological regime with one E-subband below the H subbands shows one pair of topological edge state (orange) and two pairs of trivial edge states (green). (b2) As a second E-subband crosses the H subbands for \(d_0=7\) nm one gets two topological edge states a single trivial edge state. (c2) For \(d=8.5\) nm the system reaches the full topological regime with three topological edge states and a well defined gap. (a3,b3) Zoom into the rectangles of (a2,b2) emphasizing the edge states. All of the subbands above are spin-degenerate.