Fig. 4: Tight binding calculation of linearly dispersing states within a potential well.

a Schematic of coupled Chern insulator layers (C.I.) with alternating spacer layers (S.L) , with a Chern insulator terrace (top panel), a simple stack that mimics our geometry. The red and blue circles indicate 1D chiral modes traveling out of and into the page, respectively, with the red and blue trails indicating their power-law decay into the bulk. The bottom panel is a numerical simulation of 70 full Chern insulator layers plus two partial layers as shown in the top panel. The bright regions in the bottom panel show the numerically calculated chiral edge states on the exposed terrace and their decay into the bulk. b Schematic of the narrow, confined Co₃Sn terraces. The exposed Chern insulator layer (Co₃Sn plane) hosts chiral edge states, and when the terrace is sufficiently narrow, the two counterpropagating states will overlap and interact, as shown by the red and blue curves. c Low energy dispersion for different parameters of m and V. With no mixing or potential well, two linearly dispersing bands cross at zero momentum (light yellow left panel). Adding a mixing term of five percent of the bandwidth, a gap opens as the two bands hybridize (light blue middle panel). Further adding the potential of ten percent of the bandwidth increases the energy of all states and causes five states to be confined entirely within the potential well (light green right panel), indicated by the colored dots within the gap. d Wavefunctions of the confined, linearly dispersing states shown in e. e Dispersion of the states confined within the potential well from the light green panel in c. A straight dashed line is provided as a guide to the eye.