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Z. Li et al.
Fig. 15.21 a Nanoribbon with armchair edges (closed boundaries in the x-direction and open
boundaries in the y-direction). The dashed black rectangle is the unit cell. Band dispersions with
different geometric parameters as denoted in Fig. 15.20d: d 1 = 3.6r, d 2 = 2.08r (b), d 1 = d 2 =
3.6r (c), and d 1 = 2.08r, d 2 = 3.6r (d). The dashed blue frame in (d) indicates the band of nonchiral edge states. D is the width of the nanoribbon. Images are taken from [137]
A parallelogram-shaped vortex lattice is considered to visualize the second-order
corner states, as shown in Fig. 15.20b, where d 1 = 2.08r and d 2 = 3.6r . From the
spectrum (see Fig. 15.22a), one can clearly see that there exist a few degenerate
modes in the band gap. To distinguish these states, the spatial distribution of vortex
gyrations are plotted for each mode in Fig. 15.22b–f. Three types of corner states
are confirmed, all of which have oscillations highly localized at obtuse-angled or
Z. Li et al.
Fig. 15.21 a Nanoribbon with armchair edges (closed boundaries in the x-direction and open
boundaries in the y-direction). The dashed black rectangle is the unit cell. Band dispersions with
different geometric parameters as denoted in Fig. 15.20d: d 1 = 3.6r, d 2 = 2.08r (b), d 1 = d 2 =
3.6r (c), and d 1 = 2.08r, d 2 = 3.6r (d). The dashed blue frame in (d) indicates the band of nonchiral edge states. D is the width of the nanoribbon. Images are taken from [137]
A parallelogram-shaped vortex lattice is considered to visualize the second-order
corner states, as shown in Fig. 15.20b, where d 1 = 2.08r and d 2 = 3.6r . From the
spectrum (see Fig. 15.22a), one can clearly see that there exist a few degenerate
modes in the band gap. To distinguish these states, the spatial distribution of vortex
gyrations are plotted for each mode in Fig. 15.22b–f. Three types of corner states
are confirmed, all of which have oscillations highly localized at obtuse-angled or