Fig. 5: Frequency-dependent topological routings based on HTPC structures.

a, e Illustration of frequency-dependent topological routing based on different configurations: a Z-shaped boundary with HTPC1 on the left and e Z-shaped boundary with HTPC2 on the left. In a the edge waves with a lower (higher) frequency in gap II (III) propagate from P1 to P3 (P4), as indicated by the orange (green) arrows. In e, the edge waves with a lower (higher) frequency in gap II (III) propagate from P4 (P3) to P2, as indicated by the orange (green) arrows. b, f The simulated transmission spectra for (b) and (f) that confirm the frequency-selective topological routing in (a) and (e): i.e., gap II is dominated by the straight edge channels whereas gap III is dominated by the Z-shaped and inverted Z-shaped edge channels. The light yellow (green) region refers to gap II (III). c, g Typical simulated electric field distributions of the straight edge channel in gap II for the configurations in (a) and (e). Here, the electromagnetic waves are excited by point sources (the orange stars) with a frequency of 10.8 GHz. d, h Typical simulated electric field distributions of the Z-shaped and inverted Z-shaped edge channels in gap III for the configurations in (a) and (e), which are excited by point sources (the green stars) with a frequency of 12.4 GHz.