Fig. 1. Valley TPC structure and spectrum band. (a) Artistic illustration of switchable 2D topological PC consisting of hexagonal GST and Si rods; (b) schematic illustration of honeycomb lattice unit cells of PC1 and PC2. The gray and green rods represent Si and GST rods, respectively. d₁ and d₂ denote the distances between the opposite sides of small and large hexagonal rods, respectively; (c) band structure of TM mode for PC1/PC2 when GST is in an amorphous state. The inset shows the first Brillouin zone; (d) phase vortex of E_z at the K/K' valley for PC1 and PC2. The white arrows denote the power flow

Fig. 2. TES in topological PCs. (a) Schematic of TPC constructed by PC1 and PC2 with a bearded interface (type A); (b) band structure of TPC when GST is in the amorphous phase. The blue region denotes the bulk band, and the green curve represents the edge band. The blue ring belongs to topological TES, and the red and yellow marks indicate bulk states located in the band spectrum; (c) |E|² distributions of topological TES and bulk states. The pinkish red arrows in the enlarged figure represent the direction of power flow; (d) |E|² distributions of topological TES and bulk states along the vertical midline (gray line) in Fig. 2(c). The yellow-shaded region marks the area around the interface with a width of two lattice constants

Fig. 3. Field maps of TESs and their transmission properties. (a) (b) Intensity maps of |E|² of TES on the x-y plane for straight and Z-shaped interface structures. A magnetic dipole source with f = 0.2974 c/a is located at the left end of the interface; (c) transmission spectra of the straight and Z-shaped interface structures. The colored region denotes the bandgap of TPC; (d) (e) intensity maps of |E|² for chiral point sources S_- and S₊ with f = 0.3049 c/a. The light source is located at the center of the interface. The insets show a sketch of the unidirectional transport of TESs; (f) |E|² distribution along the interfaces in Figs. 3(d) and 3(e). The data of |E|² come from the maxima along the interfaces in Figs. 3(d) and 3(e), and then we interpolate many points to create smooth curves; (g) intensity map of |E|² of TESs in the interface structure with defects of square gold rods. The side width of square gold rods is 0.2a. A magnetic dipole source with f = 0.2974 c/a is located at the left end of the interface; (h) intensity map of |E|² in the region of the sample denoted by the white dashed rectangle in Fig. 3(g). The green square gold rods denote defects, and the pinkish red arrows represent power flow; (i) |E|² distribution along the interface in Fig. 3(g)

Fig. 4. TESs switched by the phase change of GST. (a) Schematic of unit cells with rods of phase change material GST. The relative permittivities of amorphous and crystalline GSTs are taken as 16 and 34, respectively; (b) band structures of PC1 (PC2) when GST is in amorphous and crystalline phases; (c) band structure of TPC [Fig. 2(a)] when GST is in crystalline phase. The blue regions denote bulk bands of TPC, and the green curve represents edge bands; (d) (e) intensity maps of |E|² on the x-y plane for the straight and Z-shaped interface structures when GST is in the crystalline phase. A magnetic dipole source with f = 0.2419 c/a is located at the left end of the interface; (f) transmission spectra of straight and Z-shaped interface structures. The colored region denotes the bandgap of TPC; (g) (h) intensity maps of |E|² at f = 0.2325 c/a. A chiral point source S_-(S₊) is located at the center of the interface; (i) |E|² distribution along the interface in Figs. 4(g) and 4(h). The data of |E|² come from the maxima along the interface in Figs. 4(g) and 4(h), and we then interpolate many points to make a smooth curve

Fig. 5. TCSs in triangular PC structure with the interface of type C. (a) (b) Eigenfrequencies of the triangular PC structure when GST is in amorphous and crystalline phases. The blue, purple (green), and orange dots represent bulk, edge, and corner states, respectively, and the colored region indicates the range of edge bands. The inset shows a sketch of the triangular topological PC structure; (c) intensity map of |E|² of the corner state at the eigenfrequency of f = 0.2947 c/a when GST is in amorphous phase (I), and intensity map of |E|² of the corner state excited by chiral point source S₊ with f = 0.2947 c/a (II); (d) intensity maps of |E|² of corner states at the eigenfrequencies of f = 0.2293 c/a (I) and 0.2607 c/a (III) when GST is in crystalline phase, and intensity maps of |E|² of the corner states excited by chiral point source S₊ with f = 0.2293 c/a (II) and 0.2607 c/a (IV)

Fig. 6. Sketch of reconfigurable multichannel optical router. The large and small hexagons denote silicon and GST rods, respectively. The blue and red lines represent the topological interfaces of types A and B, respectively

Fig. 7. Reconfigurable multichannel optical router based on TPCs with GST. (a) Sketches of our designed optical router. I‒IV correspond to four different states of channels A (from port 1 to port 2) and B (from port 3 to port 4), respectively, i.e., the states of on-off (I), off-on (II), off-off (III), and on-on (IV). The green and purple regions denote PCs in which GST rods are in amorphous and crystalline phases, respectively. The white solid and dashed lines with arrows represent the"on"and"off"states of channels, respectively. The blue and red lines denote the interfaces of types A and B, respectively; (b) (c) maps of the power flow of four states of channels A and B. The operation frequencies of channels A and B are 0.2908 c/a (f₁) and 0.2431 c/a (f₂), respectively. A chiral point source S₊ for the excitation of TESs is set at ports 1 and 3; (d) (e) values of power flow at the outputs of channels A and B (i.e., ports 2 and 4) for four states