Fig. 1. THz CESs VPC. (a) Schematic view of the proposed all-silicon VPC. The purple and magenta structures of the VPC denote the bulk region and the VPC–air boundary region, respectively. The brown dashed lines show Wigner–Seitz and unit cells. The lattice constant a = 750 µm and thickness h = 500 µm. (b) Left panel, schematic illustration of the graphene honeycomb lattice with a zigzag edge at the bottom boundary. The magenta and black dashed rhombuses denote the bulk and outmost unite cell, respectively. Right panels, two types of unit cells with the side lengths of the equilateral triangle air holes l₁ = l₀ + Δl, l₂ = l₀− Δl, where l₀ = 375 µm, Δl = a/8, and l₃ = 550 µm. (c) Bulk band structures for the cases Δl = 0 (blue dashed line) and Δl = a/8 (red solid line). Black dashed lines indicate the air light line. The inset shows the first Brillouin zone. (d) Dispersion of the CESs with the edge parameter l₃ = 550 µm. The blue solid and dashed lines indicate positive (forward) and negative (backward) group velocity, respectively. The shaded regions denote the projections of bulk bands. The inset shows the H_z field profile at the zigzag edge. (e) Eigenmode profiles and phase profiles of K₁-state and K₂-state at the K valley. The black cones represent Poynting power flows.

Fig. 2. Robust transport of CESs. (a), (b) Diagram of the straight and 120°-turning interfaces of CESs VPC. The orange and black dashed lines mark the VPC–air interface and bulk states, respectively. Port 1 and Port 2 are the exciting and receiving ends of electromagnetic signals. (c), (d) The |H_z| intensity distributions of straight and 120°-turning interfaces at 110 GHz. (e) The |H_z| field distribution when a cuboid scatterer made of copper is placed near the interface. (f) Transmission of the bulk states and the CESs. The transmission efficiencies are calculated by the ratio of power integrations in the Supplementary Material Section S4.

Fig. 3. Unidirectional transport of CESs by using a circularly polarized chiral source. (a), (b) The |H_z| field distributions at 110 GHz when an opposite circularly polarized source marked by green or yellow stars is placed in the middle of the external boundary of VPC. Bottom side, arrangement of the four-dipole source array and the corresponding RCP and LCP phase vortex. (c), (d) The Poynting vectors of the left-handed and right-handed unidirectional waveguides, respectively.

Fig. 4. Smooth inner-chip state transition between kink states and CESs. (a) The schematic diagram of inner-chip connection between two states when the NFC chip is employed in a mobile phone, with the NFC chip positioned at the boundary of the silicon wafer. The kink states connect the NFC chip to the internal chips. (b) The VPC with both kink states and CESs. The VPC 1 and VPC 2 form a domain wall (the red line) that supports the valley kink states, and the zigzag boundary of VPC (the blue lines) with edge parameter l₃ = 550 µm that supports the CESs. The zigzag boundaries and the domain wall intersect at sharp angles. (c) Dispersion of valley kink states at the domain wall. The inset shows the profile of the H_z field around the domain wall. (d) The |H_z| field map at 110 GHz. (e) Transmission spectrum received from Port 2 and Port 3 when excited at Port 1.

Fig. 5. A fantasy of the wireless interconnection system between mobile phones based on NFC chips. (a) The schematic illustration of the interchip wireless interconnection system based on NFC chips. The internal structure diagrams of mobile phones with NFC chips are depicted to illustrate the wireless interconnection system. The VPC–air boundaries of the NFC Chip 1 and NFC Chip 2 are aligned and separated by d. Two sheets of PP film (ϵ_PP= 2.1) are added between the chips to represent the phone casing. The layers of the NFC chip are numbered by N. Port 1 is the exciting end of electromagnetic signals, and Port 2 and Port 3 are the receiving ends. (b) The |H_z| field distribution of the system with N = 10, d = 0.7 mm at 110 GHz when Port 1 is excited. (c) The S-parameters of the systems with N = 4, 7, and 10 at d = 0.7 mm. (d) The S-parameters of the systems with d = 0.9 and 2 mm at N = 10.