This PDF file includes:

• section S1. Low-energy effective Hamiltonians
  
• section S2. Nonreciprocal tunneling in photonic graphene with a single potential barrier
  
• section S3. Specific designs of spin-valley–coupled metacrystals with one-way Dirac cones
  
• fig. S1. Photonic bands and transmission spectra.
  
• fig. S2. Schematics of the meta-waveguide design and band structures.

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