Science Advances

This PDF file includes:

• Electron filling in AIs
  
• Symmetries of SG No. 199
  
• feQBI tight-binding examples
  
• Hypothetical structure for spin-orbit coupled hyperkagome material Na₃Ir₃O₈
  
• Discussions on the SE cut
  
• Fig. S1. Reproduction of Fig. 1D with different viewing conditions and extra
  annotation.
  
• Fig. S2. Energy and entanglement band structure for an alternative feQBI
  example for SG No. 199.
  
• Fig. S3. Plot of band gap for the hyperkagome model in eq. S3 at filling v = 4.
  
• Fig. S4. Plot of surface band structure against the surface crystal momentum k_||
  for the model in eq. S3.
  
• Table S1. List of symmetry elements for SG No. 199.
  
• Table S2. Spin-quantization axes corresponding to the SG symmetric spin texture.
  
• Table S3. Symmetry eigenvalues of the irreducible little group representations at
  high-symmetry momenta.
  
• Table S4. Transformation of tight-binding sites under the symmetry elements.
  
• Table S5. A full list of terms in the feQBI tight-binding example given in the text.
  
• Table S6. Terms in an alternative eight-band feQBI tight-binding example.
  
• Table S7. Measured structure of Na3Ir3O8 by Takayama et al. (19).
  
• Table S8. “Symmetry-enriched” hypothetical structure of Na3Ir3O8 in SG No.
  214.

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