We introduce a quantum spin Hall semimetal or Fermi liquid characterized with a quantized ${\mathbb{Z}}_2$ topological invariant, measurable through circularly polarized light. We propose its engineering through two topological metallic band structures in crystals on the honeycomb lattice, with spin-orbit interaction, realizable from the interplay of a charge or spin density wave substrate and Zeeman effects, in between a quantum spin Hall and a quantum anomalous Hall insulators. Also, we address time-reversal symmetry and geometrical properties of the Fermi surface through light.

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• Kane-Mele model
• Light detection
• Light-matter interaction
• Semimetals
• Topological materials
• Topological tools