Mixed crystalline-electromagnetic response in non-symmorphic topological semimetals

Characterize the structure of non-symmorphic symmetry fluxes and determine the mixed crystalline-electromagnetic response of non-symmorphic topological semimetals by constructing the appropriate discrete gauge fields for non-symmorphic symmetries and deriving quantized crystalline-electromagnetic response terms (e.g., analogs of the R∧F and discrete Wen–Zee terms).

Background

The paper develops crystalline-electromagnetic response theory for Dirac semimetals gapped by charge density waves (Dirac-CDW insulators), identifying a layered discrete Wen–Zee term and an R∧F term that capture quantized charge bound to disclination defects and a disclination filling anomaly in inversion-symmetric, commensurate cases.

These results rely on a clear understanding of symmetry fluxes for symmorphic rotations (e.g., C4z), enabling the coupling of electronic degrees of freedom to crystalline gauge fields. Extending such mixed response theories to non-symmorphic topological semimetals requires analogous flux constructions for non-symmorphic symmetries, which the authors note are currently not understood, leaving the broader mixed crystalline-electromagnetic response in the non-symmorphic setting unresolved.