Crystalline axion electrodynamics in charge-ordered Dirac semimetals
arxiv(2024)
摘要
Three-dimensional Dirac semimetals can be driven into an insulating state by
coupling to a charge density wave (CDW) order. Here, we consider the quantized
crystalline responses of such charge-ordered Dirac semimetals, which we dub
Dirac-CDW insulators, in which charge is bound to disclination defects of the
lattice. Using analytic and numeric methods we show the following. First, when
the CDW is lattice-commensurate, disclination-line defects of the lattice have
a quantized charge per length. Second, when the CDW is inversion-symmetric,
disclinations of the lattice have a quantized electric polarization. Third,
when the CDW is lattice-commensurate and inversion-symmetric, disclinations are
characterized by a "disclination filling anomaly" – a quantized difference in
the total charge bound to disclination-lines of Dirac-CDW with open and
periodic boundaries. We construct an effective response theory that captures
the topological responses of the Dirac-CDW insulators in terms of a total
derivative term, denoted the R∧ F term. The R∧ F term describes
the crystalline analog of the axion electrodynamics that are found in Weyl
semimetal-CDW insulators. We also use the crystalline responses and
corresponding response theories to classify the strongly correlated topological
phases of three-dimensions Dirac-semimetals.
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