  Three-dimensional (3D) metals/semimetals under magnetic field have an
instability toward a density wave (DW) ordering which breaks a translational
symmetry along the field direction. Effective boson models for the DW phases
take forms of XY models with/without Potts terms. Longitudinal conductivity
along the field direction is calculated in the DW phases with inclusion of
effects of low-energy charge fluctuation (phason) and disorder. A
single-particle imaginary-time Green function is identified with a partition
function of 3D XY models in the presence of pairs of magnetic monopoles. In
terms of the celebrated electromagnetic duality, electronic spectral function
is calculated near the DW phase transition. The result shows that the
single-particle spectral function acquires an additional low-energy feature due
to the strong phason fluctuation. Relevance to an in-plane conductance due to
surface chiral Fermi arc states are also discussed.
