  Two-dimensional Dirac semimetals have attracted much attention because of
their linear energy dispersion and non-trivial Berry phase. Graphene-like 2D
Dirac materials are gapless only within certain approximations, e.g., if
spin-orbit coupling (SOC) is neglected. It has recently been reported that
materials with nonsymmorphic crystal lattice possess symmetry-enforced
Dirac-like band dispersion around certain high-symmetry momenta even in the
presence of SOC. Here we calculate the optical absorption coefficient of
nonsymmorphic semimetals, such as $\alpha$-bismuthene, which hosts two
anisotropic Dirac cones with different Fermi velocities along $x$ and $y$
directions.We find that the optical absorption coefficient depends strongly on
the anisotropy factor and the photon polarization. When a magnetic field is
applied perpendicular to the plane of the material, the absorption coefficient
also depends on an internal parameter we termed the mixing angle of the band
structure. We further find that an in-plane magnetic field, while leaving the
system gapless, can induce a Van-Hove singularity in the joint density of
states: this causes a significant enhancement of the optical absorption at the
frequency of the singularity for one direction of polarization but not for the
orthogonal one, making the optical properties even more strongly dependent on
polarization. Due to the anisotropy present in our model, the Dirac cones at
two high-symmetry momenta in the Brillouin zone contribute very differently to
the optical absorbance. Consequently, it might be possible to preferentially
populate one valley or the other by varying photon polarization and frequency.
These results suggest that nonsymmorphic 2D Dirac semimetals are excellent
candidate materials for tunable magneto-optic devices.
