Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices

We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The selection of the sublattice depends on the strain orientation but is independent of the valley. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly affects the mode selection and lasing threshold while in three-dimensional photonic lattices it can be probed via the beam dynamics.