  Photonic topological materials with a broken time reversal symmetry are
characterized by nontrivial topological phases, such that they do not support
propagation in the bulk region but forcibly support a nontrivial net number of
unidirectional edge states when enclosed by an opaque type boundary, e.g., an
electric wall. The Haldane model played a central role in the development of
topological methods in condensed matter systems, as it unveiled that a broken
time reversal is the essential ingredient to have a quantized electronic Hall
phase. Recently, it was proved that the magnetic field of the Haldane model can
be imitated in photonics with a spatially varying pseudo Tellegen coupling.
Here, we use a Greens function method to determine from first principles the
band diagram and the topological invariants of the photonic Haldane model,
implemented as a Tellegen photonic crystal. Furthermore, the topological phase
diagram of the system is found, and it is shown with first principles
calculations that the granular structure of the photonic crystal can create
nontrivial phase transitions controlled by the amplitude of the pseudo Tellegen
parameter.
