  Corner states (CSs) in higher-order topological insulators (HOTIs) have
recently been of great interest in both crystals and quasicrystals. In contrast
to electronic systems, HOTIs have not been found in photonic quasicrystals
(PQCs). Here, we systemically study the higher-order topology in the
two-dimensional Thue-Morse photonic quasicrystals (TM-PQCs). Not only the
topological phase transition and the non-trivial CSs with fractional charge
induced by multipole moments, but also a new type of CSs are found due to the
complex structure of TM-PQCs near corners. The different origins of these CSs
are also analyzed based on the tight-binding model. Our work opens the door to
explore richer HOT physics beyond photonic crystals and the robustness of CSs
in PQC shows the potential for applications.
