  The light-mater interactions for an emitter coupling to the bulk region of a
Hofstadter lattice has recently investigated by De Bernardis \textit{et al.}
[D. De Bernardis, Z.-P. Cian, I. Carusotto, M. Hafezi, and P. Rabl,
\href{https://link.aps.org/doi/10.1103/PhysRevLett.126.103603}{Phys. Rev. Lett.
126, 103603 (2021)}]. We propose the light-mater interactions in an extended
Hofstadter lattice with the next-nearest neighbor (NNN) couplings. Compared
with the standard Hofstadter lattice, the NNN couplings break the mirror
symmetry and the energy bands are not flat, i.e., dispersive with nonzero group
velocity. In contrast to the study by De Bernardis \textit{et al.}, when a
two-level emitter interacts with the bulk region of extended Hofstadter
lattice, the emitter is no longer tapped by the coherent oscillations with the
flat band, and can radiate photons unidirectional. The chiral mechanism stems
from the broken parity symmetry. Both the radiation rate and the chirality
periodically change with the emitter's coupling position. All of those
particular features can be realized on the photonic lattice platform and may
find potential application in chiral quantum information processing.
