  Here we comprehensively investigate Landau levels, Hofstadter butterfly and
transport properties of a semi-Dirac nanoribbon in a perpendicular magnetic
field using a recently developed real-space implementation of the Kubo formula
based on Kernel Polynomial Method. A Dirac ribbon is considered to compare and
contrast our results for a semi-Dirac system. We find that the Landau levels
being non-equidistant from each other for the semi-Dirac case (true for a Dirac
as well), the flatness of the energy bands vanishes in the bulk and becomes
dispersive for a semi-Dirac ribbon in contrast to a Dirac system. This feature
is most discernible for intermediate values of the external field. We further
compute the longitudinal ($\sigma_{xx}$ and $\sigma_{yy}$) and the transverse
or Hall ($\sigma_{xy}$) conductivities where the Hall conductivity shows a
familiar quantization, namely, $\sigma_{xy} \propto 2n$ (the factor `2'
includes the spin degeneracy) which is highly distinct from a Dirac system,
such as graphene. We also observe anisotropic behavior in magneto-transport in
a semi-Dirac ribbon owing to the dispersion anomalies in two different
longitudinal directions. Our studies may have important ramifications for
monolayer phosphorene.
