  We investigate theoretically the Landau levels (LLs) and magneto-transport
properties of phosphorene under a perpendicular magnetic field within the
framework of the effective \textbf{\emph{k$\cdot$p}} Hamiltonian and
tight-binding (TB) model. At low field regime, we find that the LLs linearly
depend both on the LL index $n$ and magnetic field $B$, which is similar with
that of conventional semiconductor two-dimensional electron gas. The Landau
splittings of conduction and valence band are different and the wavefunctions
corresponding to the LLs are strongly anisotropic due to the different
anisotropic effective masses. An analytical expression for the LLs in low
energy regime is obtained via solving the decoupled Hamiltonian, which agrees
well with the numerical calculations. At high magnetic regime, a self-similar
Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB
spectrum is consistent with the Landau level fan calculated from the effective
\textbf{\emph{k$\cdot$p}} theory in a wide regime of magnetic fields. We find
the LLs of phosphorene nanoribbon depend strongly on the ribbon orientation due
to the anisotropic hopping parameters. The Hall and the longitudinal
conductances (resistances) clearly reveal the structure of LLs.
