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We investigate theoretically the Landau levels (LLs) and magneto-transportproperties of phosphorene under a perpendicular magnetic field within theframework of the effective \textbf{\emph{k$\cdot$p}} Hamiltonian andtight-binding (TB) model. At low field regime, we find that the LLs linearlydepend both on the LL index $n$ and magnetic field $B$, which is similar withthat of conventional semiconductor two-dimensional electron gas. The Landausplittings of conduction and valence band are different and the wavefunctionscorresponding to the LLs are strongly anisotropic due to the differentanisotropic effective masses. An analytical expression for the LLs in lowenergy regime is obtained via solving the decoupled Hamiltonian, which agreeswell with the numerical calculations. At high magnetic regime, a self-similarHofstadter butterfly (HB) spectrum is obtained by using the TB model. The HBspectrum 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 findthe LLs of phosphorene nanoribbon depend strongly on the ribbon orientation dueto the anisotropic hopping parameters. The Hall and the longitudinalconductances (resistances) clearly reveal the structure of LLs.

Landau levels and magneto-transport property of monolayer phosphorene