Development of new, high quality functional materials has been at the forefront of condensed matter research. The recent advent of two-dimensional black phosphorus has greatly enriched the material base of two-dimensional electron systems.Significant progress has been made to achieve high mobility black phosphorus twodimensional electron gas (2DEG) since the development of the first black phosphorus field-effect transistors (FETs) [1][2][3][4] . Here, we reach a milestone in developing high quality black phosphorus 2DEG -the observation of integer quantum Hall (QH) effect. We achieve high quality by embedding the black phosphorus 2DEG in a van der Waals heterostructure close to a graphite back gate; the graphite gate screens the impurity potential in the 2DEG, and brings the carrier Hall mobility up to 6000. The exceptional mobility enabled us, for the first time, to observe QH effect, and to gain important information on the energetics of the spin-split Landau levels in black phosphorus. Our results set the stage for further study on quantum transport and device application in the ultrahigh mobility regime.Quantum Hall effect, the emergence of quantized Hall resistance in 2DEG sample when subjected to low temperatures and strong magnetic fields, has had a lasting impact in modern condensed matter research. The exact, universal quantization regardless of detailed sample geometry and impurity configuration has enabled the establishment of a metrological resistance standard, and served as the basis for an independent determination of the fine structure constant 5 . Even though the exact quantization of the Hall resistance relies on certain amount of impurities 6 , the observation of QH effect, paradoxically, requires high-purity, low-defect specimens. Because of the stringent requirement on the ). In this work, we achieved high Hall mobility in black phosphorus FETs that is significantly higher than previous record value. This is accomplished by constructing a van der Waals heterostructure with the few-layer black phosphorus sandwiched between two hBN flakes (Fig. 1a,b) and placed on graphite back gate. The top hBN protects the black phosphorus flakes from sample degradation in air. More importantly, the thin bottom hBN (thickness ~ 25 nm) allows the electrons in the graphite to screen the impurity potential at the black phosphorus-hBN interface, where the 2DEG resides. The high mobility enable us, for the first time, to observe the QH effect in black Page 4 of 15 phosphorus 2DEG. Black phosphorus thus joins the selected few materials 5,7,8,11 to become the only 2D atomic crystal apart from graphene 9,10 having requisite material quality to show QH effect.We constructed the van der Waals heterostructure using the dry-transfer technique described in ref. 31. We first cleaved graphite and h-BN flakes onto SiO2/Si wafers, and black phosphorus flake onto poly-propylene carbon (PPC) film. The black phosphorus flake on the PPC film was then used to pick up the h-BN flake on the SiO2/Si wafer. Finally, the black phosphor...

We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective k·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 LL fan calculated from the effective k·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.