Integer and Fractional Quantum Hall effect in Ultra-high Quality Few-layer Black Phosphorus Transistors

As a high mobility two-dimensional semiconductor with strong structural and electronic anisotropy, atomically thin black phosphorus (BP) provides a new playground for investigating the quantum Hall (QH) effect, including outstanding questions such as the functional dependence of Landau level (LL) gaps on magnetic field B, and possible anisotropic fractional QH states. Using encapsulating few-layer BP transistors with mobility up to 55,000 cm2/Vs, we extract LL gaps over an exceptionally wide range of B for QH states at filling factors {\nu}=-1 to -4, which are determined to be linear in B, thus resolving a controversy raised by its anisotropy. Furthermore, a fractional QH state at {\nu}~ -4/3 and an additional feature at -0.56+/- 0.1 are observed, underscoring BP as a tunable 2D platform for exploring electron interactions.