Landau Level Energy Gaps in Ultrahigh Quality Black Phosphorus Devices

We report black phosphorus (BP) field effect transistors with low temperature record field effect mobility up to 55,000 cm²/Vs. Thanks to the ultrahigh device quality, the integer quantum Hall effect is observed with full spin degeneracy lifting over a wide range of magnetic field 10 T – 45 T. Landau level (LL) energy gaps of filling factors ν=-1, -2, -3, -4, -5, and -6 are measured and demonstrate a linear dependence on magnetic field. This settles a theoretical controversy on the effects of BP’s anisotropic crystal structure on its LL energetics.