Hall effect and two-dimensional electron gas in black phosphorus

The Hall coefficient and electric conductivity of black phosphorus prepared by the bismuth-flux method were measured at low temperatures. It is found that the conductivity shows log T-like behaviour below about 5 K and the Hall coefficient changes its sign from plus to minus at around 7 K with decreasing temperature. These results can be analysed successfully on the basis of a three-carrier model, in which bulk holes, variable-range-hopping holes and two-dimensional electrons take part in the electric conduction at low temperatures, except in the case of strong magnetic fields below 7 K. The present analysis supports the fact that magneto-electric properties observed at low temperatures in black phosphorus crystals originate from the 2D Anderson localization in an inversion layer on the surface.