Electrical and galvanomagnetic properties of black phosphorus single crystals

Black phosphorus (b-P) single crystals having the n-type electrical conductivity produced in a high pressure set-up (~1 GPa) with six diamond anvils at 800 °C for 12 h have been studied. The electrical conductivity σ(Т,В) and the Hall constant Rh(Т,В) have been analyzed within one-band and two-band models as functions of temperature in the 2 < Т < 300 K range and magnetic field in the 0 < В < 8 T range. Fitting of the experimental σ(Т,В) and Rh(Т,В) curves suggests the following key properties of the crystals: (1) intrinsic conductivity type, (2) approximately equal electron and hole concentrations and mobilities, (3) anisotropic behavior of electron and hole conductivities, concentrations and mobilities and (4) combination of negative and positive contributions to magnetoresistance (magnetoresistive effect, MR). In a zero magnetic field the anisotropy coefficient α = [σа (Т) – σс (Т)]/σс (Т) below 50–70 K is positive whereas above 220 K its sign changes to negative due to a specific combination of the temperature dependences of carrier concentration and mobility. It has been shown that the negative sign of relative MR (negative magnetoresistive effect) dominates at T < 25 K and B < 6 T and is presumably caused by the effects of strong localization resulting from structural disorder. The positive MR sign (positive magnetoresistive effect) is associated with the Lorentz mechanism of carrier movement and exhibits itself above 25 K in 6–8 T magnetic fields.