Dephasing in strongly anisotropic black phosphorus

Abstract

Weak localization was observed and determined in a black phosphorus (bP) field-effect transistor 65 nm thick. The weak localization behaviour was found to be in excellent agreement with the Hikami-Larkin-Nagaoka model for fields up to 1~T, from which characteristic scattering lengths could be inferred. The dephasing length $L_\phi$ was found to increase linearly with increasing hole density attaining a maximum value of 55 nm at a hole density of approximately $10^{13} cm^{-2}$ inferred from the Hall effect. The temperature dependence of $L_\phi$ was also investigated and above 1~K, it was found to decrease weaker than the $L_\phi \propto T^{-\frac{1}{2}}$ dependence characteristic of electron-electron scattering in the presence of elastic scattering in two dimensions. Rather, the observed power law was found to be close to that observed previously in other quasi-one-dimensional systems such as metallic nanowires and carbon nanotubes. We attribute our result to the crystal structure of bP which host a `puckered' honeycomb lattice forming a strongly anisotropic medium