Positive magnetoconductance and dephasing in strongly localized black phosphorus

We study the magnetoconductance and dephasing in a strongly localized regime in black phosphorus (BP) devices. The phase coherence length, l_φ obtained from the magnetoconductance follows a temperature dependence of T^–1/3 in the strongly localized regime with k_Fl_e < 1 (ξ < l_φ) based on the Ioffe–Regel criterion. Here k_F, l_e and ξ are the Fermi wave vector, mean free path and localization length, respectively. The conductance behavior as a function of temperature confirms that the transport regime of our BP is in a variable-range-hopping regime, which results in the strongly localized regime.