All-Electrical Determination of Crystal Orientation in Anisotropic Two-Dimensional Materials

The crystal orientation of an exfoliated black phosphorous flake is determined by purely electrical means. A sequence of three resistance measurements on an arbitrarily shaped flake with five contacts determines the three independent components of the anisotropic in-plane resistivity tensor, thereby revealing the crystal axes. The resistivity anisotropy ratio decreases linearly with increasing temperature T and carrier density reaching a maximum ratio of 3.0 at low temperatures and densities, while mobility indicates impurity scattering at low T and acoustic phonon scattering at high T.