Direct measurements of conductivity and mobility in millimeter-sized single-crystalline graphene via van der Pauw geometry

We report the direct measurements of conductivity and mobility in millimeter-sized single-crystalline graphene on SiO₂/Si via van der Pauw geometry by using a home-designed four-probe scanning tunneling microscope (4P-STM). The gate-tunable conductivity and mobility are extracted from standard van der Pauw resistance measurements where the four STM probes contact the four peripheries of hexagonal graphene flakes, respectively. The high homogeneity of transport properties of the single-crystalline graphene flake is confirmed by comparing the extracted conductivities and mobilities from three setups with different geometry factors. Our studies provide a reliable solution for directly evaluating the entire electrical properties of graphene in a non-invasive way and could be extended to characterizing other two-dimensional materials.