Precision Measurement of the Optical Conductivity of Atomically Thin Crystals via the Photonic Spin Hall Effect

How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. The photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By use of the weak-value-amplification technique, the optical conductivity of monolayer graphene taken as a universal constant of $(0.993\ifmmode\pm\else\textpm\fi{}0.005){\ensuremath{\sigma}}_{0}$ is detected, and a high measurement resolution of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\phantom{\rule{0.2em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ is obtained. For few-layer graphene without a twist, we find that the conductivities increase linearly with the number of layers. Our idea could provide an important measurement technique for probing other parameters of atomically thin crystals, such as the magneto-optical constant, circular dichroism, and optical nonlinear coefficient.