Optical Measurement of the Phase-Breaking Length in Graphene

In mesoscopic physics, interference effects play a central role on the transport properties of conduction electrons, giving rise to exotic phenomena such as weak localization, Aharonov-Bohm effect, and universal conduction fluctuations. Mesoscopic objects have a size on the order of the {\em phase-breaking length} $L_{\varphi }$, the length conduction electrons travel while keeping phase coherence. In this letter, we use vibrational spectroscopy in combination with a novel optical defocusing method to measure $L_{\varphi }$ of photo-excited electrons in graphene which undergo inelastic scattering by optical phonons. We extract $L_{\varphi }$ from the spatial confinement of the defect-induced Raman D band near the edges of graphene. Temperature dependent measurements in the range of 1.55,K to 300,K yield $L_{\phi} \propto 1/\sqrt{T}$, in agreement with previous magneto-transport measurements.