Investigation of density fluctuations in graphene using the fluctuation-dissipation relations

Based on the philosophy of density functional theory, the charge-density contains, in principle, all the information about a given system. Thus charge-density fluctuations determine all other fluctuation phenomena, and so are of great importance in the study of nanosystems, where quantum fluctuations strongly influence system behaviour. Despite this, little work has been done to investigate the effects of charge-density fluctuations in such systems. We present a previously uninvestigated relation connecting charge-density fluctuations and the electron energy-loss spectrum using the fluctuation-dissipation relations. Using this relation we perform an analysis of the autocorrelation function of charge-density fluctuations in graphene using linear-response time-dependant density functional theory calculations. It is found that the charge-density autocorrelation function contains information pertaining to both plasmonic resonance of a system, and noise characteristics. As the electron energy-loss spectrum can be studied both numerically and experimentally, this relation provides a useful analysis tool for the study of charge-density fluctuations.