Localization-like Effects in the Thermoelectric Properties of Graphene with Random Disorder

Previous theoretical studies have shown that the optimal electronic structure for maximizing the thermoelectric efficiency of materials is achieved when the transport distribution approaches a Dirac delta function. In this work, we demonstrate that defects in graphene can effectively narrow the energy distribution by localizing electrons at discrete energy levels. We experimentally investigated the thermoelectric properties of disordered single-layer graphene with varying levels of random disorder. Using micro-Raman spectroscopy, we quantified defect densities through the D-to-G-band ratio and examined electron-phonon renormalization in our samples. By comparing the electrical properties of graphene with different defect densities, we identified the localization length scales of electrons in disordered graphene. Additionally, we performed detailed numerical simulations using Kwant, observing a sharp increase in the density of states at the Fermi level, consistent with theoretical expectations. We found that the electron probability distribution becomes increasingly localized as the defect density rises. Using linear response theory in conjunction with Kwant, we calculated the electrical conductivity and Seebeck coefficient, showing that the randomness of the defect distribution significantly influences the electrical and thermoelectric properties of single-layer graphene.