Phonon-limited resistivity of graphene by first-principle calculations: electron-phonon interactions, strain-induced gauge field and Boltzmann equation

摘要

Electron-phonon coupling in graphene is extensively modeled and simulatedfrom first principles. We find that using an accurate model for thepolarizations of the acoustic phonon modes is crucial to obtain correctnumerical results. The interactions between electrons and acoustic phononmodes, the gauge field and deformation potential, are calculated at the DFTlevel in the framework of linear response. The zero-momentum limit of acousticphonons is interpreted as a strain pattern, allowing the calculation of theacoustic gauge field parameter in the GW approximation. The role of electronicscreening on the electron-phonon matrix elements is investigated. We then solvethe Boltzmann equation semi-analytically in graphene, including both acousticand optical phonon scattering. We show that, in the Bloch-Gr\"uneisen andequipartition regimes, the electronic transport is mainly ruled by theunscreened acoustic gauge field, while the contribution due to the deformationpotential is negligible and strongly screened. By comparing with experimentaldata, we show that the contribution of acoustic phonons to resistivity isdoping- and substrate-independent. The DFT+GW approach underestimates thiscontribution to resistivity by about 30 %. Above 270K, the calculatedresistivity underestimates the experimental one more severely, theunderestimation being larger at lower doping. We show that, beside remotephonon scattering, a possible explanation for this disagreement is theelectron-electron interaction that strongly renormalizes the coupling tointrinsic optical-phonon modes. Finally, after discussing the validity of theMatthiessen rule in graphene, we derive simplified analytical solutions of theBoltzmann equation to extract the coupling to acoustic phonons, related to thestrain-induced gauge field, directly from experimental data.