Modulation of Graphene Dirac Plasmons: A First-Principles Study

Graphene Dirac plasmons, which are collective oscillations of charge carriers behaving as massless Dirac fermions, have emerged as a transformative platform for nanophotonics due to their exceptional capability for deep subwavelength light confinement in the infrared to terahertz spectral regions and their unique dynamic tunability. While external controls such as electrostatic doping, mechanical strain, and substrate engineering are empirically known to modulate plasmonic responses, a comprehensive and quantitative theoretical framework from first principles is essential to decipher the distinct effciency and fundamental mechanisms of each tuning strategy. To address this, we present a systematic first-principles investigation into three primary modulation pathways-carrier density, biaxial strain, and substrate integration-using linear-response time-dependent density functional theory within the random-phase approximation (LR-TDDFT-RPA) as implemented in the computational code ABACUS. A truncated Coulomb potential was incorporated to accurately model the isolated two-dimensional system, while structural and electronic properties were computed using the PBE functional with SG15 norm-conserving pseudopoten- tials and van der Waals corrections for heterostructures. Our findings reveal that modulating carrier concentration shifts the plasmon dispersion following the characteristic ω∝ n1/4 scaling, enabling a wide tuning range from 0.45 eV to 1.38 eV at the Landau damping threshold-a 207% change for carrier densities from 0.005 to 0.1 electrons per unit cell, albeit with diminishing effciency at higher concentrations due to the sublinear nature of the scaling law. Biaxial strain linearly alters the plasmon energy by modifying the Fermi velocity (vF ) near the Dirac point, yielding a 30.4% tuning range (0.78-1.12 eV) under ±10% strain. Introducing an hBN substrate induces a small band gap (∼ 43 meV) and causes a general redshift in plasmon energy due to band renormalization, while remarkably preserving the linear straintuning capability with a 30.1% energy range (0.72-1.03 eV) in the heterostructure, demonstrating robust compatibility between strain engineering and substrate integration. These results quantitatively elucidate the distinct physical mechanisms-Fermi level shifting, Fermi velocity modification, and substrate-induced symmetry breaking and hybridization-underpinning each strategy, thereby providing a solid theoretical foundation for the design of dynamically tunable optoelectronic devices based on graphene and its van der Waals heterostructures.