Multi-Parameter Modulation of Dirac Plasmons in Germanene via Doping and Strain: A DFT Insight.

Based on first-principles calculations and linear-response time-dependent density functional theory within the random phase approximation (LR-TDDFT-RPA), this work systematically investigates the modulation of Dirac plasmons in germanene via carrier doping, biaxial strain, and substrate effects. The results demonstrate that carrier doping induces highly tunable Dirac plasmons whose excitation energy follows the ω ∝ n1/4 scaling relation, leading to a sublinear increase with doping concentration. Furthermore, biaxial strain effectively modulates the Fermi velocity, and the established ω ∝ √VF relationship directly explains the observed linear tuning of plasmon energy with strain. More importantly, the combined modulation of carrier density and strain enables a significantly broader plasmon energy range (0.16-0.61 eV) than achievable through individual parameter control. When supported on hBN substrates, germanene maintains the characteristic √q plasmon dispersion despite band hybridization and a redshift in energy, a behavior well explained by the 2D free electron gas model. This study provides important theoretical insights into the multi-parameter control of Dirac plasmons and supports the design of germanene-based tunable nanophotonic devices.