RPA Plasmons in Graphene Nanoribbons: Influence of a VO₂ Substrate

We study the effect of the phase-change material VO2 on plasmons in metallic arm-chair graphene nanoribbons (AGNRs) within the random-phase approximation (RPA) for intra- and inter-band transitions. We assess the influence of temperature as a knob for the transition from the insulating to the metallic phase of VO2 on localized and propagating plasmon modes. We show that AGNRs support localized and propagating plasmon modes and contrast them in the presence and absence of VO2 for intra-band (SB) transitions while neglecting the influence of a substrate-induced band gap. The presence of this gap results in propagating plasmon modes in two-band (TB) transitions. In addition, there is a critical band gap below and above which propagating modes have a linear negative or positive velocity. Increasing the band gap shifts the propagating and localized modes to higher frequencies. In addition, we show how the normalized Fermi velocity increases plasmon modes frequency.