  Graphene plasmons have advantages over noble metal plasmons, such as high
tunability and low loss. However, for graphene nanostructures smaller than 10
nm, little is known about their plasmons or whether a regular plasmonic
behavior exists, despite their potential applications. Here, we present
first-principles calculations of plasmon excitations in zigzag graphene
nanoribbon segments. Regular plasmonic behavior is found: Only one plasmon mode
exists in the low-energy regime (< 1.5 eV). The classical electrostatic scaling
law still approximately holds when the width (W) is larger than about 1.5 nm
but totally fails when W < 1.5 nm due to quantum effects. The scaling with
different doping densities shows that the plasmon is nearly free-electron
plasmon instead of Dirac plasmon.
