Carrier concentration independent plasmons in biased twisted bilayer graphene

Abstract

We calculate the density-density response function of biased twisted bilayer graphene (BTBG) and study its plasmon dispersion within the random phase approximation (RPA). At long wavelengths ($q\ensuremath{\rightarrow}0$), plasmon dispersion shows local classical behavior $\ensuremath{\omega}={\ensuremath{\omega}}_{0}\sqrt{q}$. Unlike the situation in conventional two-dimensional electron gas (2DEG), where the density dependence of the plasmon energy is of the form ${\ensuremath{\omega}}_{0}\ensuremath{\propto}\sqrt{n}$ ($n$ is the carrier concentration), the plasmon energy ${\ensuremath{\omega}}_{0}$ is independent of the carrier concentration ($n$) in biased twisted bilayer graphene. Furthermore, the plasmon energy (${\ensuremath{\omega}}_{0}$) is also independent of the Fermi energy ($\ensuremath{\mu}$) which is decided by the carrier concentration ($n$).