Moir\'e-Enhanced Plasmonics in Non-Hermitian Twisted Bilayer Graphene
We study plasmonic excitations in twisted bilayer graphene within a non-Hermitian framework that incorporates effective gain and loss. Using a non-Hermitian extension of the Bistritzer--MacDonald continuum model together with a biorthogonal Kubo formalism for the optical conductivity, we determine how the moir\'e electronic structure enters the plasmonic response of the active bilayer. We find that non-Hermiticity modifies the collective spectrum, yielding optical and acoustic plasmon branches, with the acoustic branch exhibiting strong subwavelength confinement. In the parity-time-symmetric configuration, gain--loss engineering can reduce the effective spatial damping and enhance the propagation length within the ideal linear model. The same regime produces strongly localized transverse-magnetic near fields. We argue that the enhancement is not a generic consequence of adding gain to a bilayer, but results from the combined influence of moir\'e-band reconstruction, biorthogonal optical matrix elements, and non-Hermitian modification of the plasmon pole. We also discuss the limitations imposed by disorder, substrate loss, gain saturation, and stability of the parity-time-symmetric regime. These results identify twisted bilayer graphene as a promising, but experimentally demanding, platform for tunable non-Hermitian plasmonics in moir\'e quantum materials.