▎ 摘　　要

Particle-hole continuum in Dirac sea of graphene has a unique window. It has been predicted to support a long lived neutral triplet gapless bosoinc mode that disperses over a wide energy range in entire Brillouin zone. In this work, using a repulsive Hubbard model, we study the fate of such collective mode at zero temperature, in a single layer of graphene doped with electrons or holes. Doping modifies the particle-hole continuum and creates additional windows for momenta around wave-vectors q + Q(i), i = 1, 2 connecting various Dirac cones. We find that, overlap factors are crucial for doped graphene. These factors push the collective mode inside the intra-band part of the continuum for momenta around Q(i) = 0, q similar to 0. For momenta larger than the scale of k(F), the collective mode emerges below the whole continuum. For other values of q, Q(i) such as q - K-j, j - 1, . . . , 6 this collective mode have linear dispersion near K-i point, related to inter valley scattering.