Abstract
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+Qi, 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 Qi = 0, q~0. For momenta larger than the scale of kF, the collective mode emerges below the whole continuum. For other values of q, Qi such as q = Kj, j= 1,…,6 this collective mode have linear dispersion near Ki point, related to inter valley scattering.
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