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Collective fermion excitation in a warm massless Dirac system

Basing on a self-consistent method, we predict theoretically that there occurs not only a normal (quasi) fermion mode, but also a collective fermion mode, plasmino, in a warm 2D massless Dirac system, especially in a warm intrinsic graphene system. Results of Landau damping show that both fermion and plasmino are well defined modes. We find that there are sharp differences between the discussed system and the QCD/QED system. Firstly, the thermal mass is proportional to $α_g^{3/4}T$ but not $α_g T$. Secondly, at $0<q<q_c$, the fermion channel and plasmino channel are nearly degenerate and furthermore, the energy difference between fermion and plasmino becomes more and more larger with increasing $q$ at the region $q>q_c$. Thirdly, the fermion behaves as a "relativity particles" with none zero mass and the plasmino exhibits an anormal dispersion at moderate momentum.