Charge response function and a novel plasmon mode in graphene

Polarizability of noninteracting 2D Dirac electrons has a 1/root q upsilon-omega> singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N --> infinity, where N is the color degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the nth order ladder term to the same order random phase approximation contribution is ln(n)vertical bar q upsilon-omega vertical bar/N-n. We perform an analytical summation of the infinite series of ladder diagrams which describe the excitonic effect. Beyond the threshold, q upsilon>omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.