Abstract
Polarizability of noninteracting 2D Dirac electrons has a 1/square root(qv-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)|qv-omega|/N(n). We perform an analytical summation of the infinite series of ladder diagrams which describe the excitonic effect. Beyond the threshold, qv>omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.
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