  We have developed a theoretical formalism to investigate the contribution of
fluctuation of Coulomb interaction to the shot noise based on Keldysh
non-equilibrium Green's function method. We have applied our theory to study
the behavior of dc shot noise of atomic junctions using the method of
nonequilibrium Green's function combined with the density functional theory
(NEGF-DFT). In particular, for atomic carbon wire consisting 4 carbon atoms in
contact with two Al(100) electrodes, first principles calculation within
NEGF-DFT formalism shows a negative differential resistance (NDR) region in I-V
curve at finite bias due to the effective band bottom of the Al lead. We have
calculated the shot noise spectrum using the conventional gauge invariant
transport theory with Coulomb interaction considered explicitly on the Hartree
level along with exchange and correlation effect. Although the Fano factor is
enhanced from 0.6 to 0.8 in the NDR region, the expected super-Poissonian
behavior in the NDR regionis not observed. When the fluctuation of Coulomb
interaction is included in the shot noise, our numerical results show that the
Fano factor is greater than one in the NDR region indicating a super-Poissonian
behavior.
