The role of boundary conditions in shot noise in elastic diffusive conductors

Abstract

The role played by boundary conditions at a kinetic level in determining the noise properties of mesoscopic diffusive conductors is evaluated by decomposing the current fluctuations, into fluctuations of boundaries, self-consistent electric potential and the intrinsic Langevin source. We show that the self-consistent contribution is essentially controlled by the range of energies determined by the distribution function at the contacts together with the differential conductivity in energy space. The intrinsic contribution is completely determined by the boundary conditions and is expressed in closed analytical form in these terms. The present formulation provides a unifying microscopic approach of the noise properties of mesoscopic diffusive conductors showing that (i) in the absence of Coulomb interaction the Fano factor γ takes values bounded in the range 1 3 γ 1 and (ii) in the presence of Coulomb interaction the values of γ are no longer bounded in the above range and enhanced shot noise becomes possible.

Shot noise in disordered junctions: Interaction corrections

“…If this is not the case, the eq. (51) should be modified correspondingly 39 . The "random source" δj ext is generated by short-range scattering events of conducting electrons on the impurities.…”

Shot-noise anomalies in nondegenerate elastic diffusive conductors

“…In computer simulations one can consider any value of the momentum-space dimensionality d. Thus, even if the physically relevant case is dϭ3, we will analyze also the case dϭ2, since for this value of d there exist analytical predictions based on the same assumptions on what concerns the coupling of the kinetic equation with the Poisson equation. [7][8][9][10][11][12] As indicated in Ref. 8, this case corresponds to a hypothetical ''flatland'' whose physical realization would be a layered material with each layer containing a two-dimensional electron gas.…”

“…12 concerning the shot-noise properties of nondegenerate elastic diffusive conductors. In that work, by means of a formal treatment of the Boltzmann-Langevin-Poisson set of equations it was shown that the Fano factor for this class of systems can be exactly decomposed into the sum of three contributions as ␥ϭ␥ in ϩ␥ ϩ␥ in, .…”

“…The existing analytical theories [7][8][9][10][11] provide a reasonable interpretation of these results in the limited range of values Ϫ1.5Ͻ␣Ͻ0.5, being absent 10,11 or failing completely [7][8][9] outside this range. 6 In this context, two of the authors 12 have recently pointed out the possibility that the above results only provide a partial description of the shot-noise properties of nondegenerate conductors. In particular, enhanced shot noise ͑i.e., ␥Ͼ1) was predicted for given values of ␣, and full shot noise ͑with ␥ ϭ1) was expected at asymptotically high bias for ␣ ϾϪ3/2.…”

Fractional exclusion statistics and shot noise in ballistic conductors

“…Under these conditions, one can neglect long range Coulomb interaction effects on the fluctuations, 27 thus simplifying considerably the calculations.…”