Counting statistics in nanoscale junctions

We present first-principles calculations for moments of the current up to the third order in atomic-scale junctions. The quantum correlations of the current are calculated using the current operator in terms of the wave functions obtained self-consistently within the static density-functional theory. We investigate the relationships of the conductance, the second, and the third moment of the current for carbon atom chains of various lengths bridging two metal electrodes in the linear and nonlinear regimes. The conductance, the second-, and the third-order Fano factors exhibit odd-even oscillation with the number of carbon atoms due to the full and half filled ${\pi }^{*}$ orbital near the Fermi levels. The third-order Fano factor and the conductance are positively correlated.

Figure 1

(a) Schematic of the four-carbon atomic junction. (b) The spacial distribution of partial charge density for electrons with energies near the Fermi levels shows ${\pi }^{*}$-orbital characters at $V_B=0.01$ V. Vertical black lines correspond to the edges of the jellium model and circles correspond to atomic position.

Figure 2

The density of states in the continuum region for $N$-atom carbon chains sandwiched between two metal electrodes at $V_B=0.01$ V. Zero energy corresponds to the left Fermi level.

Figure 3

Conductance [(black) square, top panel], the second-order Fano factor [(red) circle, middle panel], and the third-order Fano factor [(green) triangle, bottom panel] of the atomic wires as functions of the number of carbon atoms in the wire at $V_B=0.01$ V.

Figure 4

(a) For four-carbon atom wire and (b) for five-carbon atom wire: the differential conductance [(black) square, top panel], the second-order differential Fano factor [(red) circle, bottom panel], and the three-order differential Fano factor [(blue) triangle, bottom panel] vs bias.

Figure 5

The density of states for various source-drain biases for the (a) C4 atom chain and (b) C5 atom chain for $V_B=0.1$, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 V. The left Fermi level $E_{\mathit{FL}}$ (red-dashed lines) is set to be the zero of energy. The right Fermi level $E_{\mathit{FR}}$ (blue-dotted line) defines $V_B=(E_{\mathit{FR}}-E_{\mathit{FL}})/e$.