Negative differential conductance in nanojunctions: A current constrained approach

Prakash Parida, Swapan K. Pati, and Anna Painelli

Phys. Rev. B 83, 165404 – Published 7 April 2011

Abstract

A current constrained approach is proposed to calculate negative differential conductance in molecular nanojunctions. A four-site junction is considered where a steady-state current is forced by inserting only the two central sites within the circuit. The two lateral sites (representing, e.g., dangling molecular groups) do not actively participate in transport but exchange electrons with the two main sites. These auxiliary sites allow for a variable number of electrons within the junction, while as required by the current constrained approach, the total number of electrons in the system is kept constant. We discuss the conditions for negative differential conductance in terms of cooperativity, variability of the number of electrons in the junction, and electron correlations.

Received 12 June 2010

DOI:https://doi.org/10.1103/PhysRevB.83.165404

Authors & Affiliations

Prakash Parida¹, Swapan K. Pati^1,2, and Anna Painelli³

¹Theoretical Sciences Unit,
²New Chemistry Unit, Jawaharlal Nehru Centre For Advanced Scientific Research, Jakkur Campus, Bangalore-560064, India
³Dipartimento Chimica GIAF, Parma University, INSTM UdR-Parma, I-43100 Parma, Italy

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Vol. 83, Iss. 16 — 15 April 2011

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Images

Figure 1
(a) A schematic representation of the four-site system where current flows through the two central sites in the closed circuit while the lateral sites behave as sources/sinks of electrons. (b) The biphenyl molecule with two dangling groups $R$ and $R^{'}$ represents an example of a molecule that can be roughly described by the four-site model in (a). The red dashed arrow in panel (b) shows the direction of current flow.Reuse & Permissions
Figure 2
The color maps show differential conductance ( $\frac{\partial I}{\partial V}$ ) as a function of potential drop ( $V$ ) and of the energies of the auxiliary sites satisfying the relations (a) $ε_{1} = - ε_{4}$ and (b) $ε_{1} = ε_{4}$ . Results are shown for $U = 5$ .Reuse & Permissions
Figure 3
Color maps showing differential conductance ( $\frac{\partial I}{\partial V}$ ) as a function of potential drop ( $V$ ) and the energies of the auxiliary sites for $ε_{1} = - ε_{4}$ (left panels) and $ε_{1} = ε_{4}$ (right panels) for two different $U$ values. The blue italic numbers in the right panels show the approximate value of the number of electrons in the junction $n$ in the different regions. The same number is constant ( $n = 2$ ) in the left panels.Reuse & Permissions
Figure 4
Results for $ε_{1} = - ε_{4} = 3$ and $U = 5$ . The continuous black line in the top panel shows the characteristic curve. The dot-dashed blue and the double-dot-dashed green lines in the same panel show the two major contributions to the current as discussed in the text, the red dashed line shown the sum of the two contribution, and it is almost indistinguishable from the total current. In the bottom panel the blue dotted and double-dotted dashed (green continuous and dashed) lines show the weight of the two states responsible for the $I_{1}$ ( $I_{2}$ ) as discussed in the text. The black dotted line is shown as a guide for the eyes.Reuse & Permissions
Figure 5
Results for $ε_{1} = ε_{4} = 2$ and $U = 5$ . (a) Characteristic curve (black continuous line) and total number of electrons in the junction (blue dashed line). (b) The three main contributions to the current in the NDC regions, as discussed in the text. The red dashed lines shows their sum to be compared to the total current (black line). (c) The weight of states contributing to $I_{1}$ (blue continuous and double-dot dashed lines), $I_{2}$ (violet dashed and dot-dashed lines), and $I_{3}$ (green dot-dashed lines). More specifically, the blue continuous and double-dot dashed line refer to states $| ↑, ↓, ↑, ↓ 〉$ and $| ↑, ↓ ↑, 0, ↓ 〉$ , respectively; the green dotted and double-dash-dotted lines refer to $| ↓, ↓ ↑, ↑, 0 〉$ and $| ↓, ↑, ↓ ↑, 0 〉$ , respectively; the violet dashed and dot-dashed lines refer to $| 0, ↓ ↑, ↑, ↓ 〉$ and $| 0, ↑, ↓ ↑, ↓ 〉$ , respectively.Reuse & Permissions

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