Sources of negative differential resistance in electric nanotransport

A negative differential resistance (NDR) in nanotransport is often ascribed to electron correlations. We present a simple example revealing that finite electrode bandwidths and energy-dependent electrode density of states can cause a significant NDR, which may occur even in uncorrelated systems. So, special care is needed in assessing the role of electron correlations in the NDR.

Figure 1

(Color online) Schematic representation of a typical two-terminal setup. By gradually increasing the source-drain voltage $V_{sd}$ the energy window $\Delta E$ of the allowed elastic tunneling processes (a) increases for $e{V}_{sd}<2t$, but (b) beyond the point $e{V}_{sd}=2t$ (electrode half-bandwidth) it decreases. Elastic tunneling cannot occur for $e{V}_{sd}\ge 4t$.

Figure 2

(Color online) $I\text{−}V$ curves at resonance $\left({\epsilon }_g={\epsilon }_F=0\right)$ for $\tau =0.05,0.1,0.2,0.4$ computed exactly (thick lines) and within approximation (i) described in the text (thin lines). Current $I_{sd}$ in units $I_{sd}^s=\pi e{\Gamma }_0/h$.

Figure 3

(Color online) $I\text{−}V$ curves out of resonance for $\tau =0.1$ $\left({\Gamma }_0=0.02\right)$ computed (a) exactly and (b) within approximation (i) described in the text for ${\epsilon }_g=0,0.2,0.4,0.6,0.8,1$ (values increasing downwards). Current in units $et/h$.

Figure 4

(Color online) $I\text{−}V$ curves for $\tau =0.1$ computed exactly and within the approximations described in the text: (a) at resonance ${\epsilon }_d=0$ and (b) out of resonance, ${\epsilon }_d=0.2$. Current in units $et/h$. Labels as in Eqs. (5, 6, 7).

Figure 5

(Color online) $I\text{−}V$ curves on resonance $\left({\epsilon }_g=0\right)$ for the three electrode-dot couplings $\tau$ specified in the inset computed exactly and within approximation (ii) described in the text (label $fb$). Notice that the latter exhibit a cusp at $e{V}_{sd}=2t$ that marks the NDR onset in this approximation, which can be substantially higher than the exact NDR onset.

Figure 6

(Color online) Curves for the NDR onset voltage $V_{sd}^{NDR}$ computed from Eq. (8) for several level energies ${\epsilon }_g$. Notice that for smaller electrode-dot couplings $\tau$ and not too far away from resonance, $V_{sd}^{NDR}$ is significantly smaller than 2 (half of electrode’s bandwidth).