Disorder-enhanced exciton delocalization in an extended dendrimer

The exciton dynamics in a disordered extended dendrimer is investigated numerically. Because a homogeneous dendrimer exhibits few highly degenerate energy levels, a dynamical localization arises when the exciton is initially located on the periphery. However, it is shown that the disorder lifts the degeneracy and favors a delocalization-relocalization transition. Weak disorder enhances the delocalized nature of the exciton and improves any quantum communication, whereas strong disorder prevents the exciton from propagating in accordance with the well-known Anderson theory.

Figure 1

Polyphenylacetylene extended dendrimer D58. Each circle defines a phenyl ring, whereas a connecting line stands for an acetylene group involving two single bonds and one triple bond.

Figure 2

Time evolution of the probability $P_d\left(t\right)$ to observe the exciton on the dendron $d=d_1$ (black curve), $d=d_2$ (red [dark gray] curve), and $d=d_3$ (blue [light gray] curve) for different disorder strengths: (a) $W=0.0$, (b) $W=0.5\Phi$, and (c) $W=5.0\Phi$.

Figure 3

Time evolution of the time dependent participation ratio $R\left(t\right)$ for (a) $W=0.0$ and for (b) $W=0.5\Phi$ (red curve) and $W=5.0\Phi$ (blue curve).

Figure 4

Limiting probability ${\overline{P}}_{x|x_0}$ for (a) $W=0.0$, (b) $W=0.5\Phi$, and (c) $W=5.0\Phi$.

Figure 5

$W$ dependence of the average limiting probability $\langle {\overline{P}}_{d_1}\rangle$ that the exciton occupies $d_1$. The average was carried out by considering ${10}^4$ disordered configurations. The inset shows the average limiting probability of observing the exciton on $d_2$ and $d_3$. Dashed red (gray) curves correspond to the analytical law discussed in the text [see Eq. (5)].

Figure 6

$W$ dependence of the average limiting probability $\langle {\overline{P}}_{s_3}\rangle$ of observing the exciton on the surface of the dendron $d_3$. The average was carried out by considering ${10}^4$ disordered configurations. The dashed red (gray) curve corresponds to the analytical law discussed in the text.

Figure 7

$W$ dependence of the average of the maximum value of the probability $P_{56|45}\left(t\right)$ to observe the exciton on site $x=56$. The simulation was carried out using $5\times {10}^4$ time steps over a time interval fixed to $5\times {10}^3{\Phi }^{-1}$. The average was realized by considering 5000 disordered configurations. The dashed red curve corresponds to the analytical law discussed in the text.