Spin-charge separation in molecular wire conductance simulations

We analyze spin-charge separation in molecular wires using a combination of real-time density-functional simulations and model Hamiltonian calculations. By considering the ab initio electron dynamics of positively charged $\left({\text{C}}_{50}{\text{H}}_{52}^{+}\right)$ and negatively charged $\left({\text{C}}_{50}{\text{H}}_{52}^{-}\right)$ polyacetylene chains under a chemical potential bias, we are able to extract information about the mobility of electrons, holes, and spins in these molecules. Our results indicate that charges move more rapidly than spins in these molecules. We further supplement our ab initio data with empirical calculations employing the Pariser-Parr-Pople (PPP) model Hamiltonian. Our modeling indicates that the degree of spin-charge separation responds very strongly to the nonlocal exchange interaction, while showing little sensitivity to Coulombic forces. In particular, in order to reproduce the B3LYP results within the PPP model, it is necessary to reduce the strength of the exchange interaction by ca. 50% in the latter. We therefore conclude that many of the features present in the B3LYP spin current response are a direct result of self-interaction error in the functional.

Figure 1

(Color online) System geometry used for the DFT calculation with the source and drain labeled. The unlabeled portion is considered the molecular device. As described in the text, charge density is increased in the source and depleted in the drain before being released at $t=0$.

Figure 2

(Color online) Plot of $I_{\text{tot}}$ and $I_{\text{spin}}$ as a function of initial $N_{\text{tot}}$ and $M_{\text{spin}}$ as determined using B3LYP or HF for the anion (left) and cation (right) case. The value of the fixed initial $M_{\text{spin}}$ or $N_{\text{tot}}$ is set to 1.0.

Figure 3

(Color online) Dependence of $N_{\text{tot}}$ upon $V_{\text{tot}}$ with $V_{\text{spin}}=0.272V$ and $M_{\text{spin}}$ upon $V_{\text{spin}}$ with $V_{\text{tot}}=1.36V$ for the anion (left) and cation (right) as predicted by B3LYP, PPP, and PPP-SIE.

Figure 4

(Color online) Maximum total and spin currents plotted against initial $N_{\text{tot}}$ and $M_{\text{spin}}$, respectively, as calculated by PPP, PPP-SIE, PPP-Hartree, and Hückel propagation for the anion (left) and cation (right). The unvaried initial $N_{\text{tot}}$ or $M_{\text{spin}}$ is held to 1.0.

Figure 5

(Color online) Maximum total and spin currents plotted against initial $V_{\text{tot}}$ and $V_{\text{spin}}$, respectively, as calculated by PPP-SIE, for chains of lengths 50, 100, and 200 sites. The fixed initial potentials are $V_{\text{spin}}=0.272V$ for the total current plots and $V_{\text{tot}}=1.36V$ for the spin current plots.