Crucial role of decoherence for electronic transport in molecular wires: Polyaniline as a case study

In this work we attempt to elucidate the nature of conductivity in polymers by taking the acid-base doped polyaniline (PAni) polymer. We evaluate the PAni conductance by using realistic ab initio parameters and including decoherent processes within the minimal parametrization model of D’Amato-Pastawski. In contrast to general wisdom, which associates the conducting state with coherent propagation in a periodic polaronic lattice, we show that decoherence can account for high conductance in the strongly disordered bipolaronic lattice. Hence, according to our results, there is no need of considering a mix model of “conducting” polaronic lattice islands separated by “insulating” bipolaronic lattice strands as is usually assumed for PAni. We find that without dephasing events, even very short strands of bipolaronic lattices are not able to sustain electronic transport. We also include a discussion of specific mechanisms that should be involved in decoherence rates of PAni and relate them with Marcus-Hush theory of electron transfer.

Figure 1

Three different forms of PAni: (a) emeraldine base and two lattice models after a doping process, (b) bipolaron, and (c) polaron.

Figure 2

(Color online) Diagrammatic representation of benzenoid rings decimated to obtain equivalent renormalized units in one dimension. Incoherent channels of D’Amato-Pastawski model also shown.

Figure 3

(Color online) Conductance for both: (a) $T=0\text{K}$ and (b) $T=300\text{K}$ according to DP model for a 400 rings long PAni-HCl chain. We also show the $T=0\text{K}$ Density of state for comparison purposes.

Figure 4

(Color online) Fluctuations in total conductance at $T=300\text{K}$ in the main peak around the Fermi energy with the fraction of quinoid rings along the chain.

Figure 5

Conductance for a 400 rings long PAni-HCl chain as a function of ${\Gamma }_{\varphi }$. The value for ${\Gamma }_{\varphi }$ at $T=300K$ also shown in dash line.

Figure 6

(Color online) Total conductance at $T=300\text{K}$ as a function of the chain large. As an inset, it is shown the scale difference between coherent and total conductance.

Figure 7

Average current (black line) and currents for 50 different configurations (shadow lines) are shown.

Figure 8

(Color online) Interchain hopping at site $j$. States are written in Dirac notation including quantum numbers $s$ which label different PAni chains. This representation illustrates the similarity with Fock-space representation of the electron-phonon system.

Figure 9

(Color online) Fock-space representation of state $|j,n⟩$ and its surroundings. The middle row represents electronic states with $n$ phonons in the PAni chain. Lower and upper rows represent the same chain but with different numbers of phonons. Black dotted lines are electron-phonon couplings.

Figure 10

Fock-space representation of Eq. (A13) and its corresponding semiclassical picture in terms of vibronic degree of freedom $X$ as used in the Marcus-Hush model for electron transfer reactions. The potential surface at the right becomes shifted when represented in the polaronic basis allowing to define the reorganization energy $E_r$. In this model, the electronic coupling $V_{AB}$ must be small enough to remain perturbative. Left panel is also used to represent the decoherence by electron-phonon coupling when $V_g⪡V_{AB}$.