Unified percolation model for bipolaron-assisted organic magnetoresistance in the unipolar transport regime

The fact that in organic semiconductors the Hubbard energy is usually positive appears to be at variance with a bipolaron model to explain magnetoresistance (MR) in those systems. Employing percolation theory, we demonstrate that a moderately positive $U$ is indeed compatible with the bipolaron concept for MR in unipolar current flow, provided that the system is energetically disordered, and the density of states (DOS) distribution is partially filled, so that the Fermi level overlaps with tail states of the DOS. By exploring a broad parameter space, we show that MR becomes maximal around $U=0$ and even diminishes at large negative values of $U$ because of spin independent bipolaron dissociation. Trapping effects and reduced dimension enhance MR.

Figure 1

(a) Carrier hopping processes including (left) bipolaron formation, (middle) bipolaron motion, and (right) bipolaron dissociation. Top row: spin configurations before hopping; bottom row: spin configurations after hopping. (b) Illustration of the effective DOS and the three occupancy ranges ($D$: double occupancy; $S$: single occupancy; and $E$: empty). Only the part of $g^0\left(E-U\right)$ that is inside the range $\left[-U,0\right]$ contributes to the MR.

Figure 2

(a) The MR curve as a function of external magnetic field in a 3D system. Circular marks: MR values calculated using Eq. (7). Solid curve: fitting of the calculated data using a Lorentzian line shape. Inset: the temperature dependence of the conductance at zero magnetic field. (b) Saturated MR as functions of the bipolaron formation energy parametric in the Fermi level. (c) Saturated MR as functions of the bipolaron formation energy parametric in the disorder width. The parameters in (b) and (c) are the same as in (a) except for varying $E_F$ in (b) and varying $\sigma$ in (c). (d) Probability of a site to be empty, singly occupied, and doubly occupied at 300 K.

Figure 3

(a) MR as functions of external magnetic field at different trap depths. (b) Saturated MR as functions of the width of the trap distribution at different trap depths.

Figure 4

Effect of dimensionality of MR in a trap-free system (a) and a system containing traps (b).