Theory of the Hall Effect in Aromatic Hydrocarbon Crystals

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Abstract
The Hall effect is studied for a triangular model of a molecular crystal, with the quadratic electron–phonon interaction previously applied to triplet exciton diffusion coefficients and carrier drift mobilities. General expressions are derived for the Hall mobilities in three different limits of perturbation theory, corresponding to slow-electron hopping, slow-phonon hopping, and slow-phonon coherent transport. The results are generalized to anisotropic lattices and it is shown that the Hall mobility may be anomalous in sign in each of these limits, depending on the signs of the intermolecular exchange intergrals. The results of model calculations are compared with experimental Hall mobilities for anthracene. Of the conflicting sets of experimental data, one is chosen to analyze the contributions of various lattice triangles to the observed Hall mobilities. The analysis yields results similar to those of the previous analysis of drift mobilities and shows the necessity of considering more than one transport mechanism.

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