The sign of the Hall effect in hopping conduction

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Abstract
The absolute sign of the Hall effect is determined for several situations charac teristic of hopping in covalent materials. In particular, it is shown that the hopping of an excess electron between the antibonding orbitals of an odd-membered (three-site) ring will yield an ‘anomalously’ signed Hall effect, namely, p-type. In addition, the Hall effect for holes moving between bonding orbitals in a similar odd-membered structure will yield an n-type Hall effect. However, electron hopping between the antibonding orbitals and hole hopping between the bonding orbitals of an even-membered (four-site) ring yields the conventional result : n-type and p-type Hall effects, respectively. Other physically relevant situations are also discussed. These examples all serve to illustrate that the sign of the Hall effect for both electrons and holes depends not only on the local geometry but on the nature and relative orientations of the local orbitals between which the carrier moves. Furthermore, these results provide an explanation of the Hall effect sign anomalies observed in a number of non-crystalline solids.