Sign of the hall coefficient in hopping-type charge-transport

A prescription for the sign of the Hall coefficient for holes relative to that for electrons in hopping-type charge-transport is developed. In particular, it is found that when the elementary jump-process involves three sites ('three-site’ Hall effect), the sign for holes is the same as that for electrons—in direct contradiction to conventional semi-conductor theory; for the ‘four-site’ Hall effect, the sign for holes is opposite to that for electrons—in agreement with the conventional theory. Applications of this result to a number of special cases, including the Hall effect in the ‘atomic’ limit of the Hubbard model, are discussed.