Conditions for charge fractionalization

Abstract

We prove a theorem which gives necessary and sufficient conditions under which charge will be fractional, in a certain well-defined sense. The model of Su, Schrieffer, and Heeger, which gives fractional charge, is completed in several ways which illustrate the theorem and the postulates made to prove it. The theorem applies to a chain of arbitrary complexity which consists of charged regions separated by long stretches of electrically neutral and electrically insulating chain. The theorem states that the integral of the charge density over a charged region will be a noninteger multiple of the charge on the proton if and only if the electrical polarity of the neutral chain is different on the two sides of the charged region. In short, fractional charges in the sense here discussed exist only on ferroelectric domain walls. Further, these charges will not be simple fractions, but will be irrational multiples of the protonic charge. A brief discussion is given of how fractional charges may exist in other senses with an experimental meaning.