Publications Details
Disorder effects on small-polaron formation and hopping
Small-polarons will only form in covalent crystals whose electronic halfbandwidths are sufficiently narrow, E{sub b} > W. The absence of small polaronic carriers in most covalent crystals presumably indicates that E{sub b} < W in these instances. However, evidence of small polarons is commonly found in disordered materials despite the estimates of E{sub b} and W not being significantly different from those of crystals. This result is ration by stating that disorder has slowed carrier motion enough to permit small-polaron formation. Recently the question of how disorder affects the stability of quasifree carriers with respect to small-polaron formation has been addressed. It is found that only modest energetic disorder is required to induce small-polaron formation. Here I first succinctly describe essential elements of this work. Second, I address the role of disorder on the adiabatic hopping motion of small polarons. Energy bands in most materials in which small-polarons are found are thought to be sufficiently wide (> a phonon energy) that the small-polaronic hopping is ``adiabatic.`` That is, the electronic carriers move between sites sufficienfly rapidly to follow the atomic motions. In this situation the small-polaron jump rates are independent of intersite separations. The magnitudes of the preexponential factors of the measured hopping mobilities typically support this view. Further support for this picture is found from experiments that determine weak dependences of the mobility on hydrostatic pressure.