Conditions for Dynamic Localization in Generalized ac Electric Fields

We examine the conditions for dynamic localization of electrons in a periodic potential due to an applied ac electric field. Using a general one-band model, we establish the surprising result that only electric fields that are discontinuous at all changes of sign can lead to exact dynamic localization. We also develop a general procedure for constructing ac fields that yield dynamic localization and derive an "area condition" for such fields. We confirm this result numerically in a multiband simulation.