Pseudogaps in incommensurate charge density waves and one-dimensional semiconductors

We consider pseudogap effects for electrons interacting with gapless modes. We study generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of photoelectron or tunneling spectroscopy. Within the formalism of functional integration and adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by the presence of gapless phonons that change the usual dynamics to the quantum dissipation regime. Below the free-particle edge, the pseudogap starts with an exponential (stretched exponential for gapful phonons) decrease of the transition rates. Deeply within the pseudogap, they are dominated by a power law, in contrast to a nearly exponential law for gapful modes.