  It has been observed in fossil tracks and experiments in the layered silicate
mica muscovite the transport of charge through the cation layers sandwiched
between the layers of tetrahedra-octahedra-tetrahedra. A classical model for
the propagation of anharmonic vibrations along the cation chains has been
proposed based on first principles and empirical functions. In that model,
several propagating entities have been found as kinks or crowdions and
breathers, both with or without wings, the latter for specific velocities and
energies. Crowdions are equivalent to moving interstitials and transport
electric charge if the moving particle is an ion, but they also imply the
movement of mass, which was not observed in the experiments. Breathers, being
just vibrational entities, do not transport charge. In this work, we present a
semiclassical model obtained by adding a quantum particle, electron or hole to
the previous model. We present the construction of the model based on the
physics of the system. In particular, the strongly nonlinear vibronic
interaction between the nuclei and the extra electron or hole is essential to
explain the localized charge transport, which is not compatible with the
adiabatic approximation. The formation of vibrational localized charge carriers
breaks the lattice symmetry group in a similar fashion to the Jahn-Teller
Effect, providing a new stable dynamical state. We study the properties and the
coherence of the model through numerical simulations from initial conditions
obtained by tail analysis and other means. We observe that although the charge
spreads from an initial localization in a lattice at equilibrium, it can be
confined basically to a single particle when coupled to a chaotic quasiperiodic
breather. This is coherent with the observation that experiments imply that a
population of charge is formed due to the decay of potassium unstable isotopes.
