We describe a novel state of electrons and phonons arising in layered struc
tures, like cuprates (HTSC) and semiconductor superlattices (SSL) due to el
ectron-phonon interactions (which can be strongly enhanced by a strong magn
etic field). These states are characterized by a localization of phonons an
d a self-trapping[1-5] or locking of electrons in one or several quantum we
lls (layers) due to an additional, deformational and/or polarizational pote
ntial arising around these locking wells (layers). Using the tight-binding
and adiabatic approximations the energy spectrum of such self-trapped slate
s is found. (C) 2000 Elsevier Science B.V. All rights reserved.