As proposed originally by Landau
free electrons in a solid, introduced for example by doping or irradiation, can interact with the vibrations of the lattice to form a localized quasi-particle known as a polaron. Strongly localized polarons (also called Holstein polarons) can condensate around high-symmetry sites of the lattice with electrons or holes occupying local degenerate orbitals that experience the JTE. These Jahn–Teller polarons break both translational and point group symmetries of the lattice where they are found and have been attributed important roles in effects like colossal magnetoresistance and superconductivity.
Paramagnetic impurities in semiconducting, dielectric, diamagnetic and ferrimagnetic hosts can all be described using a JT model. For example, these models were used extensively in the 1980s and 1990s to describe ions of Cr, V and Ti substituting for Ga in GaAs and GaP.
The fullerene C can form solid compounds with alkali metals known as fullerides. CsC can be superconducting at temperatures up to 38K under applied pressure, whereas compounds of the form AC are insulating (as reviewed by Gunnarsson).  JT effects both within the C molecules (intramolecular) and between C molecules (intermolecular) play a part in the mechanisms behind various observed properties in these systems. For example, they could mean that the Migdal–Eliashberg treatment of superconductivity breaks down. Also, the fullerides can form a so-called new state of matter known as a Jahn–Teller metal, where localised electrons coexist with metallicity and JT distortions on the C molecules persist.