Vector Polarons in a Degenerate Electron System

We consider a one dimensional model of an electron in a doubly (or nearly) degenerate band that interacts with elastic distortions. We show that the electron equations of motion reduce to a set of coupled non-linear Schrodinger equations. For the case of interband electron-phonon coupling stemming from local Jahn-Teller interactions, new multicomponent self-localized polaron solutions --vector polarons-- are described and classified. The phase diagram for the different types of vector polarons in this model is presented. By interpreting the components of the orbital doublet as those of spin-1/2, our results can also be used to describe bound magnetic polarons.