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 nonlinear Schrödinger equations. For the case of interband electron-phonon coupling stemming from local Jahn-Teller interactions, 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-$\frac{1}{2}$, our results can also be used to describe bound magnetic polarons.

Figure 1

Plot of type II polaron ($\alpha =0.2$ and $\omega =0.6$). Solid line is $r_1\left(\xi \right)$, and $r_2\left(\xi \right)$ is dashed.

Figure 2

Plot of type III polaron ($\beta =1$ and $\omega =1$) for $\theta =\frac{\pi }{5}$. Solid line is $r_1\left(\xi \right)$, and $r_2\left(\xi \right)$ is dashed.

Figure 3

Plot of the polaron phase diagram. Type I polarons are stable in region I, and type II polarons are stable in region II. Type III polarons stably exist for ${\gamma }_1=0$ (horizontal semiaxis). (We take the arbitrary case of $\Delta =0.1$.)