Strong-Coupled Piezoelectric Polaron

A semiclassical, variational calculation for the strong-coupled piezoelectric polaron gives the following results for the ground-state energy and polaron radius, respectively: $U_0=-0.47\mathrm{}\left(\frac{m^{*}}{m}\right){\left(\frac{{\kappa }^2}{\epsilon }\right)}^2 \mathrm{eV},$ and $R=3.5\mathrm{}\left(\frac{\epsilon }{{\kappa }^2}\right)\left(\frac{m}{m^{*}}\right) \mathrm{\AA },$ where $m^{*}$ is the band effective mass, $\kappa$ is the electromechanical coupling constant, and $\epsilon$ is the strain-free dielectric constant. The theory is expected to be valid when $\left|U_0\right|$ is larger than thermal energies and $R$ is considerably larger than unit-cell dimensions. A calculation of the polaron effective mass, having a more limited region of validity, gives $m_p\approx m^{*}\left[1+\frac{2\left|U_0\right|}{m^{*}{v_s}^2}\right],$ where $v_s$ is the velocity of sound.