Nature of extrinsic and intrinsic self-trapping of charge carriers in underdoped cuprate high-$T_{\text{c}}$ superconductors

Nature of extrinsic and intrinsic self-trapping (ST) of charge carriers in cuprates have been studied theoretically. The binding energies and radii of the extrinsic and intrinsic large polarons and bipolarons in cuprates are calculated variationally using the continuum model and adiabatic approximation. We have shown that the extrinsic and intrinsic three-dimensional (3D) large bipolarons exist in underdoped cuprates at $\eta ={\epsilon }_{\mathrm{\infty }}\mathrm{/}{\epsilon }_0<0.127$ and $\eta <0.138$, respectively [where ${\epsilon }_{\mathrm{\infty }}$ (${\epsilon }_0$) is the optic (static) dielectric constant].