Bound polaron in a spherical quantum dot: The all-coupling variational approach

The effect of the electron-phonon interaction on an electron bound to an impurity in a spherical quantum dot embedded in a nonpolar matrix is studied theoretically. The all-coupling variational method is used to calculate the polaron energy shift including interaction with both bulk and surface LO phonons. The interaction of an electron with the image charge potential is taken into account. Comparison with the results of the adiabatic approach is also provided. General analytical results are obtained for small and large dots for different impurity positions. Numerical studies of the polaron properties have been performed for quantum dots of different radii with arbitrary strengths of the electron-phonon coupling and electron-impurity binding. It is shown that (1) as a function of the impurity position, the total value of the electron-phonon interaction has a maximum (in magnitude) when the impurity is located in the center of the dot in the case of weak coupling, and reaches its maximum at some intermediate impurity position for greater values of the electron-phonon and electron-impurity interactions and; (2) as a function of the impurity position, the interaction with surface phonons is greater for strong binding when the impurity is close to the boundary of the dot, reaches a maximum when the impurity is positioned on the surface of the dot in the weak coupling case and at some arbitrary impurity position inside the dot for the strong electron-phonon coupling and/or binding.