Lippmann–Schwinger Approach to Electron–Phonon Binding in Solid-State Materials

Electron–phonon interactions strongly influence charge transport and localization in solid-state materials, yet conventional perturbative treatments quantify them only indirectly through coupling constants, relaxation times, or scattering-derived energies. We present a framework based on the homogeneous Lippmann–Schwinger (LS) equation in momentum space to compute electron–phonon binding energies and corresponding wavefunctions directly. The interaction is modeled using a Yukawa-type potential that depends on the screening wavevector and incorporates a strength parameter to account for dielectric screening across different materials. By systematically varying the effective mass and screening wavevector, we map binding behavior from oxide semiconductors (e.g., TiO₂, small-polaron regime) to hybrid perovskites (e.g., MAPbI₃, large-polaron regime). The computed results confirm the formation of stable electron–phonon bound states, with binding energies in agreement with previous theoretical studies. This LS-based approach provides a direct, quantitative measure of electron–phonon coupling and can be extended to the scattering regime through the inhomogeneous equation, thereby connecting to experimentally accessible quantities such as the kink energy and coupling constant.