Theory of subgap photoemission in one-dimensional electron-phonon systems: An instanton approach to pseudogaps

For a one-dimensional electron-phonon system we consider photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron-phonon interactions these processes are described by nonlinear configurations of an instanton type. The one-parameter ansatz for the extremal instanton trajectory allows one to span a wide spectral rang providing qualitatively correct limits. We calculate intensities of the photoemission spectroscopy (PES) including momentum-resolved or angle-resolved PES (ARPES), and supplement known results for the optical subgap absorption. We start with the generic case of a one-dimensional semiconductor with a pronounced polaronic effect. We consider in details the Peierls model for a half-filled band of electrons coupled to a lattice which describes the polyacethylene and some commensurate charge-density waves. Particular attention was required to study the momentum dependences for the ARPES, where we face an intriguing interference between the time evolution and the translational motion of the instantons.