Holstein polaron in the presence of disorder

Non-local, inhomogeneous and retarded response observed in experiments is reproduced by introducing the Inhomogeneous Momentum Average (IMA) method to study single polaron problems with disorder in the on-site potential and/or spatial variations of the electron-phonon couplings and/or phonon frequencies. We show that the electron-phonon coupling gives rise to an additional inhomogeneous, strongly retarded potential, which makes instant approximations questionable. The accuracy of IMA is demonstrated by comparison with results from the approximation free Diagrammatic Monte Carlo (DMC) method. Its simplicity allows for easy study of many problems that were previously unaccessible. As an example, we show how inhomogeneities in the electron-phonon coupling lead to nonlocal, retarded response in scanning tunneling microscopy (STM) images.