Electron-phonon coupling in a two-dimensional inhomogeneous electron gas: consequences for surface spectral properties

We investigate the coupling of an inhomogeneous electron system to phonons. The properties of an electronic system composed of a mixture of microscopic ordered and disordered islands are changed fundamentally by a phonon mode. In high-Tc cuprates, such a phase separation scenario is supported by recent STM and nuclear quadrupole resonance studies. We show that even a weak or moderate electron-phonon coupling can be sufficient to produce dramatic changes in the electronic state of the inhomogeneous electron gas. The spectral properties calculated in our approach provide a natural explanation of the low-energy nodal ARPES features and exhibit a novel non-Fermi-liquid state stabilized through electron-phonon coupling.