Electron and phonon spectrum in a metallic nanohybrid

Recent experiments on metallic nanohybrids have revealed unusually strong electron-phonon effects emerging from nanoscale interfaces, despite the weak coupling character of the constituent bulk materials. Motivated by these observations, we investigate the electronic and lattice spectral properties of an inhomogeneous electron phonon system in which strong coupling is confined to interfacial regions embedded in a weakly coupled metallic background. Using a real-space formulation of the Holstein model combined with Langevin dynamics for lattice equilibration, we compute both electronic and phonon spectral functions in the presence of spatially varying coupling. We find that increasing the fraction of interfacial sites leads to a pronounced broadening of electronic spectral features, reflecting enhanced quasiparticle scattering from lattice distortions, but leaves the underlying band dispersion largely intact. Simultaneously, the phonon spectrum exhibits significant softening and damping, originating from strongly distorted interfacial regions. These modifications result in a redistribution of the Eliashberg spectral function toward low frequencies, producing a substantial enhancement of the effective electron-phonon coupling constant. Our results demonstrate that spatial inhomogeneity alone can strongly renormalize both electronic and lattice spectra, and provide a microscopic framework for understanding interface-driven transport and interaction effects in metallic nanohybrids.