Electron-phonon interaction on bundled structures: Static and transport properties

We study the small-polaron problem of a single electron interacting with the lattice for the Holstein model in the adiabatic limit on a comb lattice hen the electron-phonon interaction acts only on the base sites. The ground state properties can be easily deduced from the ones of a linear chain with a appropriate rescaling of the coupling constant. On the other hand, the dynamical properties, that involve the complete spectrum of the system, present an exotic behavior. In the weak coupling limit the Drude weight (zero-frequency-conductivity) is enhanced with respect to its free-case value, contrary to the linear chain case, where for every finite value one has suppression of the Drude peak. More interestingly, the loss of coherent electron motion and the polaronic localization of the carrier occurs for different coupling values. Thus for intermediate coupling, a different phase appears with large kinetic energy and no coherent motion.