Polaron Crossover and Bipolaronic Metal-Insulator Transition in the Holstein model at half-filling

The evolution of the properties of a finite density electronic system as the electron-phonon coupling is increased are investigated in the Holstein model using the Dynamical Mean-Field Theory (DMFT). We compare the spinless fermion case, in which only isolated polarons can be formed, with the spinful model in which the polarons can bind and form bipolarons. In the latter case, the bipolaronic binding occurs through a metal-insulator transition. In the adiabatic regime in which the phonon energy is small with respect to the electron hopping we compare numerically exact DMFT results with an analytical scheme inspired by the Born-Oppenheimer procedure. Within the latter approach,a truncation of the phononic Hilbert space leads to a mapping of the original model onto an Anderson spin-fermion model. In the anti-adiabatic regime (where the phonon energy exceeds the electronic scales) the standard treatment based on Lang-Firsov canonical transformation allows to map the original model on to an attractive Hubbard model in the spinful case. The separate analysis of the two regimes supports the numerical evidence that polaron formation is not necessarily associated to a metal-insulator transition, which is instead due to pairing between the carriers. At the polaron crossover the Born-Oppenheimer approximation is shown to break down due to the entanglement of the electron-phonon state.Comment: 19 pages, 15 figure

Band dispersion and electronic lifetimes in crystalline organic semiconductors

The consequences of several microscopic interactions on the photoemission spectra of crystalline organic semiconductors (OSC) are studied theoretically. It is argued that their relative roles can be disentangled by analyzing both their temperature and their momentum/energy dependence. Our analysis shows that the polaronic thermal band narrowing, that is the foundation of most theories of electrical transport in OSC, is inconsistent in the range of microscopic parameters appropriate for these materials. An alternative scenario is proposed to explain the experimental trends.Comment: 4+ pages, revised conclusions; accepted for publication in Phys. Rev. Let

Polaron Crossover and Bipolaronic Metal-Insulator Transition in the half- filled Holstein model

The formation of a finite density multipolaronic state is analyzed in the context of the Holstein model using the Dynamical Mean-Field Theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of Dynamical Mean-Field Theory is compared with weak-coupling perturbation theory, non-crossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated to a metal-insulator transition, which is instead due to bipolaron formation.Comment: 4 pages, 5 figure

On dynamical localization corrections to band transport

Bloch-Boltzmann transport theory fails to describe the carrier diffusion in current crystalline organic semiconductors, where the presence of large-amplitude thermal molecular motions causes substantial dynamical disorder. The charge transport mechanism in this original situation is now understood in terms of a transient localization of the carriers' wavefunctions, whose applicability is however limited to the strong disorder regime. In order to deal with the ever-improving performances of new materials, we develop here a unified theoretical framework that includes transient localization theory as a limiting case, and smoothly connects with the standard band description when molecular disorder is weak. The theory, which specifically adresses the emergence of dynamical localization corrections to semiclassical transport, is used to determine a "transport phase diagram" of high-mobility organic semiconductors.Comment: 14 pages, 6 figures completely revised versio

Strong interplay between electron-phonon interaction and disorder in low doped systems

The effects of doping on the spectral properties of low doped systems are investigated by means of Coherent Potential Approximation to describe the distributed disorder induced by the impurities and Phonon-Phonon Non-Crossing Approximation to characterize a wide class of electron-phonon interactions which dominate the low-energy spectral features. When disorder and electron-phonon interaction work on comparable energy scales, a strong interplay between them arises, the effect of disorder can no more be described as a mere broadening of the spectral features and the phonon signatures are still visible despite the presence of strong disorder. As a consequence, the disorder-induced metal-insulator transition, is strongly affected by a weak or moderate electron-phonon coupling which is found to stabilize the insulating phase.Comment: New version with improved bibliography and discussio

The induced charge in a Frohlich polaron: Sum rule and spatial extent

Within the path integral formalism, we derive exact expressions for correlation functions measuring the lattice charge induced by an electron and associated polarization in Frohlich polaron problem. We prove that a sum rule for the total induced charge, already obtained within approximated approaches is indeed exact. As a consequence the total induced charge is shown rigorously to be temperature independent. In addition we perform path integral Monte Carlo calculations of the correlation functions and we compare with variational results based on Feynman method. As the temperature increases the polaron radius decreases. On the other hand at high temperatures the electron motion is not hindered by the lattice. These apparently contradictory results are discussed.Comment: 5 pages, 3 figures. Submitted to Phys. Rev.

Spectral properties and isotope effect in strongly interacting systems: Mott-Hubbard insulator and polaronic semiconductor

We study the electronic spectral properties in two examples of strongly interacting systems: a Mott-Hubbard insulator with additional electron-boson interactions, and a polaronic semiconductor. An approximate unified framework is developed for the high energy part of the spectrum, in which the electrons move in a random field determined by the interplay between magnetic and bosonic fluctuations. When the boson under consideration is a lattice vibration, the resulting isotope effect on the spectral properties is similar in both cases, being strongly temperature and energy dependent, in qualitative agreement with recent photoemission experiments in the cuprates.Comment: Refs. added, revised introduction and conclusio

Phenomenological model for charge dynamics and optical response of disordered systems: application to organic semiconductors

We provide a phenomenological formula which describes the low-frequency optical absorption of charge carriers in disordered systems with localization. This allows to extract, from experimental data on the optical conductivity, the relevant microscopic parameters determining the transport properties, such as the carrier localization length and the elastic and inelastic scattering times. This general formula is tested and applied here to organic semiconductors, where dynamical molecular disorder is known to play a key role in the transport properties. The present treatment captures the basic ideas underlying the recently proposed transient localization scenario for charge transport, extending it from the d.c. mobility to the frequency domain. When applied to existing optical measurements in rubrene FETs, our analysis provides quantitative evidence for the transient localization phenomenon. Possible applications to other disordered electronic systems are briefly discussed.Comment: extended version with optical conductivity formulas for both non-degenerate and degenerate electron system

Hopping dynamics of interacting polarons

We derive an effective cluster model to address the transport properties of mutually interacting small polarons. We propose a decoupling scheme where the hopping dynamics of any given particle is determined by separating out explicitly the degrees of freedom of its environment, which are treated as a statistical bath. The general cavity method developed here shows that the long-range Coulomb repulsion between the carriers leads to a net increase of the thermal activation barrier for electrical transport, and hence to a sizable reduction of the carrier mobility. A mean-field calculation of this effect is provided, based on the known correlation functions of the interacting liquid in two and three dimensions. The present theory gives a natural explanation of recent experiments performed in organic field-effect transistors with highly polarizable gate dielectrics, and might well find application in other classes of polaronic systems such as doped transition-metal oxides