S. Ciuchi

Tunable Fröhlich polarons in organic single-crystal transistors

In organic field-effect transistors (FETs), charges move near the surface of an organic semiconductor, at the interface with a dielectric. In the past, the nature of the microscopic motion of charge carriers—which determines the device performance—has been related to the quality of the organic semiconductor. Recently, it was discovered that the nearby dielectric also has an unexpectedly strong influence. The mechanisms responsible for this influence are not understood. To investigate these mechanisms, we have studied transport through organic single-crystal FETs with different gate insulators. We find that the temperature dependence of the mobility evolves from metallic-like to insulating-like with increasing dielectric constant of the insulator. The phenomenon is accounted for by a two-dimensional Fröhlich polaron model that quantitatively describes our observations and shows that increasing the dielectric polarizability results in a crossover from the weak to the strong polaronic coupling regime. This represents a considerable step forward in our understanding of transport through organic transistors, and identifies a microscopic physical process with a large influence on device performance.

DYNAMICAL MEAN-FIELD THEORY OF THE SMALL POLARON

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground-state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion, at both zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground-state properties, such as the effective polaron mass, which show a continuous behavior as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more open in the density of states at low energy, while the high-energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence, narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such an effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum always has a multipeaked structure.

SQUEEZING PHENOMENA IN INTERACTING ELECTRON-PHONON SYSTEMS

The molecular crystal model of electrons coupled to Einstein phonons is studied as a function of the two parameters: the coupling constant A and the ratio of the electron-phonon coupling energy to the phonon energy, denoted by α. Both the one-electron and the many-electron models are studied, starting (for the former) from the adiabatic limit and (for the latter) from the anti-adiabatic one. In the “multiphonon” regime α>1, the sharp crossover between quasi-free electrons (λ≪1) and small polarons (λ≫1) is investigated, emphasizing the anomalous lattice fluctuations which occur in the intermediate regime (λ≈1). These fluctuations are due to the band motion of the electrons strongly coupled to the lattice and are shown in turn to weaken the electron mass renormalization inherent to self-trapping. In a relevant part of the intermediate region the effective electron mass slowly increases with λ, due to a competition between the phonon dressing effect and the reduction of lattice momentum fluctuations. This re...

The Transient Localization Scenario for Charge Transport in Crystalline Organic Materials

Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an original regime of transport called \textit{transient localization}, sharing features of both localized and itinerant electron systems. After a brief review of experimental observations that pose a challenge to the theory, we concentrate on a commonly studied model which describes the interaction of the charge carriers with inter-molecular vibrations. We present different theoretical approaches that have been applied to the problem in the past, and then turn to more modern approaches that are able to capture the key microscopic phenomenon at the origin of the puzzling experimental observations, i.e. the quantum localization of the electronic wavefuntion at timescales shorter than the typical molecular motions. We describe in particular a relaxation time approximation which clarifies how the transient localization due to dynamical molecular motions relates to the Anderson localization realized for static disorder, and allows us to devise strategies to improve the mobility of actual compounds. The relevance of the transient localization scenario to other classes of systems is briefly discussed.

Transient localization in crystalline organic semiconductors

A relation derived from the Kubo formula shows that optical conductivity measurements below the gap frequency in doped semiconductors can be used to probe directly the time-dependent quantum dynamics of charge carriers. This allows to extract fundamental quantities such as the elastic and inelastic scattering rates, as well as the localization length in disordered systems. When applied to crystalline organic semiconductors, an incipient electron localization caused by large dynamical lattice disorder is unveiled, implying a breakdown of semiclassical transport.

Tailoring the molecular structure to suppress extrinsic disorder in organic transistors

In organic field-effect transistors, the structure of the constituent molecules can be tailored to minimize the disorder experienced by charge carriers. Experiments on two perylene derivatives show that disorder can be suppressed by attaching longer core substituents - thereby reducing potential fluctuations in the transistor channel and increasing the mobility in the activated regime - without altering the intrinsic transport properties.

Polaron crossover and bipolaronic metal-insulator transition in the half-filled Holstein model

The formation of a finite-density polaronic 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, noncrossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated with a metal-insulator transition, which is instead due to bipolaron formation.

Molecular Fingerprints in the Electronic Properties of Crystalline Organic Semiconductors: From Experiment to Theory

By comparing photoemission spectroscopy with a nonperturbative dynamical mean field theory extension to many-body ab initio calculations, we show in the prominent case of pentacene crystals that an excellent agreement with experiment for the bandwidth, dispersion, and lifetime of the hole carrier bands can be achieved in organic semiconductors, provided that one properly accounts for the coupling to molecular vibrational modes and the presence of disorder. Our findings rationalize the growing experimental evidence that even the best band structure theories based on a many-body treatment of electronic interactions cannot reproduce the experimental photoemission data in this important class of materials.

The small-polaron crossover: Comparison between exact results and vertex correction approximation

We study the crossover from quasi-free electron to small polaron in the Holstein model for a single electron by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice. We show that the crossover occurs when both strong coupling (λ > 1) and multiphonon (α2 > 1) conditions are fulfilled leading to different relevant coupling constants (λ) in the adiabatic and (α2) antiadiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.

Band dispersion and electronic lifetimes in crystalline organic semiconductors.

The consequences of several microscopic interactions on the photoemission spectra of crystalline organic semiconductors 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, which is the foundation of most theories of electrical transport in organic semiconductors, is inconsistent in the range of microscopic parameters appropriate for these materials. An alternative scenario is proposed to explain the experimental trends.