Dynamical mean-field theory of transport of small polarons

Thermal-Stabilized Protonated TiO2 for Heat-Accelerated Photoelectrochemical Water Splitting

Enhancing the charge separation efficiency is a big challenge that limits the energy conversion efficiency of photoelectrochemical (PEC) water splitting. Surface states generated by protonation of TiO2 are the efficient charge separation passageways to massively accept or transfer the photogenerated electrons. However, a challenge is to avoid the deprotonation of a protonated TiO2 photoelectrode at the operation temperature. Here, we found that the terminal hydroxyl group (OHT) as surface states on the TiO2 surface generated via electrochemical protonation of TiO2 at 90 °C [90-TiO2-x-(OH)x] is thermally stable. As a result, the thermally enhanced photocurrent of the 90-TiO2-x-(OH)x electrode reached 1.05 mA cm-2 under 80 °C, and the stability was maintained up to 10 h with a slight photocurrent decrease of 3%. The thermally stable surface states as charge separation paths provide an effective method to couple the heat field with the PEC process via thermal-stimulating hopping of polarons.

Thermally Accelerated Surface Polaron Hopping in Photoelectrochemical Water Splitting

Electron-hole separation is a main challenge that limits the energy efficiency of photoelectrochemical water splitting for hydrogen fuel production. Surface polaron states with an energy level distribution near the conduction band are highly efficient charge separation passageways to massively accept or transfer the photogenerated electrons. Here, we found that the charge separation via surface polaron states could be further enhanced by heating (<100 °C) to accelerate the electron mobility of surface polaron states. As a result of heating from 30 to 70 °C, the saturated photocurrent increased about 34.5% under 1 sun and 18.3% under 10 suns from heat-induced increase in electron flux of surface polaron states. The heat-sensitive surface-state electron transfer provides a new heat-photoelectricity coupling mechanism to guide the design of new photoanodes that are available for complementary multienergy systems with high energy efficiency.

Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.

Reorganization energies and spectral densities for electron transfer problems in charge transport materials

Various contributions to the outer reorganization energy of an electron transfer system and their theoretical and computational aspects have been discussed.

Single-Crystal Pentacene Valence-Band Dispersion and Its Temperature Dependence

The electronic structures of the highest occupied molecular orbital (HOMO) or the HOMO-derived valence bands dominate the transport nature of positive charge carriers (holes) in organic semiconductors. In the present study, the valence-band structures of single-crystal pentacene and the temperature dependence of their energy-momentum dispersion relations are successfully demonstrated using angle-resolved ultraviolet photoelectron spectroscopy (ARUPS). For the shallowest valence band, the intermolecular transfer integral and effective mass of the holes are evaluated as 43.1 meV and 3.43 times the electron rest mass, respectively, at room temperature along the crystallographic direction for which the widest energy dispersion is expected. The temperature dependence of the ARUPS results reveals that the transfer integral values (hole effective mass) are enhanced (reduced) by ∼20% on cooling the sample to 110 K.

Disorder-Driven Metal-Insulator Transitions in Deformable Lattices

We show that, in the presence of a deformable lattice potential, the nature of the disorder-driven metal-insulator transition is fundamentally changed with respect to the noninteracting (Anderson) scenario. For strong disorder, even a modest electron-phonon interaction is found to dramatically renormalize the random potential, opening a mobility gap at the Fermi energy. This process, which reflects disorder-enhanced polaron formation, is here given a microscopic basis by treating the lattice deformations and Anderson localization effects on the same footing. We identify an intermediate "bad insulator" transport regime which displays resistivity values exceeding the Mott-Ioffe-Regel limit and with a negative temperature coefficient, as often observed in strongly disordered metals. Our calculations reveal that this behavior originates from significant temperature-induced rearrangements of electronic states due to enhanced interaction effects close to the disorder-driven metal-insulator transition.

Probing the Metal-Insulator Transition in BaTiO_{3} by Electrostatic Doping

The metal-to-insulator transition in BaTiO_{3} is investigated using electrostatic doping, which avoids effects from disorder and strain that would accompany chemical doping. SmTiO_{3}/BaTiO_{3}/SrTiO_{3} heterostructures are doped with a constant sheet carrier density of 3×10^{14}  cm^{-2} that is introduced via the polar SmTiO_{3}/BaTiO_{3} interface. Below a critical BaTiO_{3} thickness, the structures exhibit metallic behavior with high carrier mobilities at low temperatures, similar to SmTiO_{3}/SrTiO_{3} interfaces. Above this thickness, data indicate that the BaTiO_{3} layer becomes ferroelectric. The BaTiO_{3} lattice parameters increase to a value consistent with a strained, tetragonal unit cell, the structures are insulating below ∼125  K, and the mobility drops by more than an order of magnitude, indicating self-trapping of carriers. The results shed light on the interplay between charge carriers and ferroelectricity.

Current-voltage characteristics of manganite-titanite perovskite junctions

After a general introduction into the Shockley theory of current voltage (J-V) characteristics of inorganic and organic semiconductor junctions of different bandwidth, we apply the Shockley theory-based, one diode model to a new type of perovskite junctions with polaronic charge carriers. In particular, we studied manganite-titanate p-n heterojunctions made of n-doped SrTi1- y Nb y O3, y = 0.002 and p-doped Pr1- x Ca x MnO3, x = 0.34 having a strongly correlated electron system. The diffusion length of the polaron carriers was analyzed by electron beam-induced current (EBIC) in a thin cross plane lamella of the junction. In the J-V characteristics, the polaronic nature of the charge carriers is exhibited mainly by the temperature dependence of the microscopic parameters, such as the hopping mobility of the series resistance and a colossal electro-resistance (CER) effect in the parallel resistance. We conclude that a modification of the Shockley equation incorporating voltage-dependent microscopic polaron parameters is required. Specifically, the voltage dependence of the reverse saturation current density is analyzed and interpreted as a voltage-dependent electron-polaron hole-polaron pair generation and separation at the interface.

Mobility of Holstein polaron at finite temperature: an unbiased approach

We present the first unbiased results for the mobility μ of a one-dimensional Holstein polaron obtained by numerical analytic continuation combined with diagrammatic and worldline Monte Carlo methods in the thermodynamic limit. We have identified for the first time several distinct regimes in the λ-T plane including a band conduction region, incoherent metallic region, an activated hopping region, and a high-temperature saturation region. We observe that although mobilities and mean free paths at different values of λ differ by many orders of magnitude at small temperatures, their values at T larger than the bandwidth become very close to each other.

Organic/inorganic hybrid materials: challenges for ab initio methodology

CONSPECTUS: Organic/inorganic hybrid structures are most exciting since one can expect new properties that are absent in either of their building blocks. They open new perspectives toward the design and tailoring of materials with desired features and functions. Prerequisite for real progress is, however, the in-depth understanding of what happens on the atomic and electronic scale. In this respect, hybrid materials pose a challenge for electronic-structure theory. Methods that proved useful for describing one side may not be applicable for the other one, and they are likely to fail for the interfaces. In this Account, we address the question to what extent we can quantitatively describe hybrid materials and where we even miss a qualitative description. We note that we are dealing with extended systems and thus adopt a solid-state approach. Therefore, density-functional theory (DFT) and many-body perturbation theory (MBPT), the GW approach for charged and the Bethe-Salpeter equation for neutral excitations, are our methods of choice. We give a brief summary of the used methodology, focusing on those aspects where problems can be expected when materials of different character meet at an interface. These issues are then taken up when discussing hybrid materials. We argue when and why, for example, standard DFT may fall short when it comes to the electronic structure of organic/metal interfaces or where the framework of MBPT can or must take over. Selected examples of organic/inorganic interfaces, structural properties, electronic bands, optical excitation spectra, and charge-transport properties as obtained from DFT and MBPT highlight which properties can be reliably computed for such materials. The crucial role of van der Waals forces is shown for sexiphenyl films, where the subtle interplay between intermolecular and molecule-substrate interactions is decisive for growth and morphologies. With a PTCDA monolayer on metal surfaces we discuss the performance of DFT in terms of interfacial electronic structure. We face the problem of a so far hidden variable, namely, electron-vibrational coupling, regarding level alignment at interfaces between organic and inorganic semiconductors. Poly(para-phenylene) adsorbed on graphene and encapsulated in carbon nanotubes represent case studies to demonstrate the impact of polarization effects and exciton delocalization in optoelectronic excitations, respectively. Polaron-induced band narrowing and its consequences for charge transport in organic crystals is exemplified for the HOMO bandwidth in naphthalene crystals. On the basis of these prototypical systems, we discuss what is missing to reach predictive power on a quantitative level for organic/inorganic hybrid materials and, thus, open a perspective toward the computational discovery of new materials for optoelectronic applications.

Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals

Two distinct pictures are usually evoked when modeling charge transport in organic crystals, that is, band and hopping models, the signature of which is conveyed by a characteristic temperature dependence of mobility. Here, we present a novel flexible surface hopping approach compliant with general Hamiltonians that is able to grasp the crossover from hopping to band-like transport regimes. This approach is applied to solve a one-dimensional mixed quantum-classical model and to calculate the temperature dependence of charge mobility along with the degree of charge spatial localization. It is found that the roles of both local and nonlocal electron-phonon couplings strongly depend on the intrinsic charge localization strength.

Molecular photovoltaics in nanoscale dimension

This review focuses on the intrinsic charge transport in organic photovoltaic (PVC) devices and field-effect transistors (SAM-OFETs) fabricated by vapor phase molecular self-assembly (VP-SAM) method. The dynamics of charge transport are determined and used to clarify a transport mechanism. The 1,4,5,8-naphthalene-tetracarboxylic diphenylimide (NTCDI) SAM devices provide a useful tool to study the fundamentals of polaronic transport at organic surfaces and to discuss the performance of organic photovoltaic devices in nanoscale. Time-resolved photovoltaic studies allow us to separate the charge annihilation kinetics in the conductive NTCDI channel from the overall charge kinetic in a SAM-OFET device. It has been demonstrated that tuning of the type of conductivity in NTCDI SAM-OFET devices is possible by changing Si substrate doping. Our study of the polaron charge transfer in organic materials proposes that a cation-radical exchange (redox) mechanism is the major transport mechanism in the studied SAM-PVC devices. The role and contribution of the transport through delocalized states of redox active surface molecular aggregates of NTCDI are exposed and investigated. This example of technological development is used to highlight the significance of future technological development of nanotechnologies and to appreciate a structure-property paradigm in organic nanostructures.

Characteristics of small- and large-polaron motion in organic crystals

Based on a generalized theory of charge transport in organic crystals we investigate the motion of polarons of arbitrary size. Within this theory, we analyze the influence of characteristic electronic, vibronic, and thermal energies and their role for the transport regimes. The polaron bandwidth is identified as the central temperature-dependent quantity. The size of the dressed charge carriers is used to analyze the correlation between the polaron size and transport mechanism. In addition, we propose that the band and hopping transport can be distinguished by investigating the mobility anisotropy. To do this only electronic structure parameters are necessary for comparison.

Bandlike motion and mobility saturation in organic molecular semiconductors

We analyze a model that accounts for the inherently large thermal lattice fluctuations associated with the weak van der Waals intermolecular bonding in crystalline organic semiconductors. In these materials the charge mobility generally exhibits a "metalliclike" power-law behavior, with no sign of thermally activated hopping characteristic of carrier self-localization, despite apparent mean free paths comparable to or lower than the intermolecular spacing. Our results show that such a puzzling transport regime can be understood from the simultaneous presence of band carriers and incoherent states that are dynamically localized by the thermal lattice disorder.

Modelling charge transport in organic semiconductors: from quantum dynamics to soft matter

The charge carrier dynamics in organic semiconductors has been traditionally discussed with the models used in inorganic crystalline and amorphous solids but this analogy has severe limitations because of the more complicated role of nuclear motions in organic materials. In this perspective, we discuss how a new approach to the modelling of charge transport is emerging from the alliance between the conventional quantum chemical methods and the methods more traditionally used in soft-matter modelling. After describing the conventional limit cases of charge transport we discuss the problems arising from the comparison of the theory with the experimental and computational results. Several recent applications of numerical methods based on the propagation of the wavefunction or kinetic Monte Carlo methods on soft semiconducting materials are reviewed.

Charge transfer and coherence dynamics of a tunnelling system coupled to an harmonic oscillator

We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is initially displaced, a coherent dynamics of charge entangled with oscillator modes takes place. Coherency is, however, degraded as far as the oscillator mass increases, producing an increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability.

Effect of interfacial shallow traps on polaron transport at the surface of organic semiconductors

The photo-induced electron and hole transfer across the semiconductor-dielectric interface in trap-dominated p-type organic field-effect transistors has been investigated. It has been observed that the transfer of electrons into the dielectric results in a decrease of the field-effect mobility of polarons, suggesting that additional shallow traps are generated in the conduction channel. Using this effect, the dependence of the field-effect mobility on the density of shallow traps, mu(N), has been measured, which allowed us to estimate the average polaron trapping time, tau_{tr}=50+/-10 ps, and the density of shallow traps, N0=(3+/-0.5) x 10(11) cm(-2), in the channel of single-crystal tetracene devices.

Tunnelling system coupled to a harmonic oscillator: an analytical treatment

We give an analytical formula in term of continued fraction expansions for the spectral function of a tunnelling electron, coupled to a local lattice oscillation, in a two-site cluster at non-zero temperature. We also study the spectral function of the polaron, a better defined quasi-particle in the anti-adiabatic regime and at sufficiently low temperature. The exact results obtained allow us to look into a wide range of temperature and coupling. Asymptotic results can be obtained directly from the continued fraction expansions in both adiabatic and anti-adiabatic regimes. In the intermediate/strong anti-adiabatic case, in contrast to the usual Lang-Firsov approximation scheme, we found that there is no shrinking of the polaron band as temperature increases. Polaron bandwidth gets broader by temperature effects.

Quantum transport of slow charge carriers in quasicrystals and correlated systems

We show that the semiclassical model of conduction breaks down if the mean free path of charge carriers is smaller than a typical extension of their wave function. This situation is realized for sufficiently slow charge carriers and leads to a transition from a metalliclike to an insulatinglike regime when scattering by defects increases. This explains the unconventional conduction properties of quasicrystals and related alloys. The conduction properties of some heavy fermions or polaronic systems, where charge carriers are also slow, present a deep analogy.

Spin-singlet small bipolarons in Nb-doped BaTiO3

The magnetic susceptibility and the electrical resistivity of n-type BaTi1-xNbxO3 have been measured over a wide temperature range. It is found that, for 0<x<0.2, dopant electrons form immobile spin-singlet small bipolarons with binding energy around 110 meV. For x=0.2, a maximum in the electrical resistivity around 15 K indicates a crossover from band to hopping transport of the charge carriers, a phenomenon expected but rarely observed in real polaronic systems.

Band Structure of the Four Pentacene Polymorphs and Effect on the Hole Mobility at Low Temperature

The band structure of the four known polymorphs of pentacene is computed from first principles using the accurate molecular orbitals of the isolated molecule as the basis for the calculation of the crystalline orbitals. The computed bands are remarkably different for each polymorph, but their diversity can be easily rationalized using a simple analytical model that employs only three parameters. The effect of the electronic structure on the hole mobility was evaluated using a simple model based on the constant relaxation time approximation. It is found that the mobility tensor is highly anisotropic for three of the four considered polymorphs. The practical implication of this prediction on the technology of thin-film organic transistors is discussed.