Bipolaron States Research Articles

Many-body Green's function theory for electron-phonon interactions: Ground state properties of the Holstein dimer.

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.

Ground-state phase diagram of the quantum Rabi model

The Rabi model plays a fundamental role in understanding light-matter interaction. It reduces to the Jaynes-Cummings model via the rotating-wave approximation, which is applicable only to the cases of near resonance and weak coupling. However, recent experimental breakthroughs in upgrading light-matter coupling order require understanding the physics of the full quantum Rabi model (QRM). Despite the fact that its integrability and energy spectra have been exactly obtained, the challenge to formulate an exact wavefunction in a general case still hinders physical exploration of the QRM. Here we unveil a ground-state phase diagram of the QRM, consisting of a quadpolaron and a bipolaron as well as their changeover in the weak-, strong- and intermediate-coupling regimes, respectively. An unexpected overweighted antipolaron is revealed in the quadpolaron state, and a hidden scaling behavior relevant to symmetry breaking is found in the bipolaron state. An experimentally accessible parameter is proposed to test these states, which might provide novel insights into the nature of the light-matter interaction for all regimes of the coupling strengths.

Characteristics of strong-coupling bipolaron qubit in two-dimensional quantum dot in electric field

Based on Lee-Low-Pines (LLP) unitary transformation, this article adopts the variational method of the Pekar type and gets the energy and wave functions of the ground state and the first excited state of strong-coupling bipolaron in two-dimensional quantum dot in electric field, thus constructs a bipolaron qubit. The numerical results represent that the time oscillation period T 0 of probability density of the two electrons in qubit decreases with the increasing electric field intensity F and dielectric constant ratio of the medium η; the probability density Q of the two electrons in qubit oscillates periodically with the increasing time t; the probability of electron appearing near the center of the quantum dot is larger, while that appearing away from the center of the quantum dot is much smaller.

Enhanced Thermoelectric Properties of Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) by Binary Secondary Dopants

To simultaneously increase the electrical conductivity and Seebeck coefficient of poly(3,4-ethylenedioxythiophene):polystyrenesulfonate ( PSS) was a challenge for realizing efficient organic thermoelectrics. In this study, for the first time, we report both increased electrical conductivities and Seebeck coefficients, hence, enhanced thermoelectric properties of PSS thin films by doped with binary secondary dopants, dimethyl sulfoxide (DMSO) and poly(ethylene oxide) (PEO). Without modifying film morphology, the molar ratios of PEDOT to PSS are tuned by PEO, resulting in increased proportions of PEDOT in the bipolaron states. Our study provides a facile route to optimizing thermoelectric properties of PSS thin films.

Enzymatic polymerization of pyrrole with Trametes versicolor laccase and dioxygen in the presence of vesicles formed from AOT (sodium bis-(2-ethylhexyl) sulfosuccinate) as templates

The oxidative polymerization of pyrrole with the enzyme Trametes versicolor laccase (TvL) and dioxygen (O2) in aqueous solution at pH 3.5 was investigated and found to be regulated by anionic vesicles formed from sodium bis-(2-ethylhexyl) sulfosuccinate (AOT). The polymeric products obtained in the presence of the vesicular templates have high absorption at λ≈450 and 1000nm, which is indicative for polypyrrole (PPy) in its conductive bipolaron state. Absence of unpaired electrons in the bipolaronic PPy product obtained was supported by EPR measurements. Furthermore, the FTIR spectrum of isolated PPy is comparable with the FTIR spectrum reported in literature for chemically or electrochemically synthesized PPy. Under optimal reaction conditions in the presence of the vesicles, i.e., 6.0mM AOT, 8.0mM pyrrole, 3.7μM TvL, pH 3.5 (0.1M sodium dihydrogenphosphate solution), a pyrrole conversion of about 84% was obtained after 7 days reaction time at T≈25°C. Most of the dark green PPy products remained dispersed in the aqueous medium thanks to the vesicles, while the products obtained without vesicles or in presence of sodium di-n-butylsulfosuccinate (6.0mM) had a very different UV/vis/NIR absorption spectrum and almost completely precipitated from the solution. 2H NMR measurements of pyrrole-d5 and MD simulations of an AOT bilayer fragment, solvated into a sodium dihydrogenphosphate solution containing pyrrole, indicate partitioning of pyrrole at pH 3.5 into the region of the AOT membrane before pyrrole oxidation was initiated; however, a preferential binding and specific orientation of pyrrole in the vicinity of the AOT head group could be excluded. Binding of pyrrole to AOT bilayers at pH 3.5 was also compared with the binding of aniline to the same type of bilayers (vesicles) at pH 4.3. This comparison was made since it is known from previous work that aniline can also be polymerized enzymatically in the presence of AOT vesicles. The behavior of the two monomers is, however, quite different. Contrary to pyrrole, in the case of aniline at pH 4.3, anilinium cations were clearly shown by both methodologies – MD simulations and NMR measurements – to bind extensively to the vesicle surface, where the sulfonate group of AOT is localized. Therefore, it can be concluded that a specific pre-orientation of the monomers, before oxidation and polymerization are initiated by the enzymes, is not a common key feature of the two template-assisted reactions and, therefore, cannot be taken as a general explanation for the observed regulating effect of the vesicles. The origin of the vesicle template effect still needs to be elucidated.

Controlling the thermoelectric properties of polymers: application to PEDOT and polypyrrole.

Poly(3,4-ethylenedioxythiophene) (PEDOT) and polypyrrole (PPy) films have been prepared by an electrochemical method in a three electrode cell. The films have been obtained at different oxidation levels regarded as bipolaron, polaron and neutral states by varying the voltage, as is usually done in conjugated heterocyclic polymers. The voltage (-0.2 < V < 1.0 V) has been applied versus a Ag/AgCl reference electrode, producing a variation of one order of magnitude in the electrical conductivity and the Seebeck coefficient of the films. In the voltage range explored, the electrical conductivity increases from 80 to 766 S cm(-1) in PEDOT and from 15 to 160 S cm(-1) in PPy, while the Seebeck coefficient decreases from 37.0 to 9.6 μV K(-1) for PEDOT and from 51.0 to 6.7 μV K(-1) for PPy. The thermal conductivity remains unchanged with the oxidation state of the film, κ ≈ 0.35 ± 0.02 W m(-1) K(-1) for PEDOT and 0.17 ± 0.02 W m(-1) K(-1) for PPy. A maximum thermoelectric efficiency of 1.4 × 10(-2) for PEDOT and 6.8 × 10(-3) for PPy has been achieved. These changes are related to the doping level of the polymer films and they can be accurately controlled by the applied voltage. In this work, we provide a very simple method to control and optimize the power factor or the figure of merit of conducting polymers.

Charge density stabilised local electron spin pair states in insulating polymers

A model is presented that addresses the energy stability of localized electron states in insulating polymers with respect to delocalized free electron-like states at variable charge densities. The model was derived using an effective Hamiltonian for the total energy of electrons trapped in large polarons and spin-paired bipolarons, which includes the electrostatic interaction between charges that occurs when the charge density exceeds the infinite dilution limit. The phase diagram of the various electronic states with respect to the charge density is derived using parameters determined from experimental data for polyethylene, and it is found that a phase transition from excess charge in the form of stable polarons to a stable state of bipolarons with charge = 2 and spin number S = 0 is predicted for a charge density between 0.2 C/m3 and ∼2 C/m3. This transition is consistent with a change from low mobility charge transport to charge transport in the form of pulses with a mobility orders of magnitude higher that has been observed in several insulating polymers.

Electronic and magnetic properties of theTi5O9Magnéli phase

Structural, electronic and magnetic properties of Ti$_5$O$_9$ have been studied by \textit{ab initio} methods in low-, intermediate- and high-temperature phases. We have found the charge and orbital order in all three phases to be non-stable, and the formation of Ti$^{3+}$-Ti$^{3+}$ bipolaronic states less likely as compared to Ti$_4$O$_7$. Several quasidegenerate magnetic configurations were calculated to have different width of the band gap, suggesting that the reordering of the unpaired spins at Ti$^{3+}$ ions might at least partially be responsible for the changes in conductivity of this material.

Patterning a π-conjugated polyelectrolyte through sequential polymerization of a bifunctional ionic liquid monomer

An electronically conductive polyelectrolyte is prepared by the sequential polymerization of a bifunctional imidazolium-based ionic liquid (IL) monomer, composed of a thienyl and vinyl containing cation paired with a tetrafluoroborate anion. In the first step, potentiodynamic electropolymerization of the thienyl moiety forms a cationic polyalkylthiophene that is soluble in select organic solvents. Cyclic voltammetry (CV) was used to determine the polymer p-doping potential (0.31 V) and the bipolaronic state (1.49 V). The polymer exhibits electrochromism, converting from red in the neutral state (λmax = 443 nm) to dark blue in the polaronic state (λmax = 819 nm). The solution-processable polymer can be cast into a film, masked and patterned by UV-initiated free radical polymerization of the vinyl moiety. Small-angle X-ray scattering (SAXS) revealed that the insoluble crosslinked polyalkylthiophene–polyvinylimidazolium adopts a lamellar structure with a lattice spacing of 3.3 nm. Four-probe d.c. conductivity measurements determined the de-doped electrical conductivity was 1.0 × 10−2 S/cm. The results underscore the importance of the anion in controlling the polymerization of IL monomers.

In situ UV–vis spectroelectrochemical study of dye doped nanostructure polypyrrole as electrochromic film

In the present work, the electrosynthesis and the spectroelectrochemical characterization of eriochrome cyanine R (ECR) doped polypyrrole (PPy) were described. Nanostructured PPy–ECR film was electrochemically deposited onto fluorine doped tin oxide (FTO) coated/glass electrode from aqueous solution containing a water-soluble trianionic dye, ECR, as dopant. The surface morphology was studied using scanning electron microscopy (SEM) analysis. Dye doped polymer film showed spherical morphology with primary particles 70–90nm in size and 900nm thicknesses. The main characteristics of PPy–ECR film include uniformity, stability and adherent on FTO electrodes, which are better compared to that of PPy film. In situ UV–vis spectroelectrochemistry was used as a powerful tool in analyzing the evolution of the neutral, polaron and bipolaron states in prepared polymer films as they were redox cycled (from −0.6V to +0.6V) in NaClO4. As the polymers gets oxidized, the intensity of the π–π* transition (neutral state) decreases while the charge carrier bands at longer wavelengths (polaron band and bipolaron band) increases in intensity and the color of the polymers change. We found that these variations are more intense in the case of dye doped to those of PPy. The spectroelectrochemical studies showed that the electrochromic properties of dye doped polymer (PPy–ECR) such as optical contrast (27%), switching time (⩽1.5s) and film stability (100 cycles) were greatly enhanced relative to the PPy film.

Neutral, Polaron, and Bipolaron States in PEDOT Prepared by Photoelectrochemical Polymerization and the Effect on Charge Generation Mechanism in the Solid-State Dye-Sensitized Solar Cell

We investigate dye-sensitized solar cells (DSSCs) based on PEDOT as hole conductor and prepared by photoelectrochemical polymer deposition at different light intensities. We specifically investigate the effect of light intensity on the PEDOT polymer and in turn the efficiency of the solar cells. We find that the PEDOT prepared by this method is largely oxidized and contains significant amounts of polarons and bipolarons and only a small fraction of neutral PEDOT. Photoelectrochemical polymer deposition under low light intensity leads to a particularly low fraction of neutral PEDOT and a high fraction of bipolarons as measured in the UV–vis spectra. The solar cells based on PEDOT as a hole conductor prepared under these conditions are the most efficient with a higher power conversion efficiency, which can be explained by a longer electron lifetime, faster charge transport, and higher transparency of the PEDOT. Interestingly, we conclude that in this type of solid-state DSSCs the mechanism of dye regenerati...

Reduction and transition in thermal activation for charge transport through electrolyte-gated polythiophene thin films with high hole densities

We investigate the activation energy for electrical charge transport through a polythiophene thin film. The results are particularly obtained under high hole density (5.9 × 1020 holes/cm3) through electrolyte-gating and are compared with previous results attained from the same polymer film but with low induced carrier densities. Comparative analyses show that introducing high hole densities into the polymer results in (i) suppression of the transport activation energy and (ii) reduction of the temperature that yields transition in the activation energy. These results are explained based on the formation of bipolaron states, which are generated at such high hole densities.

Structural and electrical property studies on polypyrrole based organic–inorganic nanocomposites for photodiode related applications

Employing electropolymerization route, a coulombic-controlled approach was adopted to polymerize the pyrrole monomers on the TiO2:SnO2 made nanocomposite working electrodes. The absorbance values of the composite electrodes in the UV region were found to improve the rate of formation of oligomeric products from the pyrrole monomers. The role of anionic dopant in the evolution of polymer structures has been discussed using bi-polaronic states. The polymer deposits were studied using FT-IR spectroscopy to elucidate their functional groups and their three-dimensional morphological arrangements were perceived using atomic force microscopy and scanning electron microscopy. A negative shift in the flat band potential was observed from the Mott–Schottky plots, as a function of Sn composition in the composite electrodes, which favours a faster rate of electron transfer, while the Sn sites minimizes the rate of electron–hole recombination.

Polypyrrole microspheroidals decorated with Ag nanostructure: Synthesis and their characterization

In this work, polypyrrole (PPy) microspheroidals were synthesized by chronopotentiometry on conducting indium tin oxide (ITO) substrate. These prepared PPy microspheroidals were subjected to surface modification by Ag nanostructures using cyclic voltammetery (CV). The decoration of Ag nanostructures on PPy surface was characterized by UV–visible spectroscopy (UV–vis), X-ray diffraction (XRD), Fourier transform infrared (FTIR), energy dispersion X-ray spectroscopy (EDX) and scanning electron microscopy (SEM). SEM images show nanostar like structures with slight aggregation of Ag nanostructures on the PPy surface. The average particle size of PPy was found to increase from 7.3 to 30nm after decoration with Ag nanostructure. Further, the XRD patterns shows a decrease in interchain separation and inter planar distance after the impregnation of Ag nanostructures in the PPy film when compared with pure PPy film. FTIR and Raman spectra displayed main vibrational bands; including the characteristic peaks. Raman spectra also show the signature of polaron and bipolaron states. Electrical conductivity of the Ag nanostructure decorated PPy microspheroidals has been measured by the two probe method. A possible mechanism for the formation of Ag-PPy nanostructure has been proposed.

Possibility of a (bi)polaron high-temperature superconductivity in Poly A/ Poly T DNA duplexes

Dynamical equations for a polaron and bipolaron in a DNA duplex are obtained on the basis of Holstein-Hubbard Hamiltonian. It is shown that in a Poly A/Poly T duplex especially stable is a bipolaron state in which holes are localized on different chains of the duplex. With the use of the polaron and bipolaron free energy, the temperature of bipolaron decay is found to be Td ≈ 350 K which can serve as an approximate estimate of the superconducting transition temperature. The way of constructing superconducting nanowires on the basis of DNA is suggested.

Synergistic Effects in the Gas Sensitivity of Polypyrrole/Single Wall Carbon Nanotube Composites

Polypyrrole/single wall carbon nanotube composites were synthesized by in-situ chemical polymerization using pyrrole (PPy) as precursor and single wall carbon nanotubes (SWNTs) as additive component. Electron microscope images reveal that SWNTs component acts as nucleation sites for PPy growth in the form of spherical and cylindrical core-shell structures. The SWNTs/PPy core-shell results in thin n-p junctions which modify the PPy bandgap and reduce the work function of electrons. As a result of the strong coupling, Raman and IR spectra show that the PPy undergoes a transition from polaron to bipolaron state, i.e., indicating an increase in the conductivity. In the UV-Vis spectra, the 340 nm adsorption band (π*-π transition) exhibits a red shift, while the 460 nm adsorption band (bipolaron transition) experiences a blue shift indicating a change in electronic structure and a relocation of polaron levels in the band gap of PPy. The modification in PPy electronic structure brings in a synergistic effect in sensing feature. Upon exposure to oxygen (an oxidizing agent) and NH3 gas (a reducing agent), the PPy/SWNTs nanocomposite shows an enhancement in sensitivity exceeding ten folds in comparison with those of PPy or SWNTs.

Theory of High Temperature Superconductivity in Cuprates and Other Doped Polar Insulators

In the last two decades, there have been tremendous attempts to build an adequate theory of high-temperature superconductivity. Most studies used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is a priori unknown. Hence, one has to start with the generic Hamiltonian including unscreened Coulomb and Frohlich electron–phonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might fail. Using such a generic Hamiltonian, the analytical theory of high-temperature superconductivity in doped polar insulators predicting the critical temperature in excess of a hundred Kelvin without any adjustable parameters has been built. The many-particle electron system is described by an analytically solvable polaronic t–Jp Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced antiferromagnetic exchange, Jp>t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering. Here, major steps of the theory are outlined suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron–electron correlations with a significant finite-range (Frohlich) EPI, and that the theory is fully compatible with the key experiments.

In situ monitoring of polymerredox states by resonance μRaman spectroscopy and its applications in polymer modified microfluidic channels

We report the application of multi-wavelength resonance Raman (rR) spectroscopy for the characterisation of vinyl-bridged polysexithiophene films formed by electropolymerisation on gold electrodes. Resonance Raman spectroscopy of the neutral, polaronic and bipolaronic states of the polymer were determined by in situ μRaman spectroelectrochemistry. In particular the differences in the UV/Vis-NIR absorption spectra of the neutral, monopolaronic and bipolaronic states of the polymer allow for characterising the redox state of the polymer films in PDMS based microfluidic channels. The information obtained in this way allows for determination of the optimum film thickness required for achieving full electrochemical switching between neutral and charged states, which is important in their use in switching surface properties. The approach taken allows for direct analysis of polymer films formed within microchannels.

Stabilization of polyaniline by the incorporation of magnetite nanoparticles

Nanocomposites obtained from the polymerization of aniline in the presence of nanoparticles of magnetite (Fe3O4) have been investigated in previous studies. However, there is a lack of information available on the redox interaction of the nanoparticle/conductive polymer couple and the stability that such an oxide can give to the organic phase. In this work, Fe3O4 nanoparticles were incorporated into a PANi matrix by the in-situ oxidative polymerization method. A combination of X-ray diffraction, Mössbauer spectroscopy, transmission electronic microscopy, UV–visible spectroscopy as well as the cyclic voltammetric and Raman spectroscopy techniques, was used to understand the redox effect that the partially oxidized nanoparticles produced on the polymer. It was found that magnetite greatly stabilised PANi, mainly by enhancing the Leucoemeraldine/Emeraldine redox couple and also by reducing the bipolaronic state.

On the possibility of bipolaronic states in DNA

The possibility of the occurrence of bipolaronic states in homogeneous polynucleotide chains has been considered on the basis of the Holstein-Hubbard model. A phase diagram of the stability of bipolaronic states has been calculated for these chains. It was shown that, with the parameters characteristic for DNA, DNA can exhibit superconductivity with a transition temperature Tc approximately 6 K. The results obtained can serve as the basis for explaining the experiments with DNA superconductivity.