We describe a simple graphene nanoribbon and bottom gate system and present numerical algorithms for solving Poissons and Thomas-Fermi equations for electrons in the graphene nanoribbon. The Poissons equation is solved using finite difference and finite element methods. Using the Poisson and Thomas-Fermi equations we calculate an electrostatic potential and surface electron density in the graphene nanoribbon. Finally, the Poisson-Thomas-Fermi model for the graphene nanoribbon is compared to a tight-binding Hartree model. The results show a good correspondence with the tight-binding model. The developed solver of the Poissons equation can be used in the future calculations of more complex graphene and gate systems.
The coupling between charge accumulation in a conjugated polymer and the ionic charge compensation, provided from an electrolyte, defines the mode of operation in a vast array of different organic electrochemical devices. The most explored mixed organic ion-electron conductor, serving as the active electrode in these devices, is poly(3,4-ethyelenedioxythiophene) doped with polystyrelensulfonate (PEDOT:PSS). In this progress report, scientists of the Laboratory of Organic Electronics at Linkoping University review some of the achievements derived over the last two decades in the field of organic electrochemical devices, in particular including PEDOT:PSS as the active material. The recently established understanding of the volumetric capacitance and the mixed ion-electron charge transport properties of PEDOT are described along with examples of various devices and phenomena utilizing this ion-electron coupling, such as the organic electrochemical transistor, ionic-electronic thermodiffusion, electrochromic devices, surface switches, and more. One of the pioneers in this exciting research field is Prof. Olle Inganas and the authors of this progress report wish to celebrate and acknowledge all the fantastic achievements and inspiration accomplished by Prof. Inganas all since 1981.
We present experimental studies of geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum-mechanical scattering calculations and find excellent agreement with experimental results. We also carry out semiclassical calculations where the conductance is given as a sum over all classical trajectories between the leads, each of the trajectories carrying a quantum-mechanical phase. We unambiguously demonstrate that the characteristic frequencies of the oscillations in the transmission and reflection amplitudes t and r are related to the length distribution of the classical trajectories between the leads, whereas the frequencies of the probabilities T=t2 and R = r2 can be understood in terms of the length difference distribution in the pairs of classical trajectories. We also discuss the effect of nonclassical "ghost" trajectories, i.e., trajectories that include classically forbidden reflection off the lead mouths. © 2002 The American Physical Society.
We utilize a semi-classical approach to calculate conductance and weak localization corrections in a triangular billiard in non-zero magnetic field. Results of the calculations and comparison to numerical quantum mechanical simulations suggest that applicability of the standard semiclassical method for description of the geometry-specific features in the conductance of such systems is not obvious as the unitarity of the semiclassical scattering matrix is violated as well as the symmetry of the conductance/reflectance with respect to the magnetic field and the direction of the current is not satisfied. The reason for this is given. Our findings raise the question to what extend one can rely on numerous predictions for statistical properties of the conductance oscillations of ballistic cavities including the WL lineshapes and fractal conductance which were essentially based on the standard SC approach.
We utilize a semiclassical (SC) approach to calculate the conductance and weak-locatization (WL) corrections in a triangular billiard of a given shape in the presence of nonzero magnetic field. The semiclassical conductance is given as a sum of all classical trajectories between the leads, each of them carrying the quantum-mechanical phase. The present SC approach is numerically exact (i.e., free from any approximations), explicitly includes diffractive effects in the leads, and is valid for arbitrary (low) mode numbers in the leads. We find however that the symmetry of the SC conductance/reflectance with respect to the direction of magnetic field or direction of the current is not satisfied, as well as that the WL corrections for the conductance and reflectance are inconsistent with each other, the SC approach does not satisfy the current conservation requirements and does not reproduce the corresponding exact quantum-mechanical results. The reason for that is traced to the topological difference in the sets of classical trajectories between the leads for different current or magnetic field directions which determine the conductance in the SC approximation. Our findings raise a question as to what extent one can rely on numerous predictions for statistical properties of the conductance oscillations of ballistic cavities including the WL line shapes and fractal conductance which were essentially based on the standard SC approach.
We perform semi-classical and quantum mechanical calculations on square billiards and provide a semi-classical interpretation of the conductance oscillations. We outline its relation to the Gutzwiller's picture of periodic orbits. The frequencies of the conductance oscillations are shown to be due to interference of pairs of long trajectories, which in the phase space are typically situated near the corresponding periodic orbit. We identify the pair of trajectories causing the pronounced peak in a recent experiment and from this directly extract the phase coherence length.
We provide a semiclassical interpretation of the conductance oscillations in a square billiard and outline its relation to a commonly used picture of periodic orbits. We demonstrate that the characteristic frequencies in the conductance arise as a result of interference of pairs of long trajectories that typically bounce in a vicinity of the corresponding periodic orbits in the phase space. We present an unambiguous identification of the specific pairs of trajectories causing the pronounced peaks in the observed length spectrum of the conductance. This allows us to extract directly the phase coherence length from the frequency of the observed oscillations.
Inorganic transparent conductive oxides have dominated the market as transparent electrodes due to their high conductivity and transparency. Here, we report the fabrication and optimization of the synthesis of poly(3,4-ethylenedioxythiophene) trifluoromethanesulfonate via vapor phase polymerization for the potential replacement of such inorganic materials. The parameters and conditions of the polymerization were investigated and an electrical conductivity of 3800 S cm(-1) and 4500 S cm(-1) after acid treatment were obtained while maintaining an absorbance similar to that of commercial indium tin oxide. This increase in electrical conductivity was rationalized experimentally and theoretically to an increase in the oxidation level and a higher order of crystallinity which does not disrupt the pi-pi stacking of PEDOT chains.
Polymers are lightweight, flexible, solution-processable materials that are promising for low-cost printed electronics as well as for mass-produced and large-area applications. Previous studies demonstrated that they can possess insulating, semiconducting or metallic properties; here we report that polymers can also be semi-metallic. Semi-metals, exemplified by bismuth, graphite and telluride alloys, have no energy bandgap and a very low density of states at the Fermi level. Furthermore, they typically have a higher Seebeck coefficient and lower thermal conductivities compared with metals, thus being suitable for thermoelectric applications. We measure the thermoelectric properties of various poly( 3,4-ethylenedioxythiophene) samples, and observe a marked increase in the Seebeck coefficient when the electrical conductivity is enhanced through molecular organization. This initiates the transition from a Fermi glass to a semi-metal. The high Seebeck value, the metallic conductivity at room temperature and the absence of unpaired electron spins makes polymer semi-metals attractive for thermoelectrics and spintronics.
Thermoelectric generation potentially holds a solution for waste heat recovery issues provided that the availability of inexpensive, biodegradable and highly efficient thermoelectric materials is insured in the near future. Plastic thermoelectrics could successfully comply with the said requirements if the thermoelectric efficiency (ZT) of conducting polymers was higher. However, given the novelty of the subject, at present there are no clear guidelines for ZT optimization in this class of materials. The most important piece of information that is currently missing is the description of a specific electronic makeup that conducting polymers must possess in order to enable good thermoelectric performance. In the present study the thermoelectric properties of poly(3,4-ethylenedioxythiophene) derivatives with two types of counterions, i.e. poly(styrenesulfonate) (PSS) and tosylate (Tos) are evaluated. A striking variation in their thermoelectric performance is attributed to structural and morphological differences between two polymers that manifest itself in dissimilar charge transport mechanism. The superior properties of PEDOT-Tos presumably originate from a high degree of crystallinity and structural order that predetermines the tendency for bipolaron band formation. Unlike polaronic PEDOT-PSS with slowly varying density of localized states (DOS) near the Fermi level (EF), the DOS in PEDOT-Tos is characterized by higher asymmetry and higher charge carrier density at EF (similar to semimetals), which allows for higher thermopower and electrical conductivity. Therefore, we conclude that the polymers with semimetallic electronic makeup are expected to exhibit promising thermoelectric properties with bigger variation in thermopower upon doping.
We study spin polarization in a split-gate quantum wire focusing on the effect of a realistic smooth potential due to remote donors. Electron interaction and spin effects are included within the density functional theory in the local spin density approximation. We find that depending on the electron density, the spin polarization exhibits qualitatively different features. For the case of relatively high electron density, when the Fermi energy EF exceeds a characteristic strength of a long-range impurity potential Vdonors, the density spin polarization inside the wire is practically negligible and the wire conductance is spin-degenerate. When the density is decreased such that EF approaches Vdonors, the electron density and conductance quickly become spin polarized. With further decrease of the density the electrons are trapped inside the lakes (droplets) formed by the impurity potential and the wire conductance approaches the pinch-off regime. We discuss the limitations of the density functional theory in the local spin density approximation in this regime and compare the obtained results with available experimental data.
We investigate coherent transport through open lateral quantum dots using recursive Green's function technique, incorporating exchange-correlation effects within the density functional theory (DFT) in the local spin-density approximation. At low electron densities the current is spin polarized and electron density in the dot shows a strong spin polarization. As the electron density increases the spin polarization in the dot gradually diminishes. These findings are consistent with available experimental observations. Results of our DFT-based modeling indicate that utilization of the simplified approaches that use phenomenological parameters and/or model Hamiltonians might not be always reliable for theoretical predictions as well as interpretations of the experiments.
We demonstrate that the magnetoconductance of small lateral quantum dots in the strongly coupled regime (i.e. when the leads can support one or more propagating modes) shows a pronounced splitting of the conductance peaks and dips which persists over a wide range of magnetic fields (from zero field to the edge-state regime) and is virtually independent of the magnetic field strength. Our numerical analysis of the conductance based on the Hubbard Hamiltonian demonstrates that this is essentially a many-body/spin effect that can be traced to a splitting of degenerate levels in the corresponding closed dot. The above effect in open dots can be regarded as a counterpart of the Coulomb-blockade effect in weakly coupled dots, with the difference, however, that the splitting of the peaks originates from interactions between electrons of opposite spin.
We study the effect of the edge disorder on the conductance of the graphene nanoribbons (GNRs).We find that only very modest edge disorder is sufficient to induce the conduction energy gap inthe otherwise metallic GNRs and to lift any difference in the conductance between nanoribbonsof different edge geometry. We relate the formation of the conduction gap to the pronounced edgedisorder induced Anderson-type localization which leads to the strongly enhanced density of states atthe edges, formation of surface-like states and to blocking of conductive paths through the ribbons.
Deposition dynamics, crystallization, molecular packing, and electronic mobility of poly(3,4-ethylenedioxythiophene) (PEDOT) thin films are affected by the nature of the substrate. Computational microscopy has been carried out to reveal the morphology-substrate dependence for PEDOT thin films doped with molecular tosylate deposited on different substrates including graphite, Si3N4, silicon, and amorphous SiO2. It is shown that the substrate is instrumental in formation of the lamellar structure. PEDOT films on the ordered substrates (graphite, Si3N4, and silicon) exhibit preferential face-on orientation, with graphite showing the most ordered and pronounced face-on packing. In contrast, PEDOT on amorphous SiO2 exhibits the dominant edge-on orientation, except in the dry state where both packings are equally presented. The role of water and the porosity of the substrate in formation of the edge-on structure on SiO2 is outlined. On the basis of the calculated morphology, the multiscale calculations of the electronic transport and percolative analysis are performed outlining how the character of the substrate affects the electron mobility. It is demonstrated that good crystallinity (PEDOT on graphite substrate) and high content of edge-on (PEDOT on SiO2 substrate) are not enough to achieve the highest electrical in-plane mobility. Instead, the least ordered material with lower degree of the edge-on content (PEDOT on silicon substrate) provides the highest mobility because it exhibits an efficient network of pi-pi stacked chain extending throughout the entire sample.
Morphology of the conducting polymer PEDOT:TOS (poly(3,4-ethylenedioxythiopherre) doped with molecular, tosylate) and its crystallization in aqueous solution, were Studied using atomistic molecular dynamics simulations. It was foirnd that (a) PEDOT comprises crystallite aggregates consisting of 3-6 pi-pi stacked chains. The crystallites are linked by interpenetrating pi-pi stacked chains such that percolative paths in the structure are formed. (b) The size of the crystallites.deperids on the water content, but the pi-pi stacking distance is practically independent of the chain length, charge,Concentration and water content. (c) TOS counterions are located either on the top of the,chains or on the side of the crystalliteS and their distribution depends on the charge concentration but is practically independent of the water content; (d) PEDOT depends On their length and water,content. 2 chains and crystallites exhibit bending that depends On their length and water content.
A recently synthesized self-doped conducting oligomer, salt of bis[3,4-ethylenedioxythiophene]3thiophene butyric acid, ETE-S, is a novel promising material for green energy applications. Recently, it has been demonstrated that it can polymerize in vivo, in plant systems, leading to a formation of long-range conducting wires, charge storage and supercapacitive behaviour of living plants. Here we investigate the morphology of ETE-S combining the experimental characterisation using Grazing Incidence Wide Angle X-ray Scattering (GIWAXS) and atomistic molecular dynamics (MD) simulations. The GIWAXS measurements reveal a formation of small crystallites consisting of π–π stacked oligomers (with the staking distance 3.5 Å) that are further organized in h00 lamellae. These experimental results are confirmed by MD calculations, where we calculated the X-ray diffraction pattern and the radial distribution function for the distance between ETE-S chains. Our MD simulations also demonstrate the formation of the percolative paths for charge carriers that extend throughout the whole structure, despite the fact that the oligomers are short (6–9 rings) and crystallites are thin along the π–π stacking direction, consisting of only two or three π–π stacked oligomers. The existence of the percolative paths explains the previously observed high conductivity in in vivo polymerized ETE-S. We also explored the geometrical conformation of ETE-S oligomers and the bending of their aliphatic chains as a function of the oligomer lengths.
Theoretical understanding of the electronic structure and optical transitions in n-doped conducting polymers is still controversial for polaronic and bipolaronic states and is completely missing for the case of a high doping level. In the present paper, the electronic structure and optical properties of the archetypical n-doped conducting polymer, double-stranded benzimidazo-benzophenanthroline ladder (BBL), are studied using the density functional theory (DFT) and the time dependent DFT method. We find that a polaronic state in the BBL chain is a spin-resolved doublet where the spin degeneracy is lifted. The ground state of two electrons corresponds to a triplet polaron pair, which is in stark contrast to a commonly accepted picture where two electrons are postulated to form a spinless bipolaron. The total spin gradually increases until the reduction level reaches c(red) = 100% (i.e., one electron per monomer unit). With further increase of the reduction level, the total spin decreases until it becomes 0 for the reduction level c(red) = 200%. The calculated results reproduce the experimentally observed spin signal without any phenomenological parameters. A detailed analysis of the evolution of the electronic structure of BBL and its absorption spectra with increase in reduction level is presented. The calculated UV-vis-NIR spectra are compared with the available experimental results. The electronic structure and optical absorption for different reduction levels presented here are generic to a wide class of conducting polymers, which is illustrated by the corresponding calculations for another archetypical conducting polymer, poly(3,4-ethylenedioxythiophene) (best known as PEDOT).
Conjugated polymers exhibit electrically driven volume changes when included in electrochemical devices via the exchange of ions and solvent. So far, this volumetric change is limited to 40% and 100% for reversible and irreversible systems, respectively, thus restricting potential applications of this technology. A conjugated polymer that reversibly expands by about 300% upon addressing, relative to its previous contracted state, while the first irreversible actuation can achieve values ranging from 1000-10 000%, depending on the voltage applied is reported. From experimental and theoretical studies, it is found that this large and reversible volumetric switching is due to reorganization of the polymer during swelling as it transforms between a solid-state phase and a gel, while maintaining percolation for conductivity. The polymer is utilized as an electroactive cladding to reduce the void sizes of a porous carbon filter electrode by 85%.
Quasiballistic semiconductor quantum wires are exposed to localized perpendicular magnetic fields, also known as magnetic barriers. Pronounced, reproducible conductance fluctuations as a function of the magnetic barrier amplitude are observed. The fluctuations are strongly temperature dependent and remain visible up to temperatures of approximate to 10 K. Simulations based on recursive Greens functions suggest that the conductance fluctuations originate from parametric interferences of the electronic wave functions, which experience scattering between the magnetic barrier and the electrostatic potential landscape.
We present full quantum mechanical conductance calculations of a quantum point contact (QPC) performed in the framework of the density functional theory (DFT) in the local spin-density approximation (LDA). We start from a lithographical layout of the device, and the whole structure, including semi-infinitive leads, is treated on the same footing (i.e., the electron-electron interaction is accounted for in both the leads and the central device region). We show that the spin degeneracy of the conductance channels is lifted and the total conductance exhibits a broad plateaulike feature at ∼0.5×2 e2 h. The lifting of the spin degeneracy is a generic feature of all studied QPC structures (both very short and very long ones, with lengths in the range 40 l 500 nm). The calculated conductance also shows a hysteresis for forward and backward sweeps of the gate voltage. These features in the conductance can be traced to the formation of weakly coupled quasibound states (magnetic impurities) inside the QPC (also predicted in previous DFT-based studies). A comparison of the results obtained with the experimental data shows, however, that while the spin-DFT-based "first-principles" calculations exhibit spin polarization in the QPC, the calculated conductance clearly does not reproduce the 0.7 anomaly observed in almost all QPCs of various geometries. We critically examine the major features of the standard DFT-based approach to the conductance calculations and argue that its inability to reproduce the 0.7 anomaly might be related to the infamous derivative discontinuity problem of the DFT, leading to spurious self-interaction errors not corrected in the standard LDA. Our results indicate that the formation of magnetic impurities in the QPC might be an artifact of the LDA when localization of charge is expected to occur. We thus argue that an accurate description of the QPC structure would require approaches that go beyond the standard DFT+LDA schemes. © 2007 The American Physical Society.
Electronic, transport, and spin properties of grain boundaries (GBs) are investigated in electrostatically doped graphene at finite electron densities within the Hartree and Hubbard approximations. We demonstrate that depending on the character of the GBs, the states residing on them can have a metallic character with a zero group velocity or can be fully populated losing the ability to carry a current. These states show qualitatively different features in charge accumulation and spin polarization. We also demonstrate that the semiclassical Thomas-Fermi approach provides a satisfactory approximation to the calculated self-consistent potential. The conductance of GBs is reduced due to enhanced backscattering from this potential.
We calculate the nonlinear conductance of a quantum point contact using the nonequilibrium Greens function technique within the Hartree approximation of spinless electrons. We quantitatively reproduce the "0.25 anomaly" in the differential conductance (i. e., the lowest plateau at similar to 0.25-0.3 x 2e(2)/h) as well as an upward bending of higher conductance half-integer plateaus seen in the experiments, and relate these features to the nonlinear screening and pinning effects.
We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons (GNRs) in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation, studying the evolution of the magnetoband structure and formation of the compressible strips. We discuss the potential profile and the density distribution near the edges and the difference and similarities between armchair and zigzag edges. Accounting for the Zeeman interaction and describing the spin effects via the Hubbard term, we study the spin-resolved subband structure and relate the spin polarization of the system at hand to the formation of the compressible strips for the case of spinless electrons. At high magnetic field the calculated effective g factor varies around a value of andlt; g*andgt; approximate to 2.25 for armchair GNRs and andlt; g*andgt; approximate to 3 for zigzag GNRs. An important finding is that in zigzag GNRs the zero-energy mode remains pinned to the Fermi energy and becomes fully spin polarized for all magnetic fields, which, in turn, leads to a strong spin polarization of the electron density near the zigzag edge. Because of this the effective g factor in zigzag GNRs is strongly enhanced at low fields reaching values up to g* approximate to 30. This is in contrast to armchair GNRs, where the effective g factor at low field is close to its bare value, g = 2.
We calculate the band structure and the conductance of periodic edge-corrugated graphene nanoribbons within the framework of the tight-binding p-orbital model. We consider corrugated structures based on host ribbons with armchair and zigzag edges and three different types of corrugations (armchair edges, zigzag edges, as well as a rectangular corrugation). We demonstrate that for armchair host ribbons, depending on the type of corrugation, a band gap or low-velocity minibands appear near the charge neutrality point. For higher energies the allowed Bloch state bands become separated by ministopbands. By contrast, for corrugated ribbons with the zigzag host, the corrugations introduce neither band gaps nor stopbands (except for the case of the rectangular corrugations). The conductances of finite edge-corrugated ribbons are analyzed on the basis of the corresponding band structures. For a sufficiently large number of corrugations the conductance follows the number of the corresponding propagating Bloch states and shows pronounced oscillations due to the Fabry-Perot interference within the corrugated segments. Finally we demonstrate that edge disorder strongly affects the conductances of corrugated ribbons. Our results indicate that observation of miniband formation in corrugated ribbons would require clean, edge-disorder free samples, especially for the case of the armchair host lattice.
We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy-level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter, we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in the Hartree approximation, which indicate pinning and correlation of the single-particle states at the Fermi energy as well as charge oscillation when antidot-bound states depopulate. We have also found interesting phenomena of antiresonance reflection of the Fano type.
We calculate the conductivity sigma and the Seebeck coefficient S for the phonon-assisted hopping transport in conducting polymers poly(3,4-ethylenedioxythiophene) or PEDOT, experimentally studied by Bubnova et al. [J. Am. Chem. Soc. 134, 16456 (2012)]. We use the Monte Carlo technique as well as the semianalytical approach based on the transport energy concept. We demonstrate that both approaches show a good qualitative agreement for the concentration dependence of sigma and S. At the same time, we find that the semianalytical approach is not in a position to describe the temperature dependence of the conductivity. We find that both Gaussian and exponential density of states (DOS) reproduce rather well the experimental data for the concentration dependence of sigma and S giving similar fitting parameters of the theory. The obtained parameters correspond to a hopping model of localized quasiparticles extending over 2-3 monomer units with typical jumps over a distance of 3-4 units. The energetic disorder (broadening of the DOS) is estimated to be 0.1 eV. Using the Monte Carlo calculation we reproduce the activation behavior of the conductivity with the calculated activation energy close to the experimentally observed one. We find that for a low carrier concentration a number of free carriers contributing to the transport deviates strongly from the measured oxidation level. Possible reasons for this behavior are discussed. We also study the effect of the dimensionality on the charge transport by calculating the Seebeck coefficient and the conductivity for the cases of three-, two-, and one-dimensional motion.
We perform self-consistent quantum transport calculations in open quantum dots taking into account the effect of electron interaction. We demonstrate that, in the regime of the ultralow temperatures 2pkBT? (? being the mean-level spacing), the electron interaction strongly smears the conductance oscillations and thus significantly affects their statistics. Our calculations are in good quantitative agreement with the observed ultralow temperature statistics of Huibers et al.. Our findings question a conventional interpretation of the ultralow temperature saturation of the coherence time in open dots which is based on the noninteracting theories, where the agreement with the experiment is achieved by introducing additional phenomenological channels of dephasing. © 2007 The American Physical Society.
We present a microscopic picture of quantum transport in the Aharonov-Bohm (AB) interferometer taking into account the electron interaction within the Hartree and the spin density-functional theory approximations. We discuss the structure of the edge states for different number of Landau levels in the leads, their coupling to the states in the central island, and the formation of compressible/incompressible strips in the interferometer. Based on our results, we discuss the existing theories of the unexpected AB periodicity, which essentially rely on specific phenomenological models of the states and their coupling in the interferometer. Our work provides a basis for such theories, giving a detailed microscopic description of the propagating states and the global electrostatics in the system at hand. © 2008 The American Physical Society.
We present a systematic quantitative description of the magnetoconductance of split-gate quantum wires focusing on formation and evolution of the odd (spin-resolved) conductance plateaus. We start from the case of spinless electrons where the calculated magnetoconductance in the Hartree approximation shows the plateaus quantized in units of 2 e2 /h separated by transition regions, whose width grows as the magnetic field is increased. We show that the transition regions are related to the formation of the compressible strips in the middle of the wire occupied by electrons belonging to the highest (spin-degenerate) subband. Accounting for the exchange and correlation interactions within the spin density functional theory (DFT) leads to the lifting of the spin degeneracy and formation of the spin-resolved plateaus at odd values of e2 /h. The most striking feature of the magnetoconductance is that the width of the odd conductance steps in the spin DFT calculations is equal to the width of the transition intervals between the conductance steps in the Hartree calculations. A detailed analysis of the evolution of the Hartree and the spin DFT subband structure provides an explanation of this finding. Our calculations also reveal the effect of the collapse of the odd conductance plateaus for lower fields. We attribute this effect to the reduced screening efficiency in the confined (wire) geometry when the width of the compressible strip in the center becomes much smaller than the extent of the wave function. A detailed comparison to the experimental data demonstrates that the spin DFT calculations reproduce not only qualitatively but also quantitatively all the features observed in the experiment. This includes the dependence of the width of the odd and even plateaus on the magnetic field as well as the estimation of the subband index corresponding to the last resolved odd plateau in the magnetoconductance. © 2008 The American Physical Society.
We provide a systematic quantitative description of the structure of edge states and magnetosubband evolution in hard-wall quantum wires in the integer quantum Hall regime. Our calculations are based on the self-consistent Green's function technique where the electron and spin interactions are included within the density functional theory in the local spin density approximation. We analyze the evolution of the magnetosubband structure as magnetic field varies and show that it exhibits different features as compared to the case of a smooth confinement. In particular, in the hard-wall wire a deep and narrow triangular potential well (of the width of the magnetic length l(B)) is formed in the vicinity of the wire boundary. The wave functions are strongly localized in this well, which leads to an increase of the electron density near the edges. Because of the presence of this well, the subbands start to depopulate from the central region of the wire and remain pinned in the well region until they are eventually pushed up by increasing magnetic field. We also demonstrate that the spin polarization of electron density as a function of magnetic field shows a pronounced double-loop pattern that can be related to the successive depopulation of the magnetosubbands. In contrast to the case of a smooth confinement, in hard-wall wires compressible strips do not form in the vicinity of wire boundaries and spatial spin separation between spin-up and spin-down states near edges is absent.
We present a detailed comparison of the self-consistent calculations based on the Hartree-Fock and the spin density functional theory for a split-gate quantum wire in the IQH regime. We demonstrate that both approaches provide qualitatively (and, in most cases, quantitatively) similar results for the spin-resolved electron density, spin polarization, spatial spin separation at the edges and the effective g factor. Both approaches produce the same values of the magnetic fields corresponding to the successive subband depopulation and qualitatively similar evolution of the magnetosubbands. Quantitatively, however, the HF and the DFT subbands are different (even though the corresponding total electron densities are practically the same). In contrast to the HF approach, the DFT calculations predict much larger spatial spin separation near the wire edge for the low magnetic fields (when the compressible strips for spinless electrons are not formed yet). In the opposite limit of the large fields, the Hartree-Fock and the DFT approaches give very similar values for the spatial spin separation.
The role of electron-electron interaction in transport properties of open quantum dots is studied. The self-consistent full quantum-mechanical magnetotransport calculations within the Hartree, density-functional theory, and Thomas-Fermi approximations were performed, where a whole device, including the semi-infinitive leads, is treated on the same footing (i.e., the electron-electron interaction is accounted for both in the leads as well as in the dot region). The main finding of the present paper is the effect of pinning of the resonant levels to the Fermi energy due to the enhanced screening. Our results represent a significant departure from a conventional picture where a variation of external parameters (such as a gate voltage, magnetic field, etc.) causes the successive dot states to sweep past the Fermi level in a linear fashion. We instead demonstrate the highly nonlinear behavior of the resonant levels in the vicinity of the Fermi energy. The pinning of the resonant levels in open quantum dots leads to the broadening of the conduction oscillations in comparison to the one-electron picture. The effect of pinning becomes much more pronounced in the presence of the perpendicular magnetic field. This can be attributed to the enhanced screening efficiency because of the increased localization of the wave function. The strong pinning of the resonant energy levels in the presence of magnetic field can have a profound effect on transport properties of various devices operating in the edge state transport regime. We also critically examine an approximation often used in transport calculations where an inherently open system is replaced by a corresponding closed one. © 2007 The American Physical Society.
Currently, a theoretical understanding of thermodynamics and kinetics of the oxidative polymerization of poly(3,4-ethylenedioxythiophene) (best known as PEDOT) is missing. In the present study, step-by-step density functional theory calculations of the radical polymerization of PEDOT with tosylate counterions (PEDOT:TOS) using Fe3+(TOS-)(3) as oxidant and dopant are performed. We calculate the Gibbs free energy for the conventional mechanism that consists of the polymerization of neutral PEDOT oligomers first, followed by their oxidation (doping). We also propose an alternative mechanism of polymerization, in which the already oxidized oligomers are used as reactants, leading to doped (oxidized) oligomers as products during polymerization. Our calculations indicate that the alternative mechanism is more efficient for longer PEDOT oligomers (chain length N amp;gt; 6). We find that the oxidation of the EDOT monomer is the rate-limiting step for both mechanisms. Another focus of our study is the understanding of the maximum oxidation level that can be achieved during polymerization. Our calculations provide a theoretical explanation of "the magic number" of 33% for the oxidation level typically reported for the pristine (i.e., as-polymerized) materials and relate it to the change of the character of the bonds in the oligomers (aromatic to quinoid) that occurs at this oxidation level.
In this chapter, the authors summarize their understanding of Poly(3,4-ethylenedioxythiophene) (PEDOT), with respect to its chemical and physical fundamentals. They focus upon the structure of several PEDOT systems, from the angstrom level and up, and the impact on both electronic and ionic transport. The authors discuss the structural properties of PEDOT:X and PEDOT:poly(styrenesulfonate) based on experimental data probed at the scale ranging from angstrom to submicrometer. The morphology of PEDOT is influenced by the nature of counter-ions, especially at high oxidation levels. The doping anions intercalate between PEDOT chains to form a “sandwich” structure to screen the positive charges in PEDOT chains. The authors provide the main transport coefficients such as electrical conductivity s, Seebeck coefficient S, and Peltier coefficient σ, starting from a general thermodynamic consideration. The optical conductivity of PEDOT has also been examined based on the effective medium approximation, which is normally used to describe microscopic permittivity properties of composites made from several different constituents.
We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron-density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n)similar to n(-lambda), with 0 andlt;lambda less than or similar to 0.5. The exponent lambda depends on the length of the system with lambda=0.5 corresponding to short structures in the ballistic regime, whereas the diffusive regime lambda=0 (when the mobility is independent on the electron density) is reached for sufficiently long structures. Our results can be used for the interpretation of experimental data when the value of lambda can be used to distinguish the transport regime of the system (i.e., ballistic, quasiballistic, or diffusive). Based on our findings we discuss available experimental results.
We present a comparative study of the density dependence of the conductivity of graphene sheets calculated in the tight-binding (TB) Landauer approach and on the basis of the Boltzmann theory. The TB calculations are found to give the same density dependence of the conductivity, σ^{TB}∼n, for short- and long-range Gaussian scatterers. In the case of short-range scattering the TB calculations are in agreement with the predictions of the Boltzmann theory going beyond the Born approximation but in qualitative and quantitative disagreement with the standard Boltzmann approach within the Born approximation, predicting σ^{Boltz}=const. Even for the long-range Gaussian potential in a parameter range corresponding to realistic systems the standard Boltzmann predictions are in quantitative and qualitative disagreement with the TB results. This questions the applicability of the standard Boltzmann approach within the Born approximation, commonly used for the interpretation of the results of experimental studies of the transport in graphene.
Computational microscopy based on Martini coarse grained molecular dynamics (MD) simulations of a doped conducting polymer poly(3,4-ethylenedioxythiophene)polystyrene sulfonate (best known as PEDOT:PSS) was performed focussing on the formation of the granular structure and PEDOT crystallites, and the effect of pH on the material morphology. The PEDOT:PSS morphology is shown to be sensitive to the initial distribution of PEDOT and PSS in the solution, and the results of the modelling suggest that the experimentally observed granular structure of PEDOT:PSS can be only obtained if the PEDOT/PSS solution is in the dispersive state in the initial crystallization stages. Variation of the pH is demonstrated to strongly affect the morphology of PEDOT:PSS films, altering their structure between granular-type and homogeneous. It also affects the size of crystallites and the relative arrangement of PEDOT and PSS chains. It is shown that the crystallites in PEDOT:PSS are smaller than those in PEDOT with molecular counterions such as PEDOT:tosylate, which is consistent with the available experimental data. The predicted changes of the PEDOT:PSS morphology with variation of the pH can be tested experimentally, and the calculated atomistic picture of PEDOT:PSS films (not accessible by conventional experimental techniques) is instrumental for understanding the material structure and building realistic models of PEDOT:PSS morphology.
A Martini coarse-grained Molecular Dynamics (MD) model for the doped conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) is developed. The morphology of PEDOT:Tos (i.e. PEDOT doped with molecular tosylate) and its crystallization in aqueous solution for different oxidation levels were calculated using the developed method and compared with corresponding all atomistic MD simulations. The diffusion coefficients of Na+ and Cl- ions in PEDOT:Tos are studied using the developed coarse-grained MD approach. It is shown that the diffusion coefficients decrease exponentially as the hydration level is reduced. It is also predicted that the diffusion coefficients decrease when the doping level of PEDOT is increased. The observed behavior is related to the evolution of water clusters and trapping of ions around the polymer matrix as the hydration level changes. The predicted behavior of the ionic diffusion coefficients can be tested experimentally, and we believe that molecular picture of ionic diffusion in PEDOT unraveled in the present study is instrumental for the design of polymeric materials and devices for better and enhanced performance.
The spectra of conducting polymers obtained using ultraviolet photoelectron spectroscopy (UPS) exhibit a typical broadening of the tail sigma(UPS) approximate to 1 eV, which by an order of magnitude exceeds a commonly accepted value of the broadening of the tail of the density of states sigma(DOS) approximate to 0.1 eV obtained using transport measurements. In this work, an origin of this anomalous broadening of the tail of the UPS spectra in a doped conducting polymer, PEDOT (poly(3,4-ethylenedioxythiophene)), is discussed. Based on the semiempirical approach and using a realistic morphological model, the density of valence states in PEDOT doped with molecular counterions is computed. It is shown that due to a disordered character of the material with randomly distributed counterions, the localized charge carriers in PEDOT crystallites experience spatially varying electrostatic potential. This leads to spatially varying local vacuum levels and binding energies. Taking this variation into account the UPS spectrum is obtained with the broadening of the tail comparable to the experimentally observed one. The results imply that the observed broadening of the tail of the UPS spectra in PEDOT provides information about a disordered spatially varying potential in the material rather than the broadening of the DOS itself.
We report a multiscale modeling of electronic structure of a conducting polymer poly(3,4-ethylenedioxythiopehene) (PEDOT) based on a realistic model of its morphology. We show that when the charge carrier concentration increases, the character of the density of states (DOS) gradually evolves from the insulating to the semimetallic, exhibiting a collapse of the gap between the bipolaron and valence bands with the drastic increase of the DOS between the bands. The origin of the observed behavior is attributed to the effect of randomly located counterions giving rise to the states in the gap. These results are discussed in light of recent experiments. The method developed in this work is general and can be applied to study the electronic structure of other conducting polymers.
We study electronic transport in monolayer and bilayer graphene with single and many short-range defects focusing on the role of edge termination (zigzag versus armchair). Within the tight-binding approximation, we derive analytical expressions for the transmission amplitude in monolayer graphene nanoribbons with a single short-range defect. The analytical calculations are complemented by exact numerical transport calculations for monolayer and bilayer graphene nanoribbons with a single and many short-range defects and edge disorder. We find that for the case of the zigzag edge termination, both monolayer and bilayer nanoribbons in a single- and few-mode regime remain practically insensitive to defects situated close to the edges. In contrast, the transmission of both armchair monolayer and bilayer nanoribbons is strongly affected by even a small edge defect concentration. This behavior is related to the effective boundary condition at the edges, which, respectively, does not and does couple valleys for zigzag and armchair nanoribbons. In the many-mode regime and for sufficiently high defect concentration, the difference of the transmission between armchair and zigzag nanoribbons diminishes. We also study resonant features (Fano resonances) in monolayer and bilayer nanoribbons in a single-mode regime with a short-range defect. We discuss in detail how an interplay between the defect's position at different sublattices in the ribbons, the defect's distance to the edge, and the structure of the extended states in ribbons with different edge termination influence the width and the energy of Fano resonances.
We study the effect of electron-electron interaction in graphene quantum dots defined by an external electrostatic potential and a high magnetic field. To account for the electron-electron interaction, we use the Thomas-Fermi approximation and find that electron screening causes the formation of compressible strips in the potential profile and the electron density. We numerically solve the Dirac equations describing the electron dynamics in quantum dots, and we demonstrate that compressible strips lead to the appearance of plateaus in the electron energies as a function of the magnetic field. Finally, we discuss how our predictions can be observed using the Kelvin probe force microscope measurements.
Resonant tunneling diodes have been fabricated using graded Si1 - xGex (x = 0.3?0.0) spacer wells and strained Si0.4Ge0.6 barriers on a relaxed Si0.7Ge0.3 n-type substrate which demonstrates negative differential resistance at up to 100 K. This design is aimed at reducing the voltage at which the peak current density is achieved. Peak current densities of 0.08 A/cm2 with peak-to-valley current ratios of 1.67 have been achieved for a low peak voltage of 40 mV at 77 K. This represents an improvement of over an order of magnitude compared to previous work. © 2001 American Institute of Physics.
Resonant tunnelling diodes (RTDs) have been fabricated using Si/SiGe heterolayers which demonstrate room temperature performance comparable to III-V technology. Peak current densities up to 282 kA cm-2 with peak-to-valley current ratios (PVCRs) of 2.4 have been demonstrated at room temperature in devices with dimensions of 5 × 5 µm2. Scaling the device size demonstrates that the peak current density is inversely proportional to the device area. It is suggested that this is related to thermal limitations in the device structure. Estimates are also produced for the maximum frequency of oscillations of the diodes which suggest that oscillators may operate with speeds comparable to III-V diodes. © 2002 Elsevier Science B.V. All rights reserved.
Resonant tunneling diodes have been fabricated using strained-Si wells and strained Si0.4Ge0.6 barriers on a relaxed Si0.8Ge0.2 n-type substrate, which demonstrate negative differential resistance at 298 K. Peak current densities of 5 kA/cm(2) with peak-to-valley current ratios of 1.1 have been achieved. Theoretical modeling of the structure demonstrates that the major current peak results from the tunneling of light-mass electrons from the relaxed substrate and not from the heavy-mass electrons in the emitter accumulation layer. (C) 2000 American Institute of Physics. [S0003- 6951(00)02337-8].
Since their discovery in the seventies, conducting polymers have been chemically designed to acquire specific optical and electrical properties for various applications. Poly(3,4-ethylenedioxythiophene) (PEDOT) is among the most successful polymers as indicated by approximate to 12 000 articles mentioning it to date. PEDOT is found as transparent polymer electrodes in solar cells and light-emitting diodes, as printed electrodes in transistors, and as the main component of electrochromic displays, supercapacitors, and electrochemical transistors. For around seven years, PEDOT has been classified as the first thermoelectric polymer that converts heat flow into electricity. This has triggered a renewed interest in the scientific community, with about 400 publications including the keyword "PEDOT" and "thermoelectric." Among the topics covered by those scientific works are: i) the optimization of the thermoelectric properties, ii) understanding of the interplay between electrical properties and morphology, iii) the origin of the Seebeck coefficient, iv) the characterization of its thermal conductivity; and v) the design of thermoelectric devices. This work aims to be a pedagogical introduction to PEDOT but also to review the state-of-the art of its thermoelectric properties and thermoelectric devices. Hopefully, this work will inspire scientists to find chemical design rules to bring organic thermoelectrics beyond PEDOT.
Transport properties of single-layer graphene with correlated one-dimensional defects are studied theoretically using the computational model within the time-dependent real-space Kubo-Greenwood formalism. Such defects are present in epitaxial graphene, comprising atomic terraces and steps due to the substrate morphology, and in polycrystalline chemically vapor-deposited (CVD) graphene due to the grain boundaries, composed of a periodic array of dislocations, or quasi-periodic nanoripples originated from the metal substrate. The extended line defects are described by the long-range Lorentzian-type scattering potential. The dc conductivity is calculated numerically for different cases of distribution of line defects. This includes a random (uncorrelated) and a correlated distribution with a prevailing direction in the orientation of lines. The anisotropy of the conductivity along and across the line defects is revealed, which agrees with experimental measurements for epitaxial graphene grown on SiC. We performed a detailed study of the conductivity for different defect correlations, introducing the correlation angle alpha(max)-the maximum possible angle between any two lines. We find that for a given electron density, the relative enhancement of the conductivity for the case of fully correlated line defects in comparison to the case of uncorrelatecl ones is larger for a higher defect density. Finally, we, for the first time, study the conductivity of realistic samples where both extended line defects and point-like scatterers such as adatoms and charged impurities are presented.