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.
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.
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.
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.
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.
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.
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].
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.
Charge carrier transport in single-layer graphene with one-dimensional charged defects is studied theoretically. Extended charged defects, considered an important factor for mobility degradation in chemically vapor-deposited graphene, are described by a self-consistent Thomas-Fermi potential. A numerical study of electronic transport is performed by means of a time-dependent real-space Kubo approach in honeycomb lattices containing millions of carbon atoms, capturing the linear response of realistic size systems in the highly disordered regime. Our numerical calculations are complemented with a kinetic transport theory describing charge transport in the weak scattering limit. The semiclassical transport lifetimes are obtained by computing scattered amplitudes within the second Born approximation. The transport electron-hole asymmetry found in the semiclassical approach is consistent with the Kubo calculations. In the strong scattering regime, the conductivity is found to be a sublinear function of electronic density and weakly dependent on the Thomas-Fermi screening wavelength. We attribute this atypical behavior to the extended nature of one-dimensional charged defects. Our results are consistent with recent experimental reports.
Numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regimes. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study [J. Yan and M. S. Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)] and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.
We propose and analyze novel surface-state-based waveguides in bandgap photonic crystals. We discuss the surface-mode band structure, the field localization, and the effect of imperfections on the waveguiding properties of the surface modes. We demonstrate that surface-state-based waveguides can be used to achieve directional emission out of the waveguide. We also discuss the application of the surface-state waveguides as efficient light couplers for conventional photonic crystal waveguides.
We report elastic scattering theory for surface electron waves in quantum corrals defined by adatoms on the surface of noble metals. We develop a scattering-matrix technique that allows us to account for a realistic smooth potential profile of the scattering centers. Our calculations reproduce quantitatively all the experimental observations, which is in contrast to previous theories (treating the adatoms as point scatterers) that require additional inelastic channels of scattering into the bulk in order to achieve the agreement with the experiment. Our findings thus indicate that accounting for a realistic potential as well as using the exact numerical schemes is important in achieving detailed agreement as well as interpretation of the experiment.
We^{ }perform numerical studies of the effect of sidewall imperfections on^{ }the resonant state broadening of the optical microdisk cavities for^{ }lasing applications. We demonstrate that even small edge roughness (/30)^{ }causes a drastic degradation of high-Q whispering gallery (WG)-mode resonances^{ }reducing their Q values by many orders of magnitude. At^{ }the same time, low-Q WG resonances are rather insensitive to^{ }the surface roughness. The results of numerical simulation obtained using^{ }the scattering matrix technique, are analyzed and explained in terms^{ }of wave reflection at a curved dielectric interface combined with^{ }the examination of Poincaré surface of sections in the classical^{ }ray picture.
We report a computational method based on the recursive Green’s function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference time domain (FDTD) technique is that it computes Green’s function of the photonic structure recursively by adding slice by slice on the basis of Dyson’s equation. This eliminates the need for storage of the wave function in the whole structure, which obviously strongly relaxes the memory requirements and enhances the computational speed. The second advantage of this method is that it can easily account for the infinite extension of the structure both into air and into the space occupied by the photonic crystal by making use of the so-called “surface Green’s functions.” This eliminates the spurious solutions (often present in the conventional FDTD methods) related to, e.g., waves reflected from the boundaries defining the computational domain. The developed method has been applied to study scattering and propagation of the electromagnetic waves in the photonic band-gap structures including cavities and waveguides. Particular attention has been paid to surface modes residing on a termination of a semi-infinite photonic crystal. We demonstrate that coupling of the surface states with incoming radiation may result in enhanced intensity of an electromagnetic field on the surface and very high Q factor of the surface state. This effect can be employed as an operational principle for surface-mode lasers and sensors.
We develop a scattering matrix approach for the numerical calculation of resonant states and Q values of a nonideal optical disk cavity with an arbitrary shape and with an arbitrary varying refraction index. The developed method is applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness (Δr ≲ λ/50) can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of the numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface, combined with an examination of Poincaré surfaces of section and of Husimi distributions.
We study the propagation of TM- and TE-polarized light in two-dimensional arrays of silver nanorods of various diameters in a gelatin background. We calculate the transmittance, reflectance and absorption of arranged and disordered nanorod arrays and compare the exact numerical results with the predictions of the Maxwell–Garnett effective-medium theory. We show that interactions between nanorods, multipole contributions and formations of photonic gaps affect strongly the transmittance spectra that cannot be accounted for in terms of the conventional effective-medium theory. We also demonstrate and explain the degradation of the transmittance in arrays with randomly located rods as well as the weak influence of their fluctuating diameter. For TM modes we outline the importance of the skin effect, which causes the full reflection of the incoming light. We then illustrate the possibility of using periodic arrays of nanorods as high-quality polarizers.
We present an analytical description of pi electrons of a finite-size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
A junction of monolayer and bilayer graphene nanoribbons is investigated using the tight-binding approximation. An external potential is applied on the bilayer graphene layers to control the electronic transport properties of the junction. The reflection and transmission probabilities for an incident electron at the junction are analytically calculated. The dependence of the reflection probability on the external potential, the wave vector of the incident electron and the width of the nanoribbon are evaluated.
Resonant tunneling diodes (RTDs) with strained i-Si0.4 Ge06. potential barriers and a strained i-Si quantum well, all on a relaxed Si0.8 Ge0.2 virtual substrate were successfully grown by ultra high vacuum compatible chemical vapor deposition and fabricated using standard Si processing methods. A large peak to valley current ratio of 2.9 and a peak current density of 4.3 kA/cm2 at room temperature were recorded from pulsed and continuous dc current-voltage measurements, the highest reported values to date for Si/Si1-x Gex RTDs. These dc figures of merit and material system render such structures suitable and highly compatible with present high speed and low power Si/Si1-x Gex heterojunction field effect transistor based integrated circuits.