Showing papers on "Conductance published in 2004"
TL;DR: In this paper, a uniform single-walled carbon nanotube networks of varying densities have been fabricated at room temperature by a vacuum filtration method, and measurements of the sheet conductance as a function of the network density show 2D percolation behavior.
Abstract: Ultrathin, uniform single-walled carbon nanotube networks of varying densities have been fabricated at room temperature by a vacuum filtration method. Measurements of the sheet conductance as a function of nanotube network density show 2D percolation behavior. In addition, the network transparency in the visible spectral range was examined and the results are in agreement with a standard thin-film model: fits to the standard theory indicate U ac ) Udc for transmission measurements at 550 nm. Transmission measurements also indicate the usefulness of nanotube network films as a transparent, conductive coating. Avenues for improvement of the network conductance are discussed.
1,141 citations
TL;DR: In this paper, the electron transport properties of benzenedithiol and benzenedimethanethiol covalently bonded to gold electrodes by repeatedly creating a large number of molecular junctions were studied.
Abstract: We have studied electron transport properties of benzenedithiol and benzenedimethanethiol covalently bonded to gold electrodes by repeatedly creating a large number of molecular junctions. For each molecule, conductance histogram shows peaks at integer multiples of a fundamental conductance value, which is used to identify the conductance of a single molecule. The conductance values of a benzenedithiol and benzenedimethanethiol are 0.011 G0 and 0.0006 G0 (G0 = 2e2/h), respectively. The conductance peaks are broad, which reflects variations in the microscopic details of different molecular junctions. We have also studied electrochemical gate effect.
543 citations
TL;DR: This work provides an unambiguous determination of single DNA conductance and demonstrates different conduction mechanisms for different sequences.
Abstract: We have studied electron transport in DNA duplexes, covalently bonded to two electrodes in aqueous buffer solutions, by repeatedly forming a large number of DNA junctions. The histogram of conductances reveals peaks at integer multiples of a fundamental value, which is used to identify with the conductance of a single DNA molecule. The measured conductance depends on the DNA sequence and length. For (GC)n sequences, the conductance is inversely proportional to the length (greater than eight base pairs). When inserting (A:T)m into GC-rich domains, it decreases exponentially with the length of A:T base pairs (m) with a decay constant of 0.43 A-1. This work provides an unambiguous determination of single DNA conductance and demonstrates different conduction mechanisms for different sequences.
431 citations
TL;DR: In this paper, the thermal conductance associated with electron-phonon coupling in a metal near a metal-nonmetal interface can be estimated as hep=Gkp, where G is the volumetric electron and phonon or lattice thermal conductivity of the metal.
Abstract: We theoretically show that the thermal conductance associated with electron–phonon coupling in a metal near a metal–nonmetal interface can be estimated as hep=Gkp, where G is the volumetric electron–phonon coupling constant and kp is the phonon or lattice thermal conductivity of the metal. The expression suggests hep≈1/T at temperatures comparable to the Debye temperature of the metal. The predicted values of hep fall within the range of conductance values experimentally observed (0.3–1 GW/m2 K), suggesting that it cannot be ignored, and could even play a dominant role at high temperatures. Predictions of the total thermal conductance, that include both electron–phonon and phonon–phonon interfacial conductances, show reasonable agreement in its temperature dependence with experimental data for TiN/MgO interfaces.
421 citations
TL;DR: The experimental value for the zero bias conductance of organic molecules coupled by thiol groups to gold electrodes tends to be much smaller than the theoretical result based on density functional theory (DFT) calculations, often by orders of magnitude as mentioned in this paper.
Abstract: The experimental value for the zero bias conductance of organic molecules coupled by thiol-groups to gold electrodes tends to be much smaller than the theoretical result based on density functional theory (DFT) calculations, often by orders of magnitude. To address this puzzle we have analyzed the regime within which the approximations made in these calculations are valid. Our results suggest that a standard step in DFT based transport calculations, namely approximating the exchange-correlation potential in quasistatic nonequilibrium by its standard equilibrium expression, is not justified at weak coupling. We propose, that the breakdown of this approximation is the most important source for overestimating the width of the experimentally observed conductance peak and therefore also of the zero bias conductance. We present a numerical study on the conductance of an organic molecule that has recently been studied in experiments that fully agrees with this conclusion.
209 citations
TL;DR: In this paper, simultaneous measurements of conductance and work function changes induced by gaseous ambient have been performed on α-Fe2O3 thick film polycrystalline samples.
Abstract: The simultaneous measurements of conductance and work function changes induced by gaseous ambient have been performed on α-Fe2O3 thick film polycrystalline samples kept at 280 °C and exposed to different gaseous atmospheres. The switching from n- to p-type conductivity on α-Fe2O3 is shown to have an electronic origin, which is due to the oxygen adsorption and formation of a surface inversion layer and, therefore, to the inversion of the surface conduction type. The modeling of the n–p switching is described in terms of conductance dependence on the band bending induced by gaseous ambient.
156 citations
TL;DR: The results show for the first time in a molecular junction the theoretically predicted transition from coherent superexchange tunneling conductance to an activated hopping mechanism as temperature is increased.
Abstract: We report temperature dependence measurements on the conductance of individual molecular wires. The results show for the first time in a molecular junction the theoretically predicted transition from coherent superexchange tunneling conductance to an activated hopping mechanism as temperature is increased.
152 citations
TL;DR: The conductance of single peptides covalently bonded to two Au electrodes via S-Au bonds by repeatedly forming a large number of molecular junctions is measured, suggesting that tunneling is the mechanism of electron transport in the peptides.
Abstract: We have measured the conductance of single peptides covalently bonded to two Au electrodes via S−Au bonds by repeatedly forming a large number of molecular junctions. The conductance decreases exponentially with the peptide length, with a decay constant of β = 0.9 ± 0.1 A-1, suggesting that tunneling is the mechanism of electron transport in the peptides. The conductance of the peptides is sensitive to the solution pH, due to the protonation/deprotonation of the amine and carboxyl groups of the peptides, which provides titration measurements based on single-molecule conductance.
150 citations
TL;DR: First-principles calculations show that monatomic strings of carbon have high cohesive energy and axial strength, and exhibit stability even at high temperatures, and the double covalent bonding of carbon atoms underlies their unusual chemical, mechanical, and transport properties.
Abstract: First-principles calculations show that monatomic strings of carbon have high cohesive energy and axial strength, and exhibit stability even at high temperatures Because of their flexibility and reactivity, carbon chains are suitable for structural and chemical functionalizations; they also form stable ring, helix, grid, and network structures Analysis of electronic conductance of various infinite, finite, and doped string structures reveal fundamental and technologically interesting features Changes in doping and geometry give rise to dramatic variations in conductance In even-numbered linear chains, strain induces a substantial decrease of conductance The double covalent bonding of carbon atoms underlies their unusual chemical, mechanical, and transport properties
147 citations
TL;DR: In this article, the scattering-based approach for calculating the ballistic conductance of open quantum systems is generalized to deal with magnetic transition metals as described by ultrasoft pseudopotentials, and quantum-mechanical conductance calculations for monatomic Co and Ni nanowires with a magnetization reversal are presented.
Abstract: The scattering-based approach for calculating the ballistic conductance of open quantum systems is generalized to deal with magnetic transition metals as described by ultrasoft pseudopotentials. As an application we present quantum-mechanical conductance calculations for monatomic Co and Ni nanowires with a magnetization reversal. We find that in both Co and Ni nanowires, at the Fermi energy, the conductance of $d$ electrons is blocked by a magnetization reversal, while the $s$ states (one per spin) are perfectly transmitted. $d$ electrons have a nonvanishing transmission in a small energy window below the Fermi level. Here, transmission is larger in Ni than in Co.
144 citations
TL;DR: In this article, double-layer capacitance and electronic conductance of an activated carbon electrode in an aprotic electrolyte solution, 1 mol/L in acetonitrile, were measured.
Abstract: We have measured double-layer capacitance and electronic conductance of an activated carbon electrode in an aprotic electrolyte solution, 1 mol/L in acetonitrile. Both quantities show a similar dependence on the electrode potential with distinct minima near the potential of zero charge. This correlation suggests that the capacitance like the conductance is governed substantially by the electronic properties of the solid, rather than by the properties of the solution side of the double layer. These findings can be explained by treating activated carbon as a metal with a finite density of electronic states at the Fermi level, and with hopping conduction between these states. © 2003The Electrochemical Society. All rights reserved.
TL;DR: It is found that, at very low temperatures, the photon conductance is the dominant route for thermal equilibration, while at moderate temperatures this relaxation mode adds one quantum of thermal conductance to that due to phonon transport.
Abstract: Measurements of the thermal properties of nanoscale electron systems have ignored the effect of electrical noise radiated between the electron gas and the environment, through the electrical leads. Here we calculate the effect of this photon-mediated process, and show that the low-temperature thermal conductance is equal to the quantum of thermal conductance, ${G}_{Q}={\ensuremath{\pi}}^{2}{k}_{B}^{2}T/3h$, times a coupling coefficient. We find that, at very low temperatures, the photon conductance is the dominant route for thermal equilibration, while at moderate temperatures this relaxation mode adds one quantum of thermal conductance to that due to phonon transport.
TL;DR: In this article, the transition from p-to n-type response, induced by the change in the gas concentration and the operating temperature, was observed for α-Fe 2 O 3 -based semiconducting sensors.
Abstract: Transition from p- to n-type response, induced by the change in the gas concentration and the operating temperature, was observed for α-Fe 2 O 3 -based semiconducting sensors. This phenomenon is due to the formation of an inversion layer at the surface and therefore to the inversion of the type of mobile carrier at the surface. Different gas atmospheres leads to the different contribution of surface electrons and holes in the overall conductivity, which leads for the predominating either p- or n-type response.
TL;DR: A theoretical study of single molecule conduction switching of photochromic dithienylethene molecules using quantum molecular dynamics and Green's function electronic transport theory finds large on-off conductance ratios depending on the side group outside the switching core.
Abstract: We report a theoretical study of single molecule conduction switching of photochromic dithienylethene molecules. The light-induced intramolecular transformation drives a swapping of the highest occupied molecular orbital and lowest unoccupied molecular orbital between two distinct conjugated paths. The shuffling of single and double bonds produces a significant conductance change when the molecule is sandwiched between metal electrodes. We model the switching event using quantum molecular dynamics and the conductance changes using Green's function electronic transport theory. We find large on-off conductance ratios (between 10 and over 100) depending on the side group outside the switching core.
TL;DR: In this paper, the first-principles density-functional method was used to model electron transport through linear chains of monovalent atoms between two bulk electrodes and showed that the conductance oscillations are large for alkali-metal chains and their phase is opposite to that of noble metal chains.
Abstract: Using a first-principles density-functional method we model electron transport through linear chains of monovalent atoms between two bulk electrodes. For noble-metal chains the transport resembles that for free electrons over a potential barrier whereas for alkali-metal chains resonance states at the chain determine the conductance. As a result, the conductance for noble-metal chains is close to one quantum of conductance, and it oscillates moderately so that an even number of chain atoms yields a higher value than an odd number. The conductance oscillations are large for alkali-metal chains and their phase is opposite to that of noble-metal chains.
TL;DR: A commonly used heuristic approach, whereby the passive membrane time constant is replaced by a drive-dependent effective time constant, is examined and it is demonstrated that this approximation is valid in the same limit that the underlying diffusion approximation holds, both for delta correlated as well as filtered synaptic drive.
Abstract: A neuron in an active cortical circuit is subject to a fluctuating synaptic drive mediated by conductance changes. It was recently demonstrated that synaptic conductance effects in vivo significantly alter the integrative properties of neurons. These effects are missed in models that approximate the synaptic drive as a fluctuating current. Here the membrane-potential distribution and firing rate are derived for the integrate-and-fire neuron with $\ensuremath{\delta}$ correlated conductance-based synaptic input using the Fokker-Planck formalism. A number of different input scenarios are examined, including balanced drive and fluctuation changes at constant conductance, the latter of which corresponds to shifts in synchrony in the presynaptic population. This minimal model captures many experimentally observed conductance-related effects such as reduced membrane-potential fluctuations in response to increasing synaptic noise. The solvability of the model allows for a direct comparison with current-based approaches, providing a basis for assessing the validity of existing approximation schemes that have dealt with conductance change. In particular, a commonly used heuristic approach, whereby the passive membrane time constant is replaced by a drive-dependent effective time constant, is examined. It is demonstrated that this approximation is valid in the same limit that the underlying diffusion approximation holds, both for $\ensuremath{\delta}$ correlated as well as filtered synaptic drive.
DSM1
TL;DR: The conductance through a molecular device including electron-electron and electron-phonon interactions is calculated using the numerical renormalization group method using the standard Kondo model with renormalized parameters.
Abstract: The conductance through a molecular device including electron-electron and electron-phonon interactions is calculated using the numerical renormalization group method. At low temperatures and weak electron-phonon coupling the properties of the conductance can be explained in terms of the standard Kondo model with renormalized parameters. At large electron-phonon coupling a charge analog of the Kondo effect takes place that can be mapped into an anisotropic Kondo model. In this regime the molecule is strongly polarized by a gate voltage which leads to rectification in the current-voltage characteristics of the molecular junction.
TL;DR: It is demonstrated that the binding of a guest species onto a single host molecule can be studied electrically by wiring the host molecule to two electrodes, and the rectification properties of asymmetric host molecules and host–guest complexes to be studied.
Abstract: As the field of silicon-based microelectronics attempts, with difficulty, to head towards the nanoscale, the construction of electronic devices with individual molecules becomes an attractive alternative and has stimulated a recent surge of interest in the study of the electronic properties of single molecules. As well as displaying excellent electronic properties, single molecules can also recognize other molecules through specific binding interactions, which is something that current silicon-based technology is unable to offer. This capability of molecular recognition is used with astonishing accuracy and efficiency in biological systems and serves as an important design principle for chemical and biological sensors. Various molecular recognition processes have been studied and applied to sensor applications, but most methods to date measure an optical, electrochemical, or mechanical signal that arises from a large number of molecules. Herein we demonstrate that the binding of a guest species onto a single host molecule can be studied electrically by wiring the host molecule to two electrodes. The measurement of electron-transport processes through a single molecule also allows the rectification properties of asymmetric host molecules and host–guest complexes to be studied. Peptides were chosen as the host molecules because of the unlimited choice of different sequences that can be tuned to obtain optimal binding strength and specificity for a metal ion—our chosen guest. Four peptides were studied, cysteamine-Cys, cysteamine-Gly-Cys, Cys-Gly-Cys, and cysteamine-Gly-Gly-Cys (Cys= cysteine, Gly= glycine), which each have two thiol termini that can form reproducible contact to Au electrodes for electrical measurement. These peptides were expected to bind transition-metal ions, such as Cu and Ni, specifically through deprotonated peptide bonds. The binding configuration and the binding constant are sensitive to the pH of the peptide local environment. To form the most stable metal–peptide complexes and also to avoid the precipitation of metal hydroxides on the Au electrodes, the pH of the solution was maintained at 8 and 9 for Cu and Ni, respectively. Under the experimental conditions, the metal ions and the peptides were expected to form mainly 1:1 metal-to-ligand complexes. For cysteamineCys, cysteamine-Gly-Cys, and Cys-Gly-Cys, the peptide bonds are completely deprotonated so the number of deprotonated
TL;DR: In this paper, the effect of Coulomb interactions on the conductance of a singlemode quantum wire connecting two bulk leads was studied and it was shown that at low temperature T > J, the spin effect reduces the conductances to e2/h.
Abstract: We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T >J the spin effect reduces the conductance to e2/h.
TL;DR: The results suggest the formation of an unusual and highly stable pentagonal Cu nanowire with a diameter of approximately 0.45 nm and approximately 4.5 conductance quanta.
Abstract: We present a study of the structural and quantum conductance properties of atomic-size copper nanowires generated by mechanical stretching. The atomistic evolution was derived from time-resolved electron microscopy observations and molecular dynamics simulations. We have analyzed the quantum transport behavior by means of conductance measurements and theoretical calculations. The results suggest the formation of an unusual and highly stable pentagonal Cu nanowire with a diameter of approximately 0.45 nm and approximately 4.5 conductance quanta.
TL;DR: Proton conduction by F(0) was studied in chromatophores of the photosynthetic bacterium Rhodobacter capsulatus by a minimal rotary model including the rotating c-ring and two relay groups mediating proton exchange between the ring and the respective membrane surface.
TL;DR: An atomic-scale quantum conductance switch is demonstrated that allows us to open and close an electrical circuit by the controlled and reproducible reconfiguration of silver atoms within an atomic- scale junction.
Abstract: An atomic-scale quantum conductance switch is demonstrated that allows us to open and close an electrical circuit by the controlled and reproducible reconfiguration of silver atoms within an atomic-scale junction The only movable parts of the switch are the contacting atoms The switch is entirely controlled by an external electrochemical voltage applied to an independent third gate electrode Controlled switching was performed between a quantized, electrically conducting "on state" exhibiting a conductance of G(0)=2e(2)/h ( approximately 1/129 kOmega) or preselectable multiples of this value and an insulating "off state"
01 Mar 2004
TL;DR: The effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads when the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal is studied.
Abstract: We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime the electron spins form an antiferromagnetic Heisenberg chain with an exponentially small coupling J. An electric current in the wire perturbs the spin chain and gives rise to a temperature-dependent contribution of the spin subsystem to the resistance. At low temperature T >J the spin effect reduces the conductance to e2/h.
TL;DR: In this paper, a quantitative model for phase shifts observed in scanning conductance microscopy was presented, which showed excellent agreement with data on samples of (conducting) single wall carbon nanotubes and insulating poly(ethylene oxide) (PEO) nanofibers.
Abstract: We present a quantitative model for phase shifts observed in scanning conductance microscopy and show excellent agreement with data on samples of (conducting) single wall carbon nanotubes and insulating poly(ethylene oxide) (PEO) nanofibers. The model takes into account phase shifts due to the electrostatic (capacitive) forces exerted on the tip by sample and substrate, using simple approximate geometries. Data for large diameter, conducting doped polyaniline/PEO nanofibers are qualitatively explained. This quantitative approach is used to determine the dielectric constant of PEO nanofiber, a general method that can be extended to other dielectric nanowires.
TL;DR: In this article, the authors explored the low-temperature linear and nonlinear electrical conductance G of metallic carbon nanotubes (CNT's), which were grown by the chemical-vapor deposition method.
Abstract: We have explored the low-temperature linear and nonlinear electrical conductance G of metallic carbon nanotubes (CNT's), which were grown by the chemical-vapor deposition method. The high transparency of the contacts allows to study these two-terminal devices in the high conductance regime. We observe the expected four-fold shell pattern together with Kondo physics at intermediate transparency Gless than or similar to2e(2)/h and a transition to the open regime in which the maximum conductance is doubled and bound by G(max)=4e(2)/h. In the high-G regime, at the transition from a quantum dot to a weak link, the CNT levels are strongly broadened. Nonetheless, sharp resonances appear superimposed on the background which varies slowly with gate voltage. The resonances are identified by their lineshape as Fano resonances. The origin of Fano resonances is discussed along the modeling.
01 Jan 2004
TL;DR: In this paper, the authors simulated proton conduction by a minimal rotary model including the rotating c-ring and two relay groups mediating proton exchange between the ring and the respective membrane surface.
Abstract: ½AQ1� ABSTRACT The membrane portion of F0F1-ATP synthase, F0, translocates protons by a rotary mechanism. Proton conduction by F0 was studied in chromatophores of the photosynthetic bacterium Rhodobacter capsulatus. The discharge of a light-induced voltage jump was monitored by electrochromic absorption transients to yield the unitary conductance of F0. The current-voltage relationship of F0 was linear from 7 to 70 mV. The current was extremely proton-specific (.10 7 ) and varied only slightly (� threefold) from pH 6 to 10. The maximum conductance was � 10 fS at pH 8, equivalent to 6240 H 1 s � 1 at 100-mV driving force, which is an order-of-magnitude greater than that of F0F1. There was no voltage-gating of F0 even at low voltage, and proton translocation could be driven by DpH alone, without voltage. The reported voltage gating in F0F1 is thus attributable to the interaction of F0 with F1 but not to F0 proper. We simulated proton conduction by a minimal rotary model including the rotating c-ring and two relay groups mediating proton exchange between the ring and the respective membrane surface. The data fit attributed pK values of � 6 and � 10 to these relays, and placed them close to the membrane/electrolyte interface.
TL;DR: In this article, the molecular conductance of benzene connected to two Au leads through different anchoring atoms-S, Se, and Te-was calculated from density functional theory calculations for molecular electronic structure with a Green function method for electron transport.
Abstract: Combining density functional theory calculations for molecular electronic structure with a Green function method for electron transport, we calculate from first principles the molecular conductance of benzene connected to two Au leads through different anchoring atoms-S, Se, and Te. The relaxed atomic structure of the contact, different lead orientations, and different adsorption sites are fully considered. We find that the molecule-lead coupling, electron transfer, and conductance all depend strongly on the adsorption site, lead orientation, and local contact atomic configuration. For flat contacts the conductance decreases as the atomic number of the anchoring atom increases, regardless of the adsorption site, lead orientation, or bias. For small bias this chemical trend is, however, dependent on the contact atomic configuration: an additional Au atom at the contact with the (111) lead changes the best anchoring atom from S to Se, although for large bias the original chemical trend is recovered.
TL;DR: In this article, the authors analyzed the transport properties of contacts between an unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory and obtained a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface.
Abstract: We analyze the transport properties of contacts between unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory. We obtain a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface. This allows us to investigate the voltage-dependent conductance (conductance spectrum) of a diffusive normal metal (DN)/ unconventional singlet superconductor junction in both ballistic and diffusive cases. For d-wave superconductors, we calculate conductance spectra numerically for different orientations of the junctions, resistances, Thouless energies in DN, and transparencies of the interface. We demonstrate that conductance spectra exhibit a variety of features including a V-shaped gaplike structure, zero bias conductance peak (ZBCP) and zero bias conductance dip. We show that two distinct mechanisms: (i) coherent Andreev reflection (CAR) in DN and (ii) formation of midgap Andreev bound state at the interface of d-wave superconductors, are responsible for ZBCP, their relative importance being dependent on the angle alpha between the interface normal and the crystal axis of d-wave superconductors. For alpha= 0, the ZBCP is due to CAR in the junctions of low transparency with small Thouless energies. This is similar to the case of diffusive normal metal/insulator/s-wave superconductor junctions. With increase of alpha from zero to pi/4, the MABS contribution to ZBCP becomes more prominent and the effect of CAR is gradually suppressed. Such complex spectral features shall be observable in conductance spectra of realistic high-Tc junctions at very low temperature.
TL;DR: In this article, the authors define the escape time T (x, r) to be the mean exit time of a simple random walk on an infinite weighted graph starting at x from the ball centre x and radius r. They show that these are the only constraints, by constructing for each α 0, β 0 satisfying the inequalities above a graph Γ̃ which is Ahlfors α 0regular and has escape time exponent β 0.
Abstract: Let Γ = (G,E) be an infinite weighted graph which is Ahlfors αregular, so that there exists a constant c such that c−1rα ≤ V (x, r) ≤ crα, where V (x, r) is the volume of the ball centre x and radius r. Define the escape time T (x, r) to be the mean exit time of a simple random walk on Γ starting at x from the ball centre x and radius r. We say Γ has escape time exponent β > 0 if there exists a constant c such that c−1rβ ≤ T (x, r) ≤ crβ for r ≥ 1. Well known estimates for random walks on graphs imply that α ≥ 1 and 2 ≤ β ≤ 1 + α. We show that these are the only constraints, by constructing for each α0, β0 satisfying the inequalities above a graph Γ̃ which is Ahlfors α0regular and has escape time exponent β0. In addition we can make Γ̃ sufficiently uniform so that it satisfies an elliptic Harnack inequality.
TL;DR: In this paper, the electronic states and transport properties of double-wall carbon nanotubes without impurities are studied in a systematic manner, and it is revealed that scattering in the bulk is negligible and the number of channels determines the average conductance.
Abstract: The electronic states and transport properties of double-wall carbon nanotubes without impurities are studied in a systematic manner. It is revealed that scattering in the bulk is negligible and the number of channels determines the average conductance. In the case of general incommensurate tubes, separation of degenerated energy levels due to intertube transfer is suppressed in the energy region higher than the Fermi energy but not in the energy region lower than that. Accordingly, in the former case, there are few effects of intertube transfer on the conductance, while in the latter case, separation of degenerated energy levels leads to large reduction of the conductance. It is also found that in some cases antiresonance with edge states in inner tubes causes an anomalous conductance quantization ${G=e}^{2}/\ensuremath{\pi}\ensuremath{\Elzxh},$ near the Fermi energy.