Conductance of an array of elastic scatterers: A scattering-matrix approach

Cahay, M.; McLennan, Michael; Datta, Supriyo

doi:10.1103/physrevb.37.10125

Cited by 132 publications

(95 citation statements)

References 32 publications

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“…all expressions in Appendix H hold with P instead of S. In this sense, we will study in Section 5 the classical versus quantum situations (see also [47,48]). …”

Section: The Self-consistency Conditionmentioning

confidence: 99%

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ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Jacquet

2009

J Stat Phys

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We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, FermiDirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T L , µ L ) and (T R , µ R ), and adjust the parameters (T i , µ i ), for i = 1, . . . , N , so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.Mathematics Subject Classification 80A20, 81Q50, 81U20, 82C70

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“…all expressions in Appendix H hold with P instead of S. In this sense, we will study in Section 5 the classical versus quantum situations (see also [47,48]). …”

Section: The Self-consistency Conditionmentioning

confidence: 99%

“…If T L = T R , then setting µ = eV , where V denotes the electric potential, one obtains 48) where the electric conductance G e is given by…”

Section: Ohm and Fourier Lawsmentioning

confidence: 99%

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Jacquet

2009

J Stat Phys

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“…The delta function model is a convenient phenomenological approach to impurity scattering which has been widely used in spinindependent mesoscopic transport theories 25,35 as well as in ferromagnetic systems. 18,20 The spin dependence of scattering in the ferromagnet is determined by the ratio of up and down amplitudes, which we write as ρ = u − /u + .…”

Section: Delta Function Model Of Scatteringmentioning

confidence: 99%

Electron transport through disordered domain walls: Coherent and incoherent regimes

et al. 2006

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We study electron transport through a domain wall in a ferromagnetic nanowire subject to spindependent scattering. A scattering matrix formalism is developed to address both coherent and incoherent transport properties. The coherent case corresponds to elastic scattering by static defects, which is dominant at low temperatures, while the incoherent case provides a phenomenological description of the inelastic scattering present in real physical systems at room temperature. It is found that disorder scattering increases the amount of spin-mixing of transmitted electrons, reducing the adiabaticity. This leads, in the incoherent case, to a reduction of conductance through the domain wall as compared to a uniformly magnetized region which is similar to the giant magnetoresistance effect. In the coherent case, a reduction of weak localization, together with a suppression of spin-reversing scattering amplitudes, leads to an enhancement of conductance due to the domain wall in the regime of strong disorder. The total effect of a domain wall on the conductance of a nanowire is studied by incorporating the disordered regions on either side of the wall. It is found that spin-dependent scattering in these regions increases the domain wall magnetoconductance as compared to the effect found by considering only the scattering inside the wall. This increase is most dramatic in the narrow wall limit, but remains significant for wide walls.

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“…The observed electron-wave interference can be understood quantitatively based on a theoretical model shown schematically in Figure 9. In this model based on the multichannel Landauer-Büttiker formalism (59,(61)(62)(63), the nanotube is considered a coherent electron waveguide with two propagating modes, and the electron scattering is modeled by 4 × 4 scattering (S) matrices at each interface, S L and S R . Following previous theoretical studies (52,53), the electron scattering between the two modes inside the nanotube is ignored, and the phase accumulation during electron propagation is represented by a diagonal 4 × 4 matrix, S N .…”

mentioning

confidence: 99%

“…Consequently, electrons in the two propagating modes acquire different phase shifts as they traverse the nanotube, which are represented by the diagonal matrix elements of S N . The phase change as a function of electron energy is responsible for the interference patterns as a function of V and V g in Figures 7 and 8.The overall conductance behavior of a nanotube device can be calculated once the device S matrix S T is obtained from S L , S R , and S N by matrix combination (59,(61)(62)(63). Specifically, in the zero-temperature limit, dI/dV as a function of V and V g in a nanotube device is related to the matrix elements of S T as (30)…”

mentioning

confidence: 99%

TRANSPORT SPECTROSCOPY OF CHEMICAL NANOSTRUCTURES: The Case of Metallic Single-Walled Carbon Nanotubes

Liang

Bockrath

Park

2005

Annu. Rev. Phys. Chem.

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Key Words single-molecule transistor, Coulomb blockade, electronic shell filling, Kondo resonance, inelastic tunneling, electron wave interference ■ Abstract Transport spectroscopy, a technique based on current-voltage measurements of individual nanostructures in a three-terminal transistor geometry, has emerged as a powerful new tool to investigate the electronic properties of chemically derived nanostructures. In this review, we discuss the utility of this approach using the recent studies of single-nanotube transistors as an example. Specifically, we discuss how transport measurements can be used to gain detailed insight into the electronic motion in metallic single-walled carbon nanotubes in several distinct regimes, depending on the coupling strength of the contacts to the nanotubes. Measurements of nanotube devices in these different conductance regimes have enabled a detailed analysis of the transport properties, including the experimental determination of all Hartree-Fock parameters that govern the electronic structure of metallic nanotubes and the demonstration of Fabry-Perot resonators based on the interference of electron waves. INTRODUCTIONOptical spectroscopy has long served as the experimental tool of choice for investigating electronic and nuclear motions in atoms and molecules. In optical spectroscopy, the interaction between light and matter causes transitions between quantum states, and series of well-resolved spectral features are recorded as a function of the wavelength of light. The positions, intensities, and widths of the observed spectral features provide detailed information concerning the dynamics of electrons and nuclei in atoms and molecules. Optical spectroscopy has also been applied successfully to chemically derived nanostructures, such as nanocrystals (1-3), nanowires (4,5), and carbon nanotubes (6, 7), providing insight into the effects of quantum confinement on the electronic properties of these nanostructures. LIANG BOCKRATH PARKOver the last decade, a new type of spectroscopy based on electron transport measurements, often termed transport spectroscopy, has emerged as a powerful tool for investigating electronic motions in chemical nanostructures. Originally developed for lithographically-defined quantum dots (8), transport spectroscopy is based on current-voltage measurements of a three-terminal transistorlike device in which a single chemical nanostructure bridges two electrodes, and a third gate electrode couples electrostatically to the nanostructure. The electronic conduction through such devices at sufficiently low temperatures is dictated by single-electron charging and energy level quantization (9). Plots of current as a function of bias voltage exhibit features that provide detailed information on quantum-level structures in chemical nanostructures that complements optical spectroscopy.To date, transport spectroscopy has been carried out for a variety of chemical nanostructures, including molecules (10-14), nanocrystals (15)(16)(17)(18)(19), nanowires (20,21), and si...

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Conductance of an array of elastic scatterers: A scattering-matrix approach

Cited by 132 publications

References 32 publications

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

Electron transport through disordered domain walls: Coherent and incoherent regimes

TRANSPORT SPECTROSCOPY OF CHEMICAL NANOSTRUCTURES: The Case of Metallic Single-Walled Carbon Nanotubes

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