Transport Formalism Research Articles

Quantum transport through resistive nanocontacts: Effective one-dimensional theory and conductance formulas for nonballistic leads

We introduce a quantum transport formalism based on a map of a real three-dimensional lead-conductor-lead system into an effective one-dimensional (1D) system. The resulting effective 1D theory is an in principle exact formalism to calculate the conductance. Besides being more efficient than the principal layers approach, it naturally leads to a five-partitioned workbench (instead of three) where each part of the device (the true central device, the ballistic and the nonballistic leads) is explicitely treated, allowing better physical insight into the contact resistance mechanisms. Independently, we derive a generalized Fisher-Lee formula and a generalized Meir-Wingreen formula for the correlated and uncorrelated conductance and current of the system where the initial restrictions to ballistic leads are generalized to the case of resistive contacts. We present an application to graphene nanoribbons.

Incorporation of the Goudsmit–Saunderson electron transport theory in the Geant4 Monte Carlo code

The present work describes the implementation of the multiple scattering formalism for charged particle transport based on the Goudsmit–Saunderson angular distribution and satisfying the Lewis spatial displacement theories. Furthermore, the most realistic total cross sections and transport cross sections for single elastic scattering of electrons and positrons by neutral atoms were carried out using the ELSEPA code. The extended model has been incorporated in the Geant4 Monte Carlo code system (currently used in many fields of application for transport of particles and covering a large range of energies from 0.1 keV to 100 TeV). Additionally, techniques are developed that allow the distributions to be scaled to account for energy loss. This new representation allows on-the-fly sampling of Goudsmit–Saunderson angular distributions in a screened Rutherford approximation suitable for Class II condensed history Monte Carlo codes. The reliability of the model is demonstrated through a comparison of simulation results with experimental data. Good agreement is found for electrons with kinetic energies down to a few keV.

Turbulent sources in axisymmetric plasmas

Successful operation of tokamaks and other magnetic confinement schemes of fusion interest rely on the tailoring of the parallel momentum/current density and temperature profiles via resonant absorption of externally injected waves. Similarly, it is to be expected that a turbulent spectrum of waves, internally generated to free the energy stored in the gradients of the equilibrium profiles, could transfer locally momentum and energy to the particle degree of freedom of the plasma. Turbulent sources stem out nicely from the action-angle transport formalism, as a detailed derivation of the general transport law from the collision operator (which includes both the diffusion and the friction coefficients) in action-space shows. The special case of magnetic turbulence is considered, and explicit expressions for the electron parallel momentum and energy sources are presented. An interesting feature of the sources resides in their dependence on the first and second powers of the safety factor derivative, a dependence that is often found in turbulent fluxes as well. One term in the energy source depends, in a determinant way, also on the relative magnitude of the electron and ion temperature. This dependence, an output of the retention of the friction term in the collision operator, leads to an energy flow that is always directed from the hotter to the cooler species, a desirable property that is missed when a quasilinear approach is employed.

Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations.

Towards neutrino transport with flavor mixing in supernovae: the Liouville operator

The calculation of neutrino decoupling from nuclear matter requires a transport formalism capable of handling both collisions and flavor mixing. The first steps towards such a formalism are the construction of neutrino and antineutrino "distribution matrices," and a determination of the Liouville equations they satisfy in the noninteracting case. These steps are accomplished through study of a Wigner-transformed "density function," the mean value of paired neutrino quantum field operators.

Kondo peaks and dips in the differential conductance of a multi-lead quantum dot: Dependence on bias conditions

We study the differential conductance in the Kondo regime of a quantum dot coupled to multiple leads. When the bias is applied symmetrically on two of the leads ($V$ and $\ensuremath{-}V$, as usual in experiments) while the others are grounded, the conductance through the biased leads always shows the expected enhancement at zero bias. However, under asymmetrically applied bias ($V$ and $\ensuremath{\lambda}V$, with $\ensuremath{\lambda}>0$), a suppression---dip---appears in the differential conductance if the asymmetry coefficient $\ensuremath{\lambda}$ is beyond a given threshold ${\ensuremath{\lambda}}_{0}=\sqrt[3]{1+r}$ determined by the ratio $r$ of the dot-lead couplings. This is a recipe to determine experimentally this ratio which is important for the quantum-dot devices. This finding is a direct result of the Keldysh transport formalism. For the illustration we use a many-lead Anderson Hamiltonian, the Green's functions being calculated in the Lacroix approximation, which is generalized to the case of nonequilibrium.

First-Principles Calculation of the Isotope Effect on Boron Nitride Nanotube Thermal Conductivity

Isotopic composition can dramatically affect thermal transport in nanoscale heat conduits such as nanotubes and nanowires. A 50% increase in thermal conductivity for isotopically pure boron ((11)B) nitride nanotubes was recently measured, but the reason for this enhancement remains unclear. To address this issue, we examine thermal transport through boron nitride nanotubes using an atomistic Green's function transport formalism coupled with phonon properties calculated from density functional theory. We develop an independent scatterer model for (10)B defects to account for phonon isotope scattering found in natural boron nitride nanotubes. Phonon scattering from (10)B dramatically reduces phonon transport at higher frequencies and our model accounts for the experimentally observed enhancement in thermal conductivity.

Phonon thermal conductance of disordered graphene strips with armchair edges

Based on the model of lattice dynamics together with the transfer matrix technique, we investigate the thermal conductances of phonons in quasi-one-dimensional disordered graphene strips with armchair edges using Landauer formalism for thermal transport. It is found that the contributions to thermal conductance from the phonon transport near von Hove singularities is significantly suppressed by the presence of disorder, on the contrary to the effect of disorder on phonon modes in other frequency regions. Besides the magnitude, for different widths of the strips, the thermal conductance also shows different temperature dependence. At low temperatures, the thermal conductance displays quantized features of both pure and disordered graphene strips implying that the transmission of phonon modes at low frequencies are almost unaffected by the disorder.

Guiding Electrical Current in Nanotube Circuits Using Structural Defects: A Step Forward in Nanoelectronics

Electrical current could be efficiently guided in 2D nanotube networks by introducing specific topological defects within the periodic framework. Using semiempirical transport calculations coupled with Landauer-Buttiker formalism of quantum transport in multiterminal nanoscale systems, we provide a detailed analysis of the processes governing the atomic-scale design of nanotube circuits. We found that when defects are introduced as patches in specific sites, they act as bouncing centers that reinject electrons along specific paths, via a wave reflection process. This type of defects can be incorporated while preserving the 3-fold connectivity of each carbon atom embedded within the graphitic lattice. Our findings open up a new way to explore bottom-up design, at the nanometer scale, of complex nanotube circuits which could be extended to 3D nanosystems and applied in the fabrication of nanoelectronic devices.

Field-effect resistance of gated graphitic polymeric ribbons: Numerical simulations

We investigate the electronic and transport properties of undistorted gated polymers of the polyacene family by exploiting the tight-binding model for the system Hamiltonian and the nonequilibrium Keldysh formalism for charge transport. Our simulations reveal that, for smooth gate potentials varying only along the ribbon longitudinal axis, the electronic conductance as a function of the energy is quantized and presents crossover from conducting to insulating regimes. We interpret this behavior on the basis of the band structures entailed by the bipartite honeycomb topology of the lattice and the symmetry of the ribbons with even or odd number of chains (even-odd effect).

Triplet energy transfer in conjugated polymers. II. A polaron theory description addressing the influence of disorder

Motivated by experiments monitoring motion of triplet excitations in a conjugated polymer containing Pt-atoms in the main chain (see Paper I), a theoretical formalism for electronic transport has been developed. It considers the interplay between polaronic distortion of the excited chain elements and disorder treated in terms of effective-medium theory. The essential parameters are the electronic coupling $J$, the polaronic binding energy $\ensuremath{\lambda}$ that determines the activation energy of polaron motion ${E}_{a}$, and the variance $\ensuremath{\sigma}$ of the density of states distribution controlling the incoherent hopping motion. It turns out that for the weak electronic coupling associated with triplet motion ($J$ a few meV), the transfer is nonadiabatic. For a critical ratio of $\ensuremath{\sigma}/{E}_{a}l0.3$, Marcus-type multiphonon transport prevails above a certain transition temperature. At lower temperatures, transport is disorder controlled consistent with the Miller-Abrahams formalism. Theoretical results are consistent with triplet transport in the Pt-polymer. Implications for charge and triplet motion in random organic semiconductors in general are discussed.

Quantum transport in a normal metal/odd-frequency superconductor junction

Recent experimental results indicate the possible realization of a bulk odd-frequency superconducting state in the compounds ${\text{CeCu}}_{2}{\text{Si}}_{2}$ and ${\text{CeRhIn}}_{5}$. Motivated by this, we present a study of the quantum transport properties of a normal metal/odd-frequency superconductor junction in a search for probes to unveil the odd-frequency symmetry. From the Eliashberg equations, we perform a quasiclassical approximation to account for the transport formalism of an odd-frequency superconductor with the Keldysh formalism. Specifically, we consider the tunneling charge conductance and the tunneling thermal conductance. We qualitatively find distinct behavior in the odd-frequency case compared to the conventional even-frequency case in both the electrical and thermal current. This serves as a useful tool to identify the possible existence of a bulk odd-frequency superconducting state.

Direct Solution of the Boltzmann Transport Equation and Poisson–SchrÖdinger Equation for Nanoscale MOSFETs

We propose an efficient and fast algorithm to solve the coupled Poisson-Schrodinger and Boltzmann transport equations (BTE) in two dimensions. The BTE is solved in the relaxation time approximation within each subband obtained from the direct solution of the Schrodinger equation. The proposed approach, considering a subband-based transport formalism, allows to fully explore the entire range from drift-diffusion to ballistic regime in nanoscale field-effect transistors. Quantum effects are also fully taken into account by the direct solution of the Schrodinger equation. The model is implemented in the NanoTCAD2D device simulator and used to study the device performance of a 25-nm channel-length MOSFET. The influence of scattering on the electron distribution function and on device characteristics is analyzed in detail.

Coherent phonon scattering effects on thermal transport in thin semiconductor nanowires

The thermal conductance by phonons of a quasi-one-dimensional solid with isotope or defect scattering is studied using the Landauer formalism for thermal transport. The conductance shows a crossover from localized to Ohmic behavior, just as for electrons, but the nature of this crossover is modified by delocalization of phonons at low frequency. A scalable numerical transfer-matrix technique is developed and applied to model quasi-one-dimensional systems in order to confirm simple analytic predictions. We argue that existing thermal conductivity data on semiconductor nanowires, showing an unexpected linear dependence, can be understood through a model that combines incoherent surface scattering for short-wavelength phonons with nearly ballistic long-wavelength phonons. It is also found that even when strong phonon localization effects would be observed if defects are distributed throughout the wire, localization effects are much weaker when defects are localized at the boundary, as in current experiments.

Dynamics of atom scattering from 4He nanoclusters

We present a microscopic theory and results of atom scattering calculations to determine the dispersion of surface modes (ripplons) of superfluid helium-4 nanodroplets, expanding previous work [J. Chem. Phys. 115, 10161 (2001)]. A quantum transport formalism is adapted to the many-body scattering problem, yielding both elastic and inelastic fluxes. We demonstrate that, in analogy to the dynamic structure function S(k,ω) obtained from neutron scattering, a dynamic structure function σ(k,ω) can be obtained from 3He scattering. The 3He dynamic structure function σ(k,ω) is sensitive to surface dynamics, whereas the neutron dynamic structure function S(k,ω) is dominated by bulk-like excitations, in particular by rotons. Unlike for neutron-scattering, the total inelastic cross section for atom-scattering on 4He nanodroplets is large which we believe makes experimental detection feasible. We also show that scattering identical particles, i.e. 4He atoms, does not provide information about the dispersion of surface modes. Instead, inelastically scattered 4He atoms preferably lose roughly half their energy.

Particle Acceleration in Advection‐dominated Accretion Disks with Shocks: Green’s Function Energy Distribution

The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally-supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.

Dynamics of charge transfer: Rate processes formulated with nonequilibrium Green’s functions

The authors examine the connection between electron transport under bias in a junction and nonadiabatic intramolecular electron transfer (ET). It is shown that under certain assumptions it is possible to define a stationary current that allows the computation of the intramolecular transfer rate using the same formalism that is employed in the description of transport. They show that the nonequilibrium Green's function formalism of quantum transport can be used to calculate the ET rate. The formal connection between electron transport and electron transfer is made, and they work out the simple case of an electronic level coupled to a vibrational mode representing a thermal bath and show that the result is the same as expected from a Fermi golden rule treatment, and in the high-temperature limit yields the Marcus electron transfer theory. The usefulness of this alternative formulation of rates is discussed.

Band-to-Band Tunneling in a Carbon Nanotube Metal-Oxide-Semiconductor Field-Effect Transistor Is Dominated by Phonon-Assisted Tunneling

Band-to-band tunneling (BTBT) devices have recently gained a lot of interest due to their potential for reducing power dissipation in integrated circuits. We have performed extensive simulations for the BTBT operation of carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) using the nonequilibrium Green's function formalism for both ballistic and dissipative quantum transport. In comparison with recently reported experimental data (J. Am. Chem. Soc. 2006, 128, 3518-3519), we have obtained strong evidence that BTBT in CNT-MOSFETs is dominated by optical phonon assisted inelastic transport, which can have important implications on the transistor characteristics. It is shown that, under large biasing conditions, two-phonon scattering may also become important.

Nonequilibrium GW approach to quantum transport in nano-scale contacts

Correlation effects within the GW approximation have been incorporated into the Keldysh nonequilibrium transport formalism. We show that GW describes the Kondo effect and the zero-temperature transport properties of the Anderson model fairly well. Combining the GW scheme with density functional theory and a Wannier function basis set, we illustrate the impact of correlations by computing the I-V characteristics of a hydrogen molecule between two Pt chains. Our results indicate that self-consistency is fundamental for the calculated currents, but that it tends to wash out satellite structures in the spectral function.

Asymmetric heat conduction through a weak link

We study the heat conduction of two nonlinear lattices joined by a weak harmonic link. When the system reaches a steady state, the heat conduction of the system is decided by the tunneling heat flow through the weak link. We present an analytical analysis by the combination of the self-consistent phonon theory and the heat tunneling transport formalism, and then the tunneling heat flow can be obtained. Moreover, the nonequilibrium molecular dynamics simulations are performed and the simulations results are consistent with the analytical predictions.