Landauer Conductance Research Articles

LOW-DIMENSIONAL QUANTUM TRANSPORT PROPERTIES OF CHEMICALLY-DISORDERED CARBON NANOTUBES: FROM WEAK TO STRONG LOCALIZATION REGIMES

In this review, the quantum transport of nitrogen-doped metallic carbon nanotubes under magnetic field are explored. An accurate modeling of chemical disorder effects is derived from ab initio calculations. General properties for low bias Landauer conductance are investigated in the coherent regime, which enlighten the strong interplay between band structure and quantum interference effects. Characteristic transport length scales such as the elastic mean free path and localization length are extracted from phenomenological laws as well as scaling features with nanotube radius and doping level. The statistical analysis of conductance properties allow us to study the transition between weak and strong localization regimes.

All-carbon nanoswitch based on C70 molecule: A first principles study

We have demonstrated the electron transport properties of an all-carbon molecular junction based on the C70 molecule connecting with two armchair single-wall carbon nanotubes using first principles transport calculations. It is shown that the Landauer conductance of this carbon hybrid system can be tuned within several orders of magnitude not only by changing the orientation of the C70 molecule but also by rotating one of the tubes around the symmetry axis of the system at fixed distances. This fact could make this pure-carbon molecular system a possible candidate for a nanoelectronic switching device. Moreover, we have also studied the nitrogen doping effect of such a molecular device. The results reveal that molecular configuration selection and nitrogen doping would play important roles in such switching devices.

Quantum electronic transport: Linear and nonlinear conductance from the Keldysh approach

This is a review of the derivation of the Landauer conductance using the Keldysh non-equilibrium Green's function (NEGF) formalism and the equations-of-motion (EOM) method. We consider the elastic quantum electronic transport through a multi-lead device and treat the conductor in the mean-field approximation. This is suitable for open quantum dots as well as for several molecular systems where charging effects are negligible. The focus of the presentation is to unveil the technical issues involved in the formalism. We show how the Landauer conductance emerges as a linear term in the current–voltage I – V characteristics and indicate how to go beyond this regime. We address the connection of the NEGF approach to recent developments in molecular transport and discuss the problems that arise when one tries to include interaction effects beyond the mean field.

Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions

We apply the generating function technique developed by Nazarov to the computation of the density of transmission eigenvalues for a two-dimensional free massless Dirac fermion, which, e.g., underlies theoretical descriptions of graphene. By modeling ideal leads attached to the sample as a conformal invariant boundary condition, we relate the generating function for the density of transmission eigenvalues to the twisted chiral partition functions of fermionic $(c=1)$ and bosonic $(c=\ensuremath{-}1)$ conformal field theories. We also discuss the scaling behavior of the ac Kubo conductivity and compare its different dc limits with results obtained from the Landauer conductance. Finally, we show that the disorder-averaged Einstein conductivity is an analytic function of the disorder strength, with vanishing first-order correction, for a tight-binding model on the honeycomb lattice with weak real-valued and nearest-neighbor random hopping.

Calculations of spin-disorder resistivity from first principles

Spin-disorder resistivity of Fe and Ni is studied using the noncollinear density functional theory. The Landauer conductance is averaged over random disorder configurations and fitted to Ohm’s law. The distribution function is approximated by the mean-field theory. The dependence of spin-disorder resistivity on magnetization in Fe is found to be in excellent agreement with the results for the isotropic s-d model. In the fully disordered state, spin-disorder resistivity for Fe is close to experiment, while for fcc Ni it exceeds the experimental value by a factor of 2.3. This result indicates strong magnetic short-range order in Ni at the Curie temperature.

Ab initio study of transport properties of an all-carbon molecular switch based on C20 molecule

Choosing closed-ended armchair (5, 5) single-wall carbon nanotubes (CCNTs) as electrodes, we have investigated the electron transport properties across a carbon molecular junction consisting of a C20 molecule sandwiched between two semi-infinite carbon nanotubes. It is shown that the Landauer conductance of this carbon hybrid system can be tuned within several orders of magnitude not only by varying the tube-C20 distance, but more importantly by changing the orientation of the C20 molecule and rotating the C20 molecule or one of the tubes around the symmetry axis of the system at fixed distances. This fact could make this all-carbon molecular system a possible candidate for a nano-electronic switching device. Moreover, our study also reveals that molecular configuration selection and structural relaxation would play an important role in the design of such devices.

Quantized conductance without reservoirs: Method of the nonequilibrium statistical operator

We introduce a generalized non-equilibrium statistical operator (NSO) to study a current-carrying system. The NSO is used to derive a set of quantum kinetic equations based on quantum mechanical balance equations. The quantum kinetic equations are solved self-consistently together with Poisson’s equation to solve a general transport problem. We show that these kinetic equations can be used to rederive the Landauer formula for the conductance of a quantum point contact, without any reference to reservoirs at different chemical potentials. Instead, energy dissipation is taken into account explicitly through the electron-phonon interaction. We find that both elastic and inelastic scattering are necessary to obtain the Landauer conductance.

Electronic structure and transport properties of double-stranded Fibonacci DNA

We consider a class of synthetic DNA molecules based on a quasiperiodic arrangement of their constituent nucleotides. Making use of a two-step renormalization scheme the double-stranded DNA molecule is modeled in terms of a one-dimensional effective Hamiltonian, which includes contributions from the nucleobase system, the sugar-phosphate backbone, and the environment. Analytical results for the energy spectrum structure and Landauer conductance of Fibonacci DNA approximants are derived and compared with those corresponding to periodic polyGACT-polyCTGA chains. The main effect of quasiperiodic order is the emergence of a highly fragmented energy spectrum, introducing a characteristic low-energy scale in the electronic structure of aperiodic DNA chains. The presence of a series of high-conductance peaks in the transmission spectra of Fibonacci approximants indicates the existence of extended states in these systems. These results open perspectives for experimental work in nanodevices based on synthetic DNA.

Electronic transport in dielectrophoretically grown nanowires

Gold nanoparticles with mean diameter 10–15 nm have been synthesized and stabilized using capping agents in a polar solvent (water) and a non-polar solvent (dodecane). Using two gold bond wires (diameter 0.25 mm and separated by less than 10 μm) as electrodes a sinusoidal driving voltage was applied to the solution. The resulting dielectrophoresis of the solution caused deposition of these nanoparticles at the electrodes and the formation of a wire between the electrodes. Conductance studies of the wire as the final connection formed yielded evidence for low-dimensional transport character in the form of discrete (Landauer) conductance steps. Histogram analysis of the conductance data further supports the conclusion that as the wire forms the capping agents do not always contribute to the electronic transport through the wire.

Quasiclassical boundary conditions for a contact of two metals

Transparency of the interface between two metals is discussed in a frame of the quasiclassical theory. It is shown that the Kupriyanov–Lukichev expression for the boundary resistivity of the interface is essentially based on the approximation of the single-channel Landauer conductance. In the results, a systematic discrepancy between the theory and experiments on the superconducting proximity effect is observed. We propose a multi-channel derivation of the boundary conditions, and deduce a new quasiclassical expression for the boundary resistivity which provides better matching with the experimental data. Applied to the ferromagnetic metal–non-magnetic metal contacts the multi-channel quasiclassical approach offers a simple (compared to the numerical band-structure calculations) approach to estimate the magnitude and sign of the spin-asymmetry of the boundary resistance.

Rate of energy absorption by a closed ballistic ring

We make a distinction between the spectroscopic and the mesoscopic conductance of closed systems. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is related to the non-universal structure of the perturbation matrix which is generic for quantum chaotic systems. These structures may created bottlenecks that suppress the diffusion in energy space, and hence the rate of energy absorption. The resulting effect is not merely quantitative: For a ring-dot system we find that a smaller Landauer conductance implies a smaller spectroscopic conductance, while the mesoscopic conductance increases. Our considerations open the way towards a realistic theory of dissipation in closed mesoscopic ballistic devices.

Multichannel tunneling in multiband heterostructures: Heavy-hole and light-hole transmission properties

Based on the standard multiband Hamiltonians, the quadratic eigenvalue problem method and the multichannel transfer matrix technique, we develop a general approach to study multichannel-multiband transport properties through multilayered systems. In this approach we deal simultaneously with all the accessible physical channels. We are thus able to distinguish and to calculate transmission amplitudes, ${t}_{ij}$, for each pair $j,i$ of incoming and outgoing propagating modes. We apply this approach to study hole tunneling through single-barrier and multiple-barrier semiconductor heterostructures, modeled by a zero-biased $(4\ifmmode\times\else\texttimes\fi{}4)$ Kohn-Luttinger Hamiltonian. We calculate transmission coefficients and the Landauer conductance for systems with coupled and uncoupled channels. A very good agreement with experimental results is found when applied to double barrier resonant tunneling systems. We find interesting underbarrier interference and resonance effects.

Coherent transport of interacting electrons through a single scatterer

Using the self-consistent Hartree–Fock method, we calculate the persistent current of weakly interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We find that the persistent current decays with the system length ( L) asymptotically like I ∝ L - 1 - α , where α > 0 is the power depending only on the electron–electron interaction. We also simulate tunneling of the weakly interacting one-dimensional electron gas through a single δ barrier in a finite wire biased by contacts. We find that the Landauer conductance decays with the system length asymptotically like L - 2 α . The power laws L - 1 - α and L - 2 α have so far been observed only in correlated models. Their existence in the Hartree–Fock model is thus surprising.

Semiclassical Theory of Chaotic Conductors

We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit trajectories contribute, similarly to the pairs of periodic orbits making up the small-time expansion of the spectral form factor of chaotic dynamics. As a clue to the exact result we find that close self-encounters slightly hinder the escape of trajectories into leads. Our result explains why the energy-averaged conductance of individual chaotic cavities, with disorder or "clean," agrees with predictions of random-matrix theory.

Ballistic transport is dissipative: the why and how

In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire havebeen explained by coherent and dissipationless transmission of individual electrons across aone-dimensional barrier. This leaves untouched the central issue of conduction: a quantumwire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly how doesthe quantum wire shed its excess electrical energy? We show that the answer is provided,uniquely, by many-body quantum kinetics. Not only does this inevitably lead to universalquantization of the conductance, in spite of dissipation; it fully resolves a bafflingexperimental result in quantum-point-contact noise. The underlying physics restscrucially upon the action of the conservation laws in these open metallic systems.

Saturations fields in the Shubnikov–de Haas oscillations

We study the Shubnikov-de Haas oscillations in the magnetoresistance and Landauer conductance of a three strip quasi-2D semiconductor wave guide with thickness δ z and transversal width Wy. We assume that the strip in the middle, of length l H , is subject to a homogeneous magnetic field, tilted by θ H with respect to the normal z of the 2DEG. The structure of the Shubnikov-de Haas oscillations, associated with spin parallel and antiparallel to the z-component of the magnetic field, and the finiteness of l H , lead us to define, related with the limits between the corresponding Landau levels and the continuous spectrum, two characteristic saturation fields B s a t , đ= 2Φ o /l H cosθ H (2n s π - 1/δ 2 z ) 1 / 2 and B s a t , Đ defined by the positive root of B 2 s a t , Đ + 4gΦ o /πl 2 H cos 2 θ H B s a t , Đ - B 2 s a t , đ= 0. Here g is the Lande factor, Φ o the unit magnetic flux and n s the charge concentration. We also obtain the polarization field B p = Φ 0 /g 2n s - π/δ 2 z .

Modeling conduction in electron waveguides with finite-range impurities

We study the conductance of an electron waveguide with a finite range impurity using reaction matrix theory. We compute the scattering matrix for the waveguide and use it to obtain an exact expression for the Landauer conductance. In an effort to simplify the computation of conductance in such systems, we review the convergence difficulties that occur if $\ensuremath{\delta}$-function impurities in two space dimensions are used in place of finite range impurities. We compare our exact result for the waveguide conductance with a finite range impurity with the case of the $\ensuremath{\delta}$-function impurity with the finite number of modes. We determine conditions for which a $\ensuremath{\delta}$-function impurity can be used to approximate the conductance when a finite range impurity is present.

Aharonov-Bohm physics with spin. II. Spin-flip effects in two-dimensional ballistic systems

We study spin effects in the magnetoconductance of ballistic mesoscopic systems subject to inhomogeneous magnetic fields. We present a numerical approach to the spin-dependent Landauer conductance which generalizes recursive Green-function techniques to the case with spin. Based on this method we address spin-flip effects in quantum transport of spin-polarized and spin-unpolarized electrons through quantum wires and various two-dimensional Aharonov-Bohm geometries. In particular, we investigate the range of validity of a spin-switch mechanism recently found which allows for controlling spins indirectly via Aharonov-Bohm fluxes. Our numerical results are compared to a transfer-matrix model for one-dimensional ring structures presented in the first paper [Hentschel et al., Phys. Rev. B, preceding paper, Phys. Rev. B 69, 155326 (2004)] of this series.

Exchange-interaction effects on the conductance of long quantum wires

The effect of exchange-interaction on the two-terminal conductance of fully ballistic samples is studied using a many-particle wave packet formalism. The approach shows that the puzzling nonuniversal conductance quantization for long quantum wires can be explained as a fermion exchange interaction effect. The Landauer conductance step Go ≡ 2e2/h is obtained when two-electron interaction is considered. Reductions of Go are due to a wave packet many-particle exchange interaction effect. For ballistic GaAs/AlGaAs quantum wires longer than 1 µm, a conductance step reduction is obtained in agreement with experimental results.

Landauer conductance of tunnel junctions: strong impact from boundary conditions

We present model calculations for the Landauer conductance of tunnel junctions. The tunnelling of free electrons through a rectangular potential barrier is considered. The conductance of a finite number of barriers was calculated using a transfer matrix method. The periodic arrangement of the same barriers was described by a Kronig–Penney model to calculate the band structure and, from that, the conductance of a point contact in the ballistic limit. Comparison of the results showed the importance of the boundary conditions. Caused by resonant scattering in the superlattice, the conductance is overestimated by an order of 1/t, the transmission coefficient of the single barrier. In the case of metallic multilayers, these interferences are of minor importance. In conclusion, the application of the Landauer formula to periodic lattices to describe the tunnelling conductance of a single barrier is not appropriate.