Landauer-Buttiker Formalism Research Articles

Decoherence due to contacts in ballistic nanostructures

memoryless on time scales coarsened over their energy-relaxation time, and the evolution of the current- limiting active region can be considered Markovian. Therefore, we first derive a general Markovian map in the presence of a memoryless environment by coarse graining the exact short-time non-Markovian dynamics of an abstract open system over the environment memory-loss time, and we give the requirements for the validity of this map. We then introduce a model contact-active region interaction that describes carrier injection from the contacts for a generic two-terminal ballistic nanostructure. Starting from this model interaction and using the Markovian dynamics derived by coarse graining over the effective memory-loss time of the contacts, we derive the formulas for the nonequilibrium steady-state distribution functions of the forward- and backward- propagating states in the nanostructure's active region. On the example of a double-barrier tunneling structure, the present approach yields an I-V curve that shows all the prominent resonant features. We address the relationship between the present approach and the Landauer-Buttiker formalism and also briefly discuss the inclusion of scattering.

Heat transport through plasmonic interactions in closely spaced metallic nanoparticle chains

We report a numerical investigation on the heat transfer through one dimensional arrays of metallic nanoparticles closely spaced in a host material. Our simulations show that the multipolar interactions play a crucial role in the heat transport via collective plasmons. Calculations of the plasmonic thermal conductance and of the thermal conductivity in ballistic and diffusive regime, respectively have been carried out. (a) Using the Landauer-Buttiker formalism we have found that, when the host material dielectric constant takes positive values, the multipolar interactions drastically enhance by several order of magnitude the ballistic thermal conductance of collective plasmons compared with that of a classical dipolar chain. On the contrary, when the host material dielectric constant takes negative values, we have demonstrated the existence of non-ballistic multipolar modes which annihilate the heat transfer through the chains. (b) Using the kinetic theory we have also examined the thermal behavior of chains in the diffusion approximation. We have shown that the plasmonic thermal conductivity of metallic nanoparticle chains can reach 1% of the bulk metal thermal conductivity . This result could explain the anomalously high thermal conductivity observed in many colloidal suspensions, the so called nanofluids.

Heat transport through plasmonic interactions in closely spaced metallic nanoparticle chains

We report a numerical investigation on the near-field heat transfer through one-dimensional arrays of metallic nanoparticles closely spaced in a host material. Using the Landauer-Buttiker formalism we study the thermal behavior of chains in ballistic regime. It is shown that that the heat transport through plasmonic interactions can be several order of magnitude more efficient than in classical dipolar chains. This result could explain the anomalously high thermal conductivity observed in many nanoparticles based composite media such as nanofluids and could find broad practical applications in nanoscale thermal management.

Shot Noise with Interaction Effects in Single-Walled Carbon Nanotubes

We have measured shot noise in single-walled carbon nanotubes with good contacts at 4.2 K at low frequencies (f=600-850 MHz). We find a strong modulation of shot noise over the Fabry-Perot pattern; in terms of the differential Fano factor the variation ranges over 0.4-1.2. The shot noise variation, in combination with differential conductance, is analyzed using two (spin-degenerate) modes with different, energy-dependent transmission coefficients. Deviations from the predictions from Landauer-Buttiker formalism are assigned to electron-electron interactions.

An electron injection model for time-dependent simulators of nanoscale devices with electron confinement: Application to the comparison of the intrinsic noise of 3D-, 2D- and 1D-ballistic transistors

For ballistic (quasi-ballistic) devices, the noise is mainly determined by the rate of injection of electrons from the contacts. Thus, the computation of the noise can be very sensible to the boundary conditions imposed on the simulators. An algorithm for the injection of electrons in nanoscale devices with (or without) electron confinement for degenerate (or non-degenerate) conditions is presented. The injection model is conceptually similar to the boundary conditions used in the Landauer approach, but it is developed for time-dependent simulators. For a simple ballistic two-terminal device, as a test, it is shown that the injection model directly reproduces the average current and the noise obtained by the Landauer–Buttiker formalism. Finally, the injection model is applied to compute noise in nanoscale transistors (without self-consistence with the Poisson equation). The results predict an increase of the Fano factor when electron confinement is present. In addition, it is also shown that other electron injection models without correlation between the injection of consecutive electrons increase the noise of nanoscale transistors unrealistically, when degenerate conditions are present.

Finite-element method study for the spin-polarized transport in a hybrid spin valve

The giant magnetoresistance (GMR) has been observed to increase with the number of layers in a hybrid spin valve. This study shows the increase of the spin-dependent scattering for the current perpendicular to the plane (CPP) geometry with the number of layers; thus, the increase of the CPP-GMR with the number of layers by a finite element method (FEM). The CPP-GMR is evaluated by using the three spin-dependent conductance based on the Landauer–Buttiker formalism. The transmission probabilities are calculated by using a transfer-matrix method. The conduction band structure is determined by extracting the free electron model parameters from first-principles data.

Longitudinal and spin-Hall conductance of a two-dimensional Rashba system with arbitrary disorder

We calculate the longitudinal and spin-Hall conductances in four-lead bridges with Rashba - Dresselhaus spin-orbit interactions. Numerical results are obtained both within Landauer-Buttiker formalism and by the direct evaluation of the Kubo formula. The microscopic Hamiltonian is obtained in the tight-binding approximation in terms of the neareast-neighbor hopping integral $t$, the Rashba spin-orbit coupling $V_R$, the Dresselhaus spin-orbit coupling $V_D$ and an Anderson-like, on-site disorder energy strength $W$. We reconfirm that below a critical disorder threshold, the spin-Hall effect is present. Further, we study the effect on the two conductivities of the Fermi energy, Rashba/Dresselhaus coefficient ratio, and system size.

Quantum spin transport through Aharonov–Bohm ring with a tangent magnetic field

Quantum spin transport in a mesoscopic Aharonov–Bohm ring with two leads subject to a magnetic field with circular configuration is investigated by means of one-dimensional quantum waveguide theory. Within the framework of Landauer–Buttiker formalism, the polarization direction of transmitted electrons can be controlled either by the AB magnetic flux or by the tangent magnetic field. In particular, the spin flips can be induced by hopping the AB magnetic flux or the tangent field.

Spin-based quantum interference effects and dephasing in strongly disordered Au nanobridges

We investigate quantum interference effects with magnetic field (magnetofingerprints) in strongly disordered Au-nanobridges. The magnetofingerprints are unconventional because they are caused by the Zeeman effect, not by the Aharonov-Bohm effect. These spin-based magnetofingerprints are equivalent to the Ericson's fluctuations (the fluctuations in electron transmission probability with electron energy). We present a model based on the Landauer-Buttiker formalism that describes the data. We show that the dephasing time $\tau_\phi (E,T)$ of electrons at temperature $T$ and energy $E$ above the Fermi level can be obtained from the correlation magnetic field. In samples with localization length comparable to sample size, $h/\tau_\phi (E,T) \approx E$, for $E\gg k_B T$, which shows that the Fermi liquid description of electron transport breaks down at length scale comparable to the localization length.

Spin-resolved Hall effect driven by spin-orbit coupling

Spin and electric Hall currents are calculated numerically in a two-dimensional mesoscopic system with Rashba and Dresselhaus spin-orbit coupling by means of the Landauer-Buttiker formalism. It is found that both electric and spin Hall currents circulate when two spin-orbit couplings coexist, while the electric Hall conductance vanishes if either one is absent. The electric and spin Hall conductances are suppressed in strong disorder, but survive in weak disorder. Physically it can be understood that the spinomotive transverse "force" generated by spin-orbit coupling is responsible for the formation of the spin Hall current and the lack of transverse reflection symmetry is the origin of the electric Hall current.

Spin Currents and Intrinsic Spin-Hall Effect in Low Dimensional Systems

We consider the spin-Hall effect in two-dimensional electron systems (2DES) with Rashba and Dresselhaus spin-orbit couplings (SO). We find nonzero diagonal spin conductivity provided that Dresselhaus coupling is finite. In addition we consider the influence of disorder on spin conductivities in these systems. By comparing with the exact diagonalization method the finite quasiparticle lifetime (Born) approximation we argue that the latter one seems to be sufficient to describe the case when spin-orbit coupling is stronger or comparable with disorder strength. Furthermore, in the framework of Landauer–Buttiker formalism we show that the transverse and diagonal spin conductivities in Rashba plus Dresselhaus SO systems are robust against disorder for finite size systems.

Manifestation of the spin Hall effect through charge-transport in the mesoscopic regime

We study theoretically the manifestation of the spin Hall effect in a two-dimensional electronic system with Rashba spin-orbit coupling via dc-transport measurements in realistic mesoscopic H-shape structures. The Landauer-Buttiker formalism is used to model samples with mobilities and Rashba coupling strengths of current experiments and to demonstrate the appearance of a measurable Rashba-coupling dependent voltage. This type of measurement requires only metal contacts, i.e., no magnetic elements are present. We also confirm the robustness of the intrinsic spin Hall effect against disorder in the mesoscopic metallic regime in agreement with results of exact diagonalization studies in the bulk.

Thermoelectric transport properties in atomic scale conductors

The thermoelectric transport properties in atomic scale conductors consisting of a Si atom connected by two electrodes are investigated. It is found that both the electrical current and the heat current have two contributions, one from the voltage and the other from the temperature gradient. The quantities such as the Seebeck thermopower and the thermal conductance that characterize the thermoelectric transport properties of the tunnel atomic junction are studied quantitatively with a first-principles technique within the framework of Landauer-Buttiker formalism in the linear response regime. A finite thermopower only exists in a very narrow range where the energy derivative of the transmission function is nonzero. The thermopower anomaly is observed in the tunneling regime in this device but this does not violate the thermodynamic law with respect to the heat current.

Theoretical study of electrical transport in a fullerene-doped semiconducting carbon nanotubes

Using a tight-binding model and the Landauer–Büttiker formalism, we have calculated the current–voltage characteristics of a semiconducting single-walled carbon nanotube and that of a fullerene (C60)-doped carbon nanotube (peapod) structure. Our calculation shows that fullerene encapsulation in a semiconducting nanotube enhances the electrical conductivity of the nanotube, which is consistent with recent experimental measurements. We explain the increased electronic conduction in the semiconducting nanopeapod structure by analyzing the density of states of both pristine and C60-doped nanotubes. A first-principles density functional calculation shows a significant amount of charge transfer (0.62e−) from the nanotube to C60, suggesting that holes are the primary charge carriers in the peapod.

Suppression of Quantum Decoherence in an Aharonov–Bohm Ring

Quantum coherence is one of the most important topics in fundamental physics. In mesoscopic systems, decoherence has often been studied using Aharonov-Bohm (AB) interferometers, and in such a coherent transport, it is well known that probes of a sample play an essential role and transport property has been successfully described by the Landauer-Buttiker (LB) formalism. Here we present evidence that the quantum coherence itself is also affected by the probe configuration.

The Rashba Effect Within the Coherent Scattering Formalism with Applications to Electron Quantum Optics

The influence of spin–orbit coupling in electron quantum optics experiments is investigated within the framework of the Landauer–Buttiker coherent scattering formalism. We begin with a brief review of our electron quantum optics toolbox: an electron intensity interferometer (Hanbury Brown and Twiss-type experiment), an electron collision analyzer (Hong–Ou–Mandel-type experiment), and a proposed Bell state analyzer. These experiments are performed or proposed in two-dimensional electron gas systems and, therefore, may be influenced by the Rashba spin–orbit coupling. To quantify this effect, we define the creation/annihilation operators for the stationary states of the Rashba spin–orbit coupling Hamiltonian and use them to derive the current operator within the Landauer–Buttiker formalism. The current is expressed as it is in the standard spin-independent case, but with the spin label replaced by a new label that we call the spin–orbit coupling label. The spin–orbit coupling effects can then be represented in a scattering matrix that relates the spin–orbit coupling stationary states in different leads. We apply this new formalism to the case of a four-port beamsplitter, and it is shown to mix states with different spin–orbit coupling labels in a manner that depends on the angle between the leads. A noise measurement after the collision of spin-polarized electrons at an electron beamsplitter provides a new experimental means to measure the Rashba parameter α. It is also shown that the degree of electron bunching in an entangled-electron collision experiment is reduced by the spin–orbit coupling according the beamsplitter lead angle.

Temperature dependence of conductance of electrostatically disordered quasi-2D semiconductor systems near an insulator-metal percolation transition

The experimental temperature dependence (4.2–300 K) of the conductance of mesoscopic quasi-2D electronic systems under conditions of the insulator-metal percolation transition are discussed for the case of metal-nitride-oxide-semiconductor silicon transistor structures with an inversion n channel and an extremely high (≥1013 cm−2) built-in charge density (source of electrostatic fluctuation potential). Saddle domains of the fluctuation potential are analyzed within the framework of the Landauer-Buttiker formalism. These domains, being point quantum contacts between wells in the chaotic potential distribution, determine both the nature of electron transport and the conditions of the insulator-metal transitions. The results of analyzing the dependence of the conductivity on temperature and field (on the gate voltage) are shown to be consistent. The shape of the effective potential barrier for the electron tunneling transport across the saddle domains is reconstructed.

Transport in quantum dots from the integrability of the Anderson model

In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a Landauer-Buttiker formalism. Although we use integrability, the nature of the problem is such that our results are not generically exact, but must only be considered as excellent approximations which nonetheless are valid all the way through crossover regimes. The key to our approach is to identify the excitations that correspond to scattering states and then to compute their associated scattering amplitudes. We are able to do so both in and out of equilibrium. In equilibrium and at zero temperature, we reproduce the Friedel sum rule for an arbitrary magnetic field. At finite temperature, we study the linear response conductance at the symmetric point of the Anderson model, and reproduce Costi et al.'s numerical renormalization group computation of this quantity. We then explore the out-of-equilibrium conductance for a near-symmetric Anderson model, and arrive at quantitative expressions for the differential conductance, both in and out of a magnetic field. We find the expected splitting of the differential conductance peak into two in a finite magnetic field, $H$. We determine the width, height, and position of these peaks. In particular we find for H >> T_k, the Kondo temperature, the differential conductance has maxima of e^2/h occuring for a bias V close to but smaller than H. The nature of our construction of scattering states suggests that our results for the differential magneto-conductance are not merely approximate but become exact in the large field limit.

Study of Noise Properties in Nanoscale Electronic Devices Using Quantum Trajectories

Noise properties in nanoscale devices are studied extending, via quantum trajectories, the classical particle Monte Carlo techniques to devices in which quantum non-local effects are important. This approach can be used to study noise in a wide range of frequencies and can also be easily coupled to a Poisson solver to study long range Coulomb effects in noise characteristics. As a numerical example, we have studied noise in a tunneling barrier showing that the results obtained within our approach exactly reproduce those of the standard Landauer-Buttiker formalism in the zero frequency limit.

Conductance of quasi-two-dimensional semiconductor systems with electrostatic disorder in the region of the percolation metal-insulator transition

Special features of the percolation transition in quasi-two-dimensional (quasi-2D) electron systems (metal-nitride-oxide-semiconductor structures with n-type inversion channels) with a strong fluctuation potential (FP) and a gate length smaller than the correlation radius of a percolation cluster (in which case the structure conductance is controlled by isolated saddle-point regions of the FP) are considered. Experimentally measured dependences of the conductance on the field-electrode potential and the temperature are analyzed in the context of the Landauer-Buttiker formalism. Energy parameters of the FP saddle-point regions and effective density of electron states (NSS ∝ m/πℏ2) near the percolation level are determined from the experimental data. Consistency between the experimental results and the proposed statistical model of the formation of FP saddle-point regions in quasi-2D systems is demonstrated. It is shown that saddles transform into potential troughs extended in the direction of the percolation route as the percolation trough is approached.