Transport Formalism Research Articles

Efficient quantum transport simulation for bulk graphene heterojunctions

The quantum transport formalism based on tight-binding models is known to be powerful in dealing with a wide range of open physical systems subject to external driving forces but is, at the same time, limited by the memory requirement's increasing with the number of atomic sites in the scattering region. Here we demonstrate how to achieve an accurate simulation of quantum transport feasible for experimentally sized bulk graphene heterojunctions at a strongly reduced computational cost. Without free tuning parameters, we show excellent agreement with a recent experiment on Klein backscattering [A. F. Young and P. Kim, Nature Phys. 5, 222 (2009)].

Fano-Kondo oscillations of the conductance and thermopower in a mesoscopic transistor

We study the conductance G and Seebeck coefficient S of a side-coupled double quantum dot system. The transport properties are the result of the competition between the Fano interference and Kondo correlations, being also controlled by the Coulomb blockade of the multilevel side-dot. The external parameters are the gate potential Vg applied on the side-dot and the temperature. When Vg is varied continuously the blockade is switched on and off periodically, resulting in oscillations of the transport coefficients. The profile of the oscillations and the temperature dependence are studied. An extended Anderson model and the Keldysh transport formalism are used.

Electronic, vibrational, and transport properties of pnictogen-substituted ternary skutterudites

First principles calculations are used to investigate electronic band structure and vibrational spectra of pnictogen-substituted ternary skutterudites. We compare the results with the prototypical binary composition CoSb${}_{3}$ to identify the effects of substitutions on the Sb site, and evaluate the potential of ternary skutterudites for thermoelectric applications. Electronic transport coefficients are computed within the Boltzmann transport formalism assuming a constant relaxation time, using a methodology based on maximally localized Wannier function interpolation. Our results point to a large sensitivity of the electronic transport coefficients to carrier concentration and to scattering mechanisms associated with the enhanced polarity. The ionic character of the bonds is used to explain the detrimental effect on the thermoelectric properties.

Low‐temperature spin transport in the S = 1 one‐ and two‐dimensional antiferromagnets with Dzyaloshinskii–Moriya interaction

AbstractWe present a study of the spin transport at low‐temperature in the quantum S = 1 one‐ and two‐dimensional Heisenberg antiferromagnet with the Dzyaloshinskii–Moriya interaction (DM). The spin conductivity is calculated using the Schwinger boson representation and the Kubo formalism of transport in the one‐dimensional case and using the self‐consistent harmonic approximation and the Kubo formalism in the two‐dimensional case. The objective is to determine the regular part of the spin conductivity and the Drude weight DS. This determines if the spin transport has a ballistic or diffusive character. We calculate the regular part of the spin conductivity, σreg(ω), as function of the frequency at T = 0 only and the Drude weight at zero and finite temperatures. We obtained that the spin transport is governed by the multimagnon processes in all cases analyzed since the symmetry of the isotropic Heisenberg antiferromagnetic model is broken with the addition of the DM term.

Effects of chemical functionalization on electronic transport in carbon nanobuds

Carbon nanobuds form a class of hybrid structures consisting of carbon nanotubes onto which fullerene types of units are covalently grown. Due to higher electrophilicity and curvature of the fullerene moiety a carbon nanobud exhibits higher reactivity compared to a plain nanotube. In this paper we study how the electronic structure and transport properties of carbon nanobuds are affected by chemical modification. The studied model systems comprise carbon nanobuds that are chemically modified by attaching Li and F atoms as well as tetrathiafulvalene molecules. We use the density functional theory combined with Landauer-B\"uttiker electron transport formalism. According to the simulations, the attached units change the relative positions of the Fermi levels, creating a distinctive effect on the electronic transport properties along associated carbon nanotubes. In semiconducting nanotubes the change in the conductance is systematic and should be detectable in experiments. Hence, the carbon nanobuds are potential candidates for sensor applications.

Zero bias anomalies in the Kondo regime of single and double quantum dots

The zero bias anomaly of the differential conductance of mesoscopic systems is a fingerprint of the electron-electron interaction. The common example is the peak of the differential conductance in Kondo mesoscopic systems.We show that in complex mesoscopic systems, in particular in the side-coupled double dot, the dip of the differential conductance at zero bias is also possible due to simultaneous effects of interference and correlations. The external parameters that control this effect are the temperature and the gate potential on the lateral dot. We argue that even in single dots, in a multiple lead configuration, the shift from suppression to enhancement of dI/dV with increasing bias is allowed if the bias applied on the leads is not symmetric. The differential conductance exhibits a peak-dip crossover, the effect being controlled by the strength of the asymmetry and the ratio of the dot-lead couplings.The scaling of the differential conductance for the double-dot system is also discussed. The results are obtained using an extended Anderson model, the Keldysh transport formalism and the equation of motion technique extended to the non-equilibrium.

Numerical study of the thermoelectric power factor in ultra-thin Si nanowires

Low dimensional structures have demonstrated improved thermoelectric (TE) performance because of a drastic reduction in their thermal conductivity, κ l . This has been observed for a variety of materials, even for traditionally poor thermoelectrics such as silicon. Other than the reduction in κ l , further improvements in the TE figure of merit ZT could potentially originate from the thermoelectric power factor. In this work, we couple the ballistic (Landauer) and diffusive linearized Boltzmann electron transport theory to the atomistic sp3d5s*-spin-orbit-coupled tight-binding (TB) electronic structure model. We calculate the room temperature electrical conductivity, Seebeck coefficient, and power factor of narrow 1D Si nanowires (NWs). We describe the numerical formulation of coupling TB to those transport formalisms, the approximations involved, and explain the differences in the conclusions obtained from each model. We investigate the effects of cross section size, transport orientation and confinement orientation, and the influence of the different scattering mechanisms. We show that such methodology can provide robust results for structures including thousands of atoms in the simulation domain and extending to length scales beyond 10 nm, and point towards insightful design directions using the length scale and geometry as a design degree of freedom. We find that the effect of low dimensionality on the thermoelectric power factor of Si NWs can be observed at diameters below ∼7 nm, and that quantum confinement and different transport orientations offer the possibility for power factor optimization.

Noise calculations within the second-order von Neumann approach

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher-order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches.

Atomistic simulations of low-field mobility in Si nanowires: Influence of confinement and orientation

A simulation framework that couples atomistic electronic structures to Boltzmann transport formalism is developed and applied to calculate the transport characteristics of thin silicon nanowires (NWs) up to 12 nm in diameter. The sp${}^{3}$d${}^{5}$s${}^{*}$-spin-orbit-coupled atomistic tight-binding model is used for the electronic structure calculation. Linearized Boltzmann transport theory is applied, including carrier scattering by phonons, surface roughness (SRS), and impurities. We present a comprehensive investigation of the low-field mobility in silicon NWs considering i) $n$- and $p$-type NWs, ii) [100], [110], and [111] transport orientations, and iii) diameters from $D$ = 12 nm (electronically almost bulk-like) down to $D$ = 3 nm (ultra-scaled). The simulation results display strong variations in the characteristics of the different NW types. For $n$-type NWs, phonon scattering and SRS become stronger as the diameter is reduced and drastically degrade the mobility by up to an order of magnitude depending on the orientation. For the [111] and [110] $p$-type NWs, on the other hand, large mobility enhancements (on the order of \ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}) can be achieved as the diameter scales down to $D$ = 3 nm. This enhancement originates from the increase in the subband curvatures as the diameter is scaled. It overcompensates for the mobility reduction caused by SRS in narrow NWs and offers an advantage with diameter scaling. Our results may provide understanding of recent experimental measurements, as well as guidance in the design of NW channel devices with improved transport properties.

Spin and charge transport in U-shaped one-dimensional channels with spin-orbit couplings

A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian to a tight-binding version, the Landauer--Keldysh formalism (LKF) for nonequilibrium transport can be applied. Spin transport through the U-channel based on the LKF is compared with previous quantum mechanical approaches. The role of a curvature-induced geometric potential which was previously neglected in the literature of the ring issue is also revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is discussed. Based on the LKF, interesting charge and spin transport properties are further revealed. For the charge transport, the interplay between the Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation to the local charge density in the half-ring part of the U-channel, which is shown to originate from the angle-dependent spin-orbit potential. For the spin transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus rings, and the persistent spin-helix state are numerically tested by the present quantum transport calculation.

Comment on “Critical analysis of a variational method used to describe molecular electron transport”

B\^aldea and K\"oppel [Phys. Rev. B 80, 165301 (2009)] have generalized our correlated transport formalism [P. Delaney and J. C. Greer, Phys. Rev. Lett. 93, 036805 (2004)] to constrain the occupancies of single-electron orbitals, and then claimed that zero conductivity $G=0$ in linear response follows and that our method is invalid. We show here that it was their incorrect choice to constrain the occupancies of real orbitals that resulted in $G=0$. In a scattering state incident to a barrier with values at $\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ differing by $\mathit{eV}$, only the incoming plane wave component has the bias-independent amplitude of 1, while the outgoing has $r$ which depends on the voltage $V$ and the barrier geometry. Thus, if occupancies are to be constrained to bias-independent values in transport, those of complex orbitals such as an incoming plane wave on each side are suitable, while real orbitals such as sines are not. This is true whether constant current constraints are additionally imposed or not.

Sedimentation of nanoparticles in nanoscale colloidal suspensions

A theoretical model is developed to study the sedimentation characteristics of nanoscale colloidal suspensions (nanofluids). The influences of various deterministic and stochastic forcing parameters in the transport characteristics of the suspended nanoparticles are investigated by employing a Langevin formalism of particle transport. The role of collective particle interaction phenomena in the sedimentation of nanoparticles is analyzed by invoking the fundamental considerations of agglomeration–deagglomeration kinetics of the particulate phases. The model demonstrates the effect of particle volume fraction, particle size, and aggregate structure on the sedimentation velocity of the suspended nanoparticles. Predictions from the present model agree well with the experimental results reported in the literature.

Transient Energy and Heat Transport in Metals: Effect of the Discrete Character of the Lattice

A recently developed Shastry’s formalism for energy transport is used to analyze the temporal and spatial behaviors of the electron energy and heat transport in metals under delta function excitation at the surface. Comparison with Cattaneo’s model is performed. Both models show the transition between nonthermal (ballistic) and thermal (ballistic-diffusive) regimes. Furthermore, because the new model considers the discrete character of the lattice, it highlights some new phenomena, such as damped oscillations, in the energy transport both in time and in space. The energy relaxation of the conduction band electrons in metals is considered to be governed by the electron-phonon scattering, and the scattering time is taken to be averaged over the Fermi surface. Using the new formalism, one can quantify the transfer from nonthermal modes to thermal ones as energy propagates in the material and it is transformed into heat. While the thermal contribution shows a wave-front and an almost exponentially decaying behavior with time, the nonthermal part shows a wave-front and a damped oscillating behavior. Two superimposed oscillations are identified, a fast oscillation that is attributed to the nonthermal nature of energy transport at very short time scales and a slow oscillation that describes the nature of the transition from the nonthermal regime to the thermal regime of energy transport.

Signatures of Wigner localization in epitaxially grown nanowires

It was predicted by Wigner in 1934 that the electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made towards the detection of electronic Wigner states, their clear and direct experimental verification still remains a challenge. Here we address signatures of Wigner molecule formation in the transport properties of InSb nanowire quantum dot systems, where a few electrons may form localized states depending on the size of the dot (i.e. the electron density). By a configuration interaction approach combined with an appropriate transport formalism, we are able to predict the transport properties of these systems, in excellent agreement with experimental data. We identify specific signatures of Wigner state formation, such as the strong suppression of the antiferromagnetic coupling, and are able to detect the onset of Wigner localization, both experimentally and theoretically, by studying different dot sizes.

Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit

We extend the input-output formalism of quantum optics to analyze few-photon transport in waveguides with an embedded qubit. We provide explicit analytical derivations for one and two-photon scattering matrix elements based on operator equations in the Heisenberg picture.

Effects of edge chemistry doping on graphene nanoribbon mobility

Doping of semiconductor is necessary for various device applications. Exploiting chemistry at its reactive edges was shown to be an effective way to dope an atomically thin graphene nanoribbon (GNR) for realizing new devices in recent experiments. The carrier mobility limited by edge doping is studied as a function of the GNR width, doping density, and carrier density by using ab initio density functional and parameterized tight binding simulations combined with the non-equilibrium Green's function formalism for quantum transport. The results indicate that for GNRs wider than about 4 nm, the mobility scales approximately linearly with the GNR width, inversely proportional to the edge doping concentration and decreases for an increasing carrier density. For narrower GNRs, dependence of the mobility on the GNR width and carrier density can be qualitatively different.

Low-temperature transport properties of TaxN thin films (0.72 ⩽ x ⩽ 0.83)

We report on low-temperature (4–320 K) transport properties of TaxN thin films deposited on an amorphous SiO2 substrate. In this work, TaxN thin films were restricted to a narrow range of x: 0.72 ⩽ x ⩽ 0.83 yet show considerable and nonmonotonic variation of their transport properties with Ta concentration. This behaviour is consistent with a local minimum in the density of electronic states at the Fermi level, as calculated for the rock salt intermetallic Ta4N5, and a rigid band model for describing the transport. The temperature dependence of the resistivity is best fit to the unusual form exp(−T/T0). Interestingly enough, the fit parameter T0 correlates well with the temperature of the maximum of the corresponding thermopower. Both of these characteristics, the fit and the correlation with the thermopower, are consistent with the Jonson–Mahan many-body formalism for charge and thermal transport when one has a nontrivial temperature dependence of the chemical potential. At the lowest temperatures measured, we have also found that the resistivity and thermopower show signatures of electron–electron interactions. We discuss also our results in the light of some theories usually used for describing transport of thin films and to other experimental investigations that have been performed on TaxN.

Ballistic spin-dependent transport of Rashba rings with multi-leads

Using the Landauer–Büttiker formula with the transfer matrix technique, we develop a formalism of the ballistic spin-dependent electron transport in the multi-lead Rashba rings. We give analytic formulas of the total conductance G j , spin- σ conductance g j σ and spin polarization P j of each outgoing lead j, and their resonant and antiresonant conditions. Analytic studying with numerical investigating Rashba rings with several symmetric and asymmetric leads, we find that G j , g j σ and P j oscillate with the incoming electron energy and the spin–orbit interaction (SOI) strength, and their antiresonances depend on the incoming electron energy, the SOI strength and the outgoing-lead angle with the incoming lead. For the symmetric-lead rings, G j , g j σ and P j have some symmetries, G j = G N - j , g j σ = g N - j - σ , and P j = − P N− j for symmetric leads, j and N − j, where the angles between the symmetric outgoing leads j and N − j and the incoming lead are γ N− j = 2 π − γ j . The spin polarization of the outgoing lead with γ j = π is exactly zero for even- N-symmetric-lead rings. These symmetries originate from the lead symmetry and time reversal invariance. For asymmetry-lead rings these symmetries vanish.

Coupling optical and electrical gating for electronic readout of quantum dot dynamics

We explore the coherent transfer of electronic signatures from a strongly correlated, optically gated nanoscale quantum dot to a weakly interacting, electrically backgated microscale channel. In this unique side-coupled ``$T$'' geometry for transport, we predict a mechanism for detecting Rabi oscillations induced in the dot through quantum, rather than electrostatic means. This detection shows up directly in the dc conductance-voltage spectrum as a field-tunable split in the Fano lineshape arising due to interference between the dipole coupled dot states and the channel continuum. The split is further modified by the Coulomb interactions within the dot that influence the detuning of the Rabi oscillations. Furthermore, time resolving the signal we see clear beats when the Rabi frequencies approach the intrinsic Bohr frequencies in the dot. Capturing these coupled dynamics requires attention to memory effects and quantum interference in the channel as well as many-body effects in the dot. We accomplish this coupling by combining a Fock-space master equation for the dot dynamics with the phase-coherent, non-Markovian time-dependent nonequilibrium Green's function transport formalism in the channel through a properly evaluated self-energy and a Coulomb integral. The strength of the interactions can further be modulated using a backgate that controls the degree of hybridization and charge polarization at the transistor surface.

A deterministic computational procedure for space environment electron transport

A deterministic computational procedure for describing the transport of electrons in condensed media is formulated to simulate the effects and exposures from spectral distributions typical of electrons trapped in planetary magnetic fields. The primary purpose for developing the procedure is to provide a means of rapidly performing numerous repetitive transport calculations essential for electron radiation exposure assessments for complex space structures. The present code utilizes well-established theoretical representations to describe the relevant interactions and transport processes. A combined mean free path and average trajectory approach is used in the transport formalism. For typical space environment spectra, several favorable comparisons with Monte Carlo calculations are made which have indicated that accuracy is not compromised at the expense of the computational speed.