Nonequilibrium Green Function Calculations Research Articles

CALCULATION OF ELECTRICAL SWITCHING AND MAGNETORESISTIVE PROPERTIES OF MOLECULAR TUNNEL JUNCTIONS

Switching properties of metal/polymer/metal junctions is studied under application of twist using a combination of the tight-binding and nonequilibrium Green function calculations. The junction is taken to be composed of a short chain of cis-polyacetylene sandwiched between two ferromagnetic electrodes. It is shown that the current flow across the polymer can effectively be controlled by torsion applied through rotating the the electrodes about the junction's axis. It is found out that twisting the polymer leads to widening of its HUMO–LOMO energy gap which, in consequence, hinders the electron tunneling. The ferromagnetic electrodes are assumed to be single-band and their tight-binding parameters are chosen so as to simulate the ab initio density functional calculations of the band structure of Fe along its [001] crystallographic direction. According to our calculations it is also possible to adjust tunneling magnetoresistance of the junction by applying specific amounts of torsion.

The non-equilibrium Green function approach to inhomogeneous quantum many-body systems using the generalized Kadanoff–Baym ansatz

In the non-equilibrium Green function calculations, the use of the generalized Kadanoff–Baym ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green function from its time-diagonal value. With this, a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present the results for a two-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for a correct description of the equilibrium and dynamic properties.

Nonmonotonic inelastic tunneling spectra due to surface spin excitations in ferromagnetic junctions

The paper addresses inelastic spin-flip tunneling accompanied by surface spin excitations (magnons) in ferromagnetic junctions. The inelastic tunneling current is proportional to the magnon density of states which is energy-independent for the surface waves and, for this reason, cannot account for the bias-voltage dependence of the observed inelastic tunneling spectra. This paper shows that the bias-voltage dependence of the tunneling spectra can arise from the tunneling matrix elements of the electron-magnon interaction. These matrix elements are derived from the Coulomb exchange interaction using the itinerant-electron model of magnon-assisted tunneling. The results for the inelastic tunneling spectra, based on the nonequilibrium Green's function calculations, are presented for both parallel and antiparallel magnetizations in the ferromagnetic leads.

Assessment of approximations in nonequilibrium Green’s function theory

A nonequilibrium Green's function (NEGF) method for stationary carrier dynamics in open semiconductor nanodevices is presented that includes all relevant incoherent scattering mechanisms. A consistent lead model is developed that ensures all observables to reflect intrinsic device properties. By restricting the charge self-consistent calculations to vertical transport through heterostructures, the Green's functions and self-energies can be determined very accurately. This allows us to assess many commonly used approximations, such as ballistic leads, decoupling of Dyson's and Keldysh's equations, truncated or momentum-averaged self-energies, and local self-energies in the NEGF formalism in detail, and to study limiting cases such as diffusive transport in resistors. The comparison of exact and approximated NEGF calculations illustrates the physical implications and validity of common approximations and suggests numerically efficient simplifications.

The role of transition metal interfaces on the electronic transport in lithium–air batteries

Low electronic conduction is expected to be a main limiting factor in the performance of reversible lithium–air, Li–O 2, batteries. Here, we apply density functional theory and non-equilibrium Green's function calculations to determine the electronic transport through lithium peroxide, Li 2O 2, formed at the cathode during battery discharge. We find the transport to depend on the orientation and lattice matching of the insulator–metal interface in the presence of Au and Pt catalysts. Bulk lithium vacancies are found to be available and mobile under battery charging conditions, and found to pin the Fermi level at the top of the anti bonding peroxide π*(2p x ) and π*(2p y ) levels in the Li 2O 2 valence band. Under an applied bias, this can result in a reduced transmission, since the anti bonding σ*(2p z ) level in the Li 2O 2 conduction band is found to couple strongly to the metal substrate and create localized interface states with poor coupling to the Li 2O 2 bulk states. These observations provide a possible explanation for the higher overpotential observed for charging than discharge.

Density functional theory based many-body analysis of electron transport through molecules

We present a method which uses density functional theory (DFT) to treat transport through a single molecule connected to two conducting leads for the weak and intermediate coupling. This case is not accessible to standard nonequilibrium Green's function calculations. Our method is based on a mapping of the Hamiltonian on the molecule to a limited set of many-body eigenstates. This generates a many-body Hamiltonian with parameters obtained from ground-state local (spin) density approximation-DFT calculations. We then calculate the transport using many-body Green's function theory. We compare our results with existing density matrix renormalization group calculations for spinless and for spin-1/2 fermion chains and find good agreement.

Ferromagnetically Coupled Cobalt−Benzene−Cobalt: The Smallest Molecular Spin Filter with Unprecedented Spin Injection Coefficient

Here, we predict that the ferromagnetically coupled cobalt-benzene-cobalt system will act as the smallest molecular spin filter with unprecedented spin injection coefficient. To validate our in-silico observation, we have performed state-of-the-art nonequilibrium Green's function calculations and analyzed the density of states of cobalt at the relativistic and nonrelativistic level of theory. Remarkably, we found that unpaired 3d electrons of cobalt are not participating in the spin transport process like other transition metal containing multidecker complexes. Instead, an admixture of the outer-sphere 4s and 4p orbitals of cobalt along with the 2p orbital of carbon of the benzene moiety is contributing to the singly occupied highest molecular orbital in the majority spin channel that creates a path for coherent spin transport leading to the extremely high spin injection coefficient of the system. The absence of the 3d electrons of cobalt in the spin transport process has been carefully examined, and it was found that the nodal structure of the 3d orbital of cobalt is not at all suitable for bonding in the cobalt-benzene-cobalt system. The whole study indicates that the underlying mechanism of the spin filter action in cobalt-benzene-cobalt is completely distinctive from the other known materials.

A DFT study on molecular junction devices with cyclic disulfide anchors: Effect of anchor oxidation on electron transport

AbstractA molecular‐scale electronic device can be built with programmable molecular switches sandwiched between two electrodes. A cyclic disulfide, 1,2‐dithiolane, is a promising anchor group for attaching molecules to gold electrodes in such molecular junction devices, since its dithiol–Au linkage (with the disulfide bond broken) can provide added stabilities and reduced current fluctuations. However, operations of the molecular switches under redox conditions might lead to redox processes involving the AuS bonds at the contact. Formation of the disulfide linkage can be induced, and the dithiolate group (AuS) can be converted into disulfoxide (AuSO) or disulfone (AuSO2) groups. Coexistence of these various oxidation states at the contact or the conversion between them can be a potential source of current fluctuation in the junction. However, our nonequilibrium Green's function calculations combined with the density functional theory show that the molecular junctions with different oxidation states of the 1,2‐dithiolane alligator clips to two gold electrodes exhibit essentially the same insulating current–voltage characteristics at moderate bias voltages. Therefore, the robustness of the molecular junctions would not be affected by the state change of the disulfide alligator clips at the contact. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

A Self-Consistent SDD-NEGF Approach for Modelling Magnetic Tunnel Junctions

Most contemporary work on magnetic tunnel junctions either consider ballistic quantum transport across the tunneling barrer, for instance via the Non Equilibrium Green's Function (NEGF) formalism, or treat the tunneling region as a lump resistance connected to bulk metallic leads in the Spin Drift-Diffusion (SDD) approach. The effects of interfacial barriers and central device physics on the spin accumlation in the leads have largely been ignored in most NEGF calculations. In this work we introduce a self consistent approach that combines the NEGF and SDD methods. We calculate the effects of the barrier potential height and spin orbit interaction on the spin injection from a ferromagnet to a semiconductor through the barrier.

Atomic-Scale Control of Electron Transport through Single Molecules

Tin-phthalocyanine molecules adsorbed on Ag(111) were contacted with the tip of a cryogenic scanning tunneling microscope. Orders-of-magnitude variations of the single-molecule junction conductance were achieved by controllably dehydrogenating the molecule and by modifying the atomic structure of the surface electrode. Nonequilibrium Green's function calculations reproduce the trend of the conductance and visualize the current flow through the junction, which is guided through molecule-electrode chemical bonds.

Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models

In this contribution, we discuss the finite-element discrete variable representation (FE-DVR) of the nonequilibrium Green's function and its implications on the description of strongly inhomogeneous quantum systems. In detail, we show that the complementary features of FEs and the DVR allow for a notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym equations compared to a general basis approach. Particularly, the use of the FE-DVR leads to an essential speedup in computing the self-energies.As atomic and molecular examples we consider the He atom and the linear version of H+3 in one spatial dimension. For these closed-shell models we, in Hartree-Fock and second Born approximation, compute the ground-state properties and compare with the exact findings obtained from the solution of the few-particle time-dependent Schrödinger equation.

Prediction of giant intrinsic spin-Hall effect in strained p-GaAs quantum wells

We perform spin resolved non-equilibrium Green's function calculations in nanostructured, strained two-dimensional GaAs electron and hole gases. Inelastic scattering is taken into account. We show theoretically that the intrinsic inverse spin-Hall effect provides a simple, sensitive, and purely electrical scheme to measure the spin polarization in nanostructures. We predict large spin polarizations and spin-Hall voltages for several concrete device geometries. We propose tensile strained p-GaAs as being optimally suited for detecting the inverse spin Hall effect and show that the effect is absent in n-GaAs.

Ballistic calculation of nonequilibrium Green's function in nanoscale devices using finite element method

A ballistic calculation of a full quantum mechanical system is presented to study 2D nanoscale devices. The simulation uses the nonequilibrium Green's function (NEGF) approach to calculate the transport properties of the devices. While most available software uses the finite difference discretization technique, our work opts to formulate the NEGF calculation using the finite element method (FEM). In calculating a ballistic device, the FEM gives some advantages. In the FEM, the floating boundary condition for ballistic devices is satisfied naturally. This paper gives a detailed finite element formulation of the NEGF calculation applied to a double-gate MOSFET device with a channel length of 10 nm and a body thickness of 3 nm. The potential, electron density, Fermi functions integrated over the transverse energy, local density of states and the transmission coefficient of the device have been studied. We found that the transmission coefficient is significantly affected by the top of the barrier between the source and the channel, which in turn depends on the gate control. This supports the claim that ballistic devices can be modelled by the transport properties at the top of the barrier. Hence, the full quantum mechanical calculation presented here confirms the theory of ballistic transport in nanoscale devices.

Hyperfine switching triggered by resonant tunneling for the detection of a single nuclear spin qubit

A novel detection mechanism and a robust control of a single nuclear spin-flip by hyperfine interactions between the nuclear spin and tunneling electron spin are proposed on the basis of ab initio non-equilibrium Green's function calculations. The calculated relaxation times of the nuclear spin of proton in a nano-contact system, Pd(electrode)–H 2–Pd(electrode), show that ON/OFF switching of hyperfine interactions is effectively triggered by resonant tunneling mediated through the d-orbitals of Pd. The relaxation times at ON-resonance are ∼ 10 3 times faster than those at OFF-resonance, indicating that ON-resonance is suitable for the detection (read-out) of nuclear spin states. In addition, the effectiveness of bias voltage applications at OFF-resonance for selective operations on the proton qubit is demonstrated in the calculations of the resonant frequencies of proton using the gauge-invariant atomic orbital method.

Hyperfine switching triggered by resonant tunneling for the detection of a single nuclear spin qubit

Abstract A novel detection mechanism and a robust control of a single nuclear spin-flip by hyperfine interactions between the nuclear spin and tunneling electron spin are proposed on the basis of ab initio non-equilibrium Green's function calculations. The calculated relaxation times of the nuclear spin of proton in a nano-contact system, Pd(electrode)–H2–Pd(electrode), show that ON/OFF switching of hyperfine interactions is effectively triggered by resonant tunneling mediated through the d-orbitals of Pd. The relaxation times at ON-resonance are ∼ 10 3 times faster than those at OFF-resonance, indicating that ON-resonance is suitable for the detection (read-out) of nuclear spin states. In addition, the effectiveness of bias voltage applications at OFF-resonance for selective operations on the proton qubit is demonstrated in the calculations of the resonant frequencies of proton using the gauge-invariant atomic orbital method.

Quantum thermal transport in nanostructures

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.

Transmission eigenchannels from nonequilibrium Green’s functions

The concept of transmission eigenchannels is described in a tight-binding nonequilibrium Green's function (NEGF) framework. A simple procedure for calculating the eigenchannels is derived using only the properties of the device subspace and quantities normally available in a NEGF calculation. The method is exemplified by visualization in real space of the eigenchannels for three different molecular and atomic wires.

The effect of reciprocal-space sampling and basis set quality on the calculated conductance of a molecular junction

We perform density functional theory and non-equilibrium Green's function calculations of the conductance of a gold wire and a 1,4-phenylenedimethanethiol (XYL) molecule adsorbed between Au(111) electrodes using the TranSIESTA software package. The effect of varying different computational parameters is investigated. We find that the conductance is more sensitive to the reciprocal-space sampling grid than the quality of the basis set employed. The conductance can vary up to a factor of five as a result of the choice of computational parameters. We report a set of computational parameters that yields a well-converged conductance value.

Computational Design of a Rectifying Diode Made by Interconnecting Carbon Nanotubes with Peptide Linkages

With the use of first-principles total energy calculations, the optimized geometrical structures of seven different junctions constructed from different carbon nanotube units (metallic and semiconducting) and different covalent linkages (peptide bonds, −CONH−C6H4−CONH−, and >CON−C6H4−CON<) are investigated. By performing a set of nonequilibrium Green's function calculations combined with density functional theory, the I−V characteristics of some of the designer junctions are obtained. The results show that the junction made of two different types of carbon nanotube units (metallic and semiconducting) acts as a rectifying diode. On the other hand, the junctions made of carbon nanotube units with the same chirality (zigzag or armchair) show almost symmetric I−V curves under positive and negative applied voltages. Our results are expected to contribute in the design and implementation of various electronic logic functions based on carbon nanotubes for applications in the field of nanoelectronics.

Understanding Coulomb Effects in Nanoscale Schottky-Barrier-FETs

We employ a novel multiconfigurational self-consistent Green's function approach (MCSCG) for the simulation of nanoscale Schottky-barrier-field-effect transistors (SB-FETs). This approach allows the calculation of electronic transport with a seamless transition from the single-electron regime to room-temperature FET operation. The particular improvement of the MCSCG stems from a self-consistent division of the channel system into a small subsystem of resonantly trapped states for which a many-body Fock space approach becomes numerically feasible and the rest of the system which can be treated adequately on a conventional mean-field level. The Fock space description allows for the calculation of few-electron Coulomb charging effects beyond the mean-field. We compare a conventional Hartree nonequilibrium Green's function calculation with the results of the MCSCG approach. Using the MCSCG method, Coulomb blockade effects are demonstrated at low temperatures while, under strong nonequilibrium and high-temperature conditions, the Hartree approximation is retained. Finally, the visibility of quantum and single-electron effects in scaled transistor structures is discussed