We present a Green's function technique for studying the nonlinear conductance of a nanocontact system with two electrodes at different chemical potentials. The retarded Green's function for a single-impurity Anderson model with two reservoirs is obtained in terms of a $5\times 5$ matrix in which the effect of bias is contained. A complete set of basis vectors for the single-impurity Anderson model has been provided before formulating the Green's function. Finally, we present a self-consistent method to fix the undetermined quantities existing in the matrix elements for the retarded Green's function.
We develop a theory for the nonequilibrium coherent transport through a mesoscopic region, based on the nonequilibrium Green function technique. The theory requires the weak coupling between the central mesoscopic region and the multiple electrodes connected to it, but allows arbitrary hopping and interaction in the central region. An equation determining the nonequilibrium distribution in the central interacting region is derived and plays an important role in the theory. The theory is applied to two special cases for demonstrations, revealing the novel effects associated with the combination…
Electron transport properties of a non-interacting mesoscopic ring sandwiched between two metallic electrodes are investigated by the use of Green's function formalism. We introduce a parametric approach based on the tight-binding model to study the transport properties. The electronic transport characteristics are investigated in three aspects: (a) ring-electrode interface geometry, (b) coupling strength of the ring to the electrodes and (c) magnetic flux threaded by the ring.
Transport through a molecule sandwiched between two metallic electrodes and coupled to a mesoscopic ring that threads a magnetic flux $ϕ$ is studied. An analytic approach for the electron transport through the molecular bridge system is presented. Electronic transport properties are discussed in two aspects: (a) presence of external magnetic filed and (b) strength of molecule-to-electrode coupling.
We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantitie…
A generalized Landauer formula, derived with the methods due to Keldysh, and Baym and Kadanoff, is gaining widespread use in the modeling of transport in a large number of different mesoscopic systems. We review some of the recent developments, including transport in semiconductor superlattices, calculation of noise, and nanoelectromechanical systems.
We study the I-V characteristic of mesoscopic systems or Quantum dot attached of a pair of superconducting leads. Interaction effects in the quantum dot are considered through the charging energy of the quantum dot; the treatment of such effects are considered within a Poisson-non-equilibrium function scheme.
Using the two-loop analysis and the background field method we demonstrate that the local pure scaling operators without derivatives in the Finkel'stein nonlinear sigma model can be constructed by straightforward generalization of the corresponding operators for the noninteracting case. These pure scaling operators demonstrate multifractal behavior and describe mesoscopic fluctuations of the single-particle Green's function. We determine anomalous dimensions of all such pure scaling operators in the interacting theory within the two-loop approximation.
The Liouville-space Green function formalism is used to compute the current density profile across a single molecule attached to electrodes. Time ordering is maintained in real, physical, time, avoiding the use of artificial time loops and backward propagations. Closed expressions for molecular currents, which only require DFT calculations for the isolated molecule, are derived to fourth order in the molecule/electrode coupling.
We present a formulation of a nonequilibrium Green's function method for thermal current in nanojunction atomic systems with nonlinear interactions. This first-principle approach is applied to the calculation of the thermal conductance in carbon nanotube junctions. It is shown that nonlinearity already becomes important at low temperatures. Nonlinear interactions greatly suppress phonon transmission at room temperature. The peak of thermal conductance is found to be around 400K, in good agreement with experiments. High-order phonon scattering processes are important for diffusive heat transpor…
The influence of contacts on linear transport through a molecular wire attached to mesoscopic tubule leads is studied. It is shown that low dimensional leads, such as carbon nanotubes, in contrast to bulky electrodes, strongly affect transport properties. By focusing on the specificity of the lead-wire contact, we show, in a fully analytical treatment, that the geometry of this hybrid system supports a mechanism of channel selection and a sum rule, which is a distinctive hallmark of the mesoscopic nature of the electrodes.
Electron transport properties are investigated in an array of mesoscopic rings, where each ring is threaded by a magnetic flux $ϕ$. The array is attached to two semi-infinite one-dimensional metallic electrodes, namely, source and drain, where the rings are considered either in series or in parallel configuration. A simple tight-binding model is used to describe the system and all the calculations are done based on the Green's function formalism. Here, we present conductance-energy and current-voltage characteristics in terms of ring-to-electrode coupling strength, ring-electrode interface geo…
Electronic transport through a quantum wire sandwiched between two metallic electrodes and coupled to a quantum ring, threaded by a magnetic flux $ϕ$, is studied. An analytic approach for the electron transport through the bridge system is presented based on the tight-binding model. The transport properties are discussed in three aspects: (a) presence of an external magnetic filed, (b) strength of the wire to electrode coupling, and (c) presence of in-plane electric field.
With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green's function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach f…
Recent experiments on mesoscopic normal-metal--superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energy $k_B T \le E_{Th}$. We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.
Excess conductance fluctuations with peculiar temperature-dependence from 1.4 to 250 K were observed in curved nano-graphite sheets with an electrode gap length of 300 and 450 nm, whereas the conductance fluctuation is greatly suppressed above 4.2 K when the electrode gap length increases to 800 and 1000 nm. The former is discussed in the context of the presence of a small energy bandgap in the nano-graphite sheets, while the latter is attributed to the crossover from coherent transport to diffusive transport regime.
A short introduction to the theory of matrix quasiclassical Green's functions is given and possible applications of this theory to transport properties of mesoscopic superconducting-normal metal (S/N) structures are considered. We discuss a simplified version of these equations in the diffusive regime and in the case of a weak proximity effect. These equations are used for the calculation of the conductance of different S/N structures. Long-range, phase-coherent effects are studied in a 4-terminal S/N/S structures under conditions when the Josephson critical current is negligible. It is shown …
We generalize the representation of the real time Green's functions introduced by Langreth and Nordlander [Phys. Rev. B 43 2541 (1991)] and Meir and Wingreen [Phys. Rev. Lett. 68 2512 (1992)] in stationary quantum transport in order to study problems with hybrid structures containing normal (N) and superconducting (S) pieces. We illustrate the treatment in a S-N junction under a stationary bias and investigate in detail the behavior of the equilibrium currents in a normal ring threaded by a magnetic flux with attached superconducting wires at equilibrium. We analyze the flux sensitivity of the…
We present electrical transport experiments performed on submicron hybrid devices made of a ferromagnetic conductor (Co) and a superconducting (Al) electrode. The sample was patterned in order to separate the contributions of the Co conductor and of the Co-Al interface. We observed a strong influence of the Al electrode superconductivity on the resistance of the Co conductor. This effect is large only when the interface is highly transparent. We characterized the dependence of the observed resistance decrease on temperature, bias current and magnetic field. As the differential resistance of th…
We experimentally study spin accumulation in an aluminium island with all dimensions smaller than the spin relaxation length, so that the spin imbalance throughout the island is uniform. Electrical injection and detection of the spin accumulation are carried out in a four terminal geometry by means of four cobalt electrodes connected to the island through tunnel barriers. We model the system theoretically and we investigate the role of the ferromagnetic electrodes on the spin accumulation at the limit at which the electron diffusion time can be neglected. We present measurements of spin accumu…
Magneto-transport properties in closed and open loop structures are carefully reviewed within a tight-binding formalism. A novel mesoscopic phenomenon where a non-vanishing current is observed in a conducting loop upon the application of an Aharonov-Bohm flux $ϕ$ and we explore its behavior in the aspects of quantum phase coherence, electron-electron correlation and disorder. The essential results are analyzed in three different parts. First, we examine the behavior of persistent current in different branches of a zigzag carbon nanotube within a Hartree-Fock mean field approach using the secon…
The method of the quasiclassical Green's function is used to determine the equilibrium properties of one-dimensional (1D) interacting Fermi systems, in particular, the bulk and the local (near a hard wall) density of states. While this is a novel approach to 1D systems, our findings do agree with standard results for Luttinger liquids obtained with the bosonization method. Analogies to the so-called $P(E)$ theory of tunneling through ultrasmall junctions are pointed out and are exploited. Further applications of the Green's function method for 1D systems are discussed.
We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We separate time scales in the Green's functions on fast relative time and slow central time. The derivative with respect to the central time serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym equations for molecular Green's functions using Wigner representation and keep terms up to the second order with respect to the central time d…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the quantity measured in such experiments. Efficient means that the computational effort scales like $M^3 N$ ($M$ is the width of the tight-binding lattice used, and $N$ is its length), which is a factor $MN$ better than the standard recursive technique for the same problem. Moreover, within our numerical framework it is also possible to calculate (with the same com…
We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallely magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe t…
We explore OR gate response in a mesoscopic ring threaded by a magnetic flux $ϕ$. The ring is symmetrically attached to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the two inputs of the OR gate. All the calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the gate voltages, ring-to-electrodes coupling strengths and magnetic flux. Our theoretical study show…
NAND gate response in a mesoscopic ring threaded with a magnetic flux $ϕ$ is investigated by using Green's function formalism. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, namely, $V_a$ and $V_b$, are applied in one arm of the ring those are treated as the two inputs of the NAND gate. We use a simple tight-binding model to describe the system and numerically compute the conductance-energy and current-voltage characteristics as functions of the gate voltages, ring-to-electrode coupling strength and magnetic flux. Our theoreti…
We describe XNOR gate response in a mesoscopic ring threaded by a magnetic flux $ϕ$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the inputs of the XNOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strength, magnetic flux and gate voltages. Our theoretical study shows tha…
We address XOR gate response in a mesoscopic ring threaded by a magnetic flux $ϕ$. The ring, composed of identical quantum dots, is symmetrically attached to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied, respectively, in each arm of the ring which are treated as the two inputs of the XOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-electrodes coupling strengths, magnetic fl…
We study the spin-dependent transport through a quantum dot coupled to two ferromagnetic electrodes using the equation of motion method for the nonequilibrium Green's functions. Our results show that the conductance and the density of states (DOS) are strongly dependent on the configurations of the magnetic electrodes. In parallel configuration of magnetic electrodes the conductance is affected by the spin-flip process and the Coulomb repulsion on the dot. The Kondo peak for spin-dependent transport is splitted into two peaks by the spin-flip process. The locations of the two peaks are symmetr…
We present a description of spin-polarized transport in mesoscopic ferromagnet-superconductor (F/S) systems, where the transport is diffusive, and the interfaces are transparent. It is shown that the spin reversal associated with Andreev reflection generates an excess spin density close to the F/S interface, which leads to a spin contact resistance. Expressions for the contact resistance are given for two terminal and four terminal geometries. In the latter the sign depends on the relative magnetization of the ferromagnetic electrodes.
Quantum transport properties through single polycyclic hydrocarbon molecules attached to two metallic electrodes are studied by the use of Green's function technique. A parametric approach based on the tight-binding model is introduced to investigate the electronic transport through such molecular bridge systems. The transport properties are discussed in the aspects of (a) molecule-to-electrode coupling strength and (b) quantum interference effect.
When two metal electrodes are separated, a nanometer sized wire (nanowire) is formed just before the contact breaks. The electrical conduction measured during this retraction process shows signs of quantized conductance in units of G_0=2e^2/h. Recent experiments show that the force acting on the wire during separation fluctuates, which has been interpreted as being due to atomic rearrangements. In this report we use a simple free electron model, for two simple geometries, and show that the electronic contribution to the force fluctuations is comparable to the experimentally found values, about…
We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using the random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study th…
The proximity effect in mesoscopic ferromagnet/superconductor ($FS$) Ni/Al structures of various geometries was studied experimentally on both $F$- and $S$-sides of the structures. Samples with a wide range of interface transparency were fabricated. The dependence of the effect on $FS$ interface transparency was investigated. The amplitude of this effect was found to be larger than expected from classical theory of proximity effect. Preliminary experiments showed no phase-sensitive oscillations in Andreev interferometer geometry. Various theoretical models are discussed.
Effects of impurity on the spin-dependent transport in a single wall carbon nanotube spin-valve, as ferromagnetic electrode/carbon nanotube/ferromagnetic electrode model junction is numerically investigated. Using a generalized Green's function method and the Landauer-Buttiker formalism, the impurity conditions are determined by randomly substitution of carbon atoms in the honeycomb carbon nanotube lattice by nitrogen and boron atoms. We have found that transport characteristics, including the spin-dependent current and tunnel magnetoresistance are strongly influenced by the impurity effects. …
We present an overview of electronic device modeling using non-equilibrium Green function techniques. The basic approach developed in the early 1970s has become increasingly popular during the last 10 years. The rise in popularity was driven first by the experimental investigations of mesoscopic physics made possible by high quality semiconductor heterostructures grown by molecular beam epitaxy. The theory has continuously been adapted to address current systems of interest moving from the mesoscopic physics of the late 1980s to single electronics to molecular electronics to nanoscaled FETs. W…
Using a scattering matrix approach and quasiclassical Green's function technique, we calculate the conductance of the S/N system (see Fig.1). We establish that the difference between the superconducting and normal state conductance $(δG = G_s - G_n)$ is negative for large S/N interface resistances $(R_{S/N})$ and changes sign with decreasing $R_{S/N}$. The comparision of the result obtained with experimental data is carried out.
The objective of this paper is to describe a simple phenomenological approach for including incoherent dephasing processes in quantum transport models. The presented illustrative numerical results show this model provides the flexibility of adjusting the degree of phase and momentum relaxation independently that is not currently available in mesoscopic physics and in device simulations while retaining the simplicity of other phenomenological models.
We explore spin dependent transport through a magnetic quantum wire which is attached to two non-magnetic metallic electrodes. We adopt a simple tight-binding Hamiltonian to describe the model where the quantum wire is attached to two semi-infinite one-dimensional non-magnetic electrodes. Based on single particle Green's function formalism all the calculations are performed numerically which describe two-terminal conductance and current-voltage characteristics through the wire. Quite interestingly we see that, beyond a critical system size probability of spin flipping enhances significantly th…
Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of th…
We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes ($N_e\ge1$) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour opti- mizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a gen…
In both research and textbook literature one often finds two ``different'' Kubo formulas for the zero-temperature conductance of a non-interacting Fermi system. They contain a trace of the product of velocity operators and single-particle (retarded and advanced) Green operators: $\text{Tr} (\hat{v}_x \hat{G}^r \hat{v}_x \hat{G}^a)$ or $\text{Tr} (\hat{v}_x \text{Im} \hat{G} \hat{v}_x \text{Im} \hat{G})$. The study investigates the relationship between these expressions, as well as the requirements of current conservation, through exact evaluation of such quantum-mechanical traces for a nanosca…
We study the statistical properties of currents in two particular systems of capacitively coupled parallel transport channels. In the first system, each transport channel contains a single quantum dot in contact with two electron reservoirs. The second system we study is constituted of a double quantum dot coupled to two electrodes and probed by a quantum point contact detector. Thermodynamic forces are applied to each transport channel that generate fluctuating stationary currents. The full counting statistics of the currents is obtained starting from a microscopic Hamiltonian describing the …
We consider plane junctions with graphene electrodes, which are formed by a single-level system ("molecule") placed between the edges of two single-layer graphene half planes. We calculate the edge Green functions of the electrodes and the corresponding lead self-energies for the molecular levels in the cases of semi-infinite single-layer electrodes with armchair and zigzag edges. We show two main effects: first, a peculiar energy-dependent level broadening, reflecting at low energies the linear energy dependence of the bulk density of states in graphene, and, second, the shift and splitting o…
We discuss the conductance of a molecular bridge between mesoscopic electrodes supporting low-dimensional transport and bearing an internal structure. As an example for such nanoelectrodes we assume semi-infinite (carbon) nanotubes. In the Landauer scattering matrix approach, we show that the conductance of this hybrid is very sensitive to the geometry of the contact unlike the usual behaviour in the presence of bulk electrodes.
We study spin and charge currents pumped by precessing magnetization of a single ferromagnetic layer within F|I|N or F|I|F (F-ferromagnet; I-insulator; N-normal-metal) multilayers of nanoscale thickness attached to two normal metal electrodes with no applied bias voltage between them. Both simple one-dimensional model, consisting of a single precessing spin and a potential barrier as the "sample," and realistic three-dimensional devices are investigated. In the rotating reference frame, where the magnetization appears to be static, these junctions are mapped onto a four-terminal dc circuit who…
We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state or local currents in mesoscopic quantum systems. Within the non equilibrium Green function formalism, we generalize the recursive Green function technique to tackle multiterminal devices with arbitrary geometries. We apply our method to analyze two recent experiments: an electronic Mach-Zehnder interferometer in a 2D gas and a Hall bar made of graphene nanoribbons in quantum Hall regime. In the latter case, we find that the Landau edge state pinned to th…
We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferomet…
This thesis describes the merging of the two fields of Coulomb drag and mesoscopic physics. The thesis presents a theory for Coulomb drag between two mesoscopic systems based on linear-response theory. The formalism expresses the drag in terms of either scattering matrices and wave functions or Green functions, and its range of validity covers both ballistic and disordered phase-coherent systems. The consequences are worked out either by analytic means, such as the random matrix theory, or by numerical simulations. The formalism is applied to i) drag between mesoscopic quantum wires and ii) dr…
We consider the possibility to employ a quantum wire realized in a two-dimensional electron gas (2DEG) as a spin ratchet. We show that a net spin current without accompanying net charge transport can be induced in the nonlinear regime by an unbiased external driving via an ac voltage applied between the contacts at the ends of the quantum wire. To achieve this we make use of the coupling of the electron spin to inhomogenous magnetic fields created by ferromagnetic stripes patterned on the semiconductor heterostructure that harbours the 2DEG. Using recursive Green function techniques we numeric…
We numerically investigate the electronic transport properties between two mesoscopic graphene disks with a twist by employing the density functional theory coupled with non-equilibrium Green's function technique. By attaching two graphene leads to upper and lower graphene layers separately, we explore systematically the dependence of electronic transport on the twist angle, Fermi energy, system size, layer stacking order and twist axis. When choose different twist axes for either AA- or AB-stacked bilayer graphene, we find that the dependence of conductance on twist angle displays qualitative…
Here we address two nonequilibrium Green's functions approaches for a resonant tunneling structure under a sudden switch of a bias. Our aim is to stress that the time-dependent Keldysh formulation of Jauho, Wingreen and Meir, and the partition-free scheme of Stefanucci and Almbladh are formally equivalent in the ubiquitous case of wide-band limit and noninteracting electrons, if leads and dot are in equilibrium before the time-dependent perturbation. We develop explicit closed formulas of the lesser Green's function and time-dependent current, reminding that the different integration limits pr…
Single-molecule biosensing, with a promise of being applied in protein and DNA sequencing, could be achieved using tunneling current approach. Electrode-molecule-electrode tunneling current critically depends on whether molecular levels contribute to electronic transport or not. Here we found employing DFT and Non-Equilibrium Green's Function formalism that energies of benzene molecular levels placed between graphene electrodes are strongly influenced by electrode termination. Termination-dependent dipoles formed at the electrode ends induce in-gap field effect that is responsible for shifting…
Resonant electron transport through a mesoscopic region (quantum dot or single molecule) with electron-phonon interaction is considered at finite voltage. In this case the standard Landauer-Büttiker approach cannot be applied. Using the nonequilibrium Green function method we show that due to a nonequilibrium distribution function of electrons in the mesoscopic region, the inelastic scattering rate and spectral function of the dot become functions of the voltage and have to be calculated self-consistently.
Novel intrinsic two-dimensional materials have attracted many researchers' attention. The unusual transport and optical properties of these materials originate mainly from triangular lattices (TLs). Therefore, the application of energy harvesting calls for a study of the thermoelectric properties of 2D TLs coupled to electrodes. The transmission coefficient of 2D TLs is calculated by using the Green's function technique to treat ballistic transports. Especially important among our findings is the electron-hole asymmetric behavior of the power factor ($PF$). Specifically, the maximum $PF$ of el…
We study all-carbon-hydrogen molecular transistors where zigzag graphene nanoribbons play the role of three metallic electrodes connected to a ring-shaped 18-annulene molecule. Using the nonequilibrium Green function formalism combined with density functional theory, recently extended to multiterminal devices, we show that the proposed nanostructures exhibit exponentially small transmission when the source and drain electrodes are attached in a configuration that ensures destructive interference of electron paths around the ring. The third electrode, functioning either as an attached infinite-…
