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Three main ambipolar compact models for Two-Dimensional (2D) materials based Field-Effect Transistors (2D-FETs) are reviewed: (1) Landauer model, (2) 2D Pao-Sah model, and (3) virtual Source Emission-Diffusion (VSED) model. For the Landauer model, the Gauss quadrature method is applied, and it summarizes all kinds of variants, exhibiting its state-of-art. For the 2D Pao-Sah model, the aspects of its theoretical fundamentals are rederived, and the electrostatic potentials of electrons and holes are clarified. A brief development history is compiled for the VSED model. In summary, the Landauer model is naturally appropriate for the ballistic transport of short channels, and the 2D Pao-Sah model is applicable to long-channel devices. By contrast, the VSED model offers a smooth transition between ultimate cases. These three models cover a fairly completed channel length range, which enables researchers to choose the appropriate compact model for their works.

Steep-slope transistors are required for low-power electronic applications. However, the strategy to lower the subthreshold swing (SS) remains elusive. Here, we present a method based on altering capacitance constitution to lower the SS of 2-D transistors close to thermionic limit (60 mV/dec). By inducing other 2-D materials with opposite carrier type into the channel, the extra junction capacitance is in series with the channel capacitance, leading to lower semiconductor capacitance and lower SS. The electrical performance of conventional 2-D transistor with pure WSe2 channel and WSe2-BP-MoS2 heterojunction channel is studied and compared. The 2-D transistor with pure WSe2 channel shows SS ~ 110 mV/dec. After forming WSe2-BP-MoS2 heterojunction channel, the SS reduces to ~62 mV/dec and maintains over three orders of magnitude. To reveal the mechanism, a compact model based on Landauer formula has been established. The simulation results indicate that lower SS has strong relation with the reduction of semiconductor capacitance. The proposed structure provides a new way to develop steep-slope transistors.

Magneto-conductance in magnetic bilayers of the form ferromagnetic metal (FM)/monolayer transition metal dichalcogenide (TMD) is investigated in the linear response regime. It is assumed that spin–orbit proximity (SOP) effect in FM monolayers is created by the adjacent monolayer TMD. The transmission function is calculated from the Landauer formula in terms of non-equilibrium Green’s function formalism. It is presented here how the magneto-conductance (magneto-resistance) can be tuned in the presence of SOP for FM/TMD bilayers.

Ballistic graphene samples in a multimode regime show the sub-Sharvin charge transport, characterized by the conductance reduced by a factor of $\pi/4$ comparing to standard Sharvin contacts in two-dimensional electron gas, and the shot-noise power enhanced up to $F\approx{}1/8$ (with $F$ the Fano factor) [Phys. Rev. B 104, 165413 (2021)]. Here we consider the disk-shaped (Corbino) setup in graphene, with inner radius $r_1$ and outer radius $r_2$, finding that the multimode conductance is slightly enhanced for any $r_1, Comment: Refs. added; new Sec. V on transport via a finite disk section

A single unified analytical model is presented to predict the shot noise for both the source-to-drain (SD) and the gate tunneling current in sub-10 nm MOSFETs with ultrathin oxide. Based on the Landauer formula, the model is constructed from the sequential tunneling flows associated with number fluctuations. This approach provides the analytical formulation of the shot noise as a function of the applied voltages. The model performs well in predicting the Fano factor for shot noise in the SD and gate tunneling currents.

We study spin-scattering asymmetry at the interface of two ferromagnets (FMs) based on a half-metallic ${\mathrm{Co}}_{2}{\mathrm{Fe}}_{0.4}{\mathrm{Mn}}_{0.6}\mathrm{Si}$ (CFMS)/CoFe interface. First-principles ballistic transport calculations based on Landauer formula for (001)-CoFe/CFMS/CoFe indicate strong spin-dependent conductance at the CFMS/CoFe interface, suggesting a large interface spin-scattering asymmetry coefficient ($\ensuremath{\gamma}$). Fully epitaxial current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) pseudo-spin-valve (PSV) devices involving CoFe/CFMS/Ag/CFMS/CoFe structures exhibit an enhancement in MR output owing to the formation of the CFMS/CoFe interface at room temperature (RT). This is well reproduced qualitatively by a simulation based on a generalized two-current series-resistor model with considering the presence of $\ensuremath{\gamma}$ at the CFMS/CoFe interface, half-metallicity of CFMS, and combinations of terminated atoms at the interfaces in the CPP-GMR PSV structure. We show direct evidence for a large $\ensuremath{\gamma}$ at a half-metallic FM/FM interface and its impact on the CPP-GMR effect even at RT.

Ideal Sharvin contact in a multimode regime shows the conductance $G\approx{}G_{\rm Sharvin}=g_0k_F{}W/\pi$ (with $g_0$ the conductance quantum, $k_F$ the Fermi momentum, and $W$ the contact width) accompanied by strongly suppressed shot-noise quantified by small Fano factor $F\approx{}0$. For ballistic graphene away from the charge-neutrality point the sub-Sharvin transport occurs, characterised by suppressed conductance $G\approx{}(\pi/4)\,G_{\rm Sharvin}$ and enhanced shot noise $F\approx{}1/8$. All these results can be derived from a basic model of quantum scattering, involving assumptions of infinite height and perfectly rectangular shape of the potential barrier in the sample. Here we have carried out the numerical analysis of the scattering on a family of smooth barriers of finite height interpolating between parabollic and rectangular shapes. We find that tuning the barrier shape one can modify the asymmetry between electron- and hole-doped systems. For electronic dopings, the system crosses from Sharvin to sub-Sharvin transport regime (indicated by both the conductance and the Fano factor) as the potential becomes closer to the rectangular shape. In contrast, for hole dopings, the conductivity is strongly suppressed when the barrier is parabolic and slowly converges to $G\approx{}(\pi/4)\,G_{\rm Sharvin}$ as the potential evolves towards rectangular shape. In such a case the Sharvin transport regime is inaccessible, shot noise is generically enhanced (with much slower convergence to $F\approx{}1/8$) comparing to the electron-doped case, and aperiodic oscillations of both $G$ and $F$ are prominent due to the formation of quasibound states., Comment: RevTeX, 7 pages, 5 figures

We report on the possibility of detecting hinge spin polarization in magnetic topological insulators by resistance measurements. By implementing a three-dimensional model of magnetic topological insulators into a multiterminal device with ferromagnetic contacts near the top surface, local spin features of the chiral edge modes are unveiled. We find local spin polarization at the hinges that inverts the sign between the top and bottom surfaces. At the opposite edge, the topological state with inverted spin polarization propagates in the reverse direction. A large resistance switch between forward and backward propagating states is obtained, driven by the matching between the spin polarized hinges and the ferromagnetic contacts. This feature is general to the ferromagnetic, antiferromagnetic, and canted antiferromagnetic phases, and enables the design of spin-sensitive devices, with the possibility of reversing the hinge spin polarization of the currents., We acknowledge the European Union Horizon 2020 research and innovation programme under Grant Agreement No. 824140 (TOCHA, H2020-FETPROACT-01-2018). ICN2 is funded by the CERCA Programme/Generalitat de Catalunya, and is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706).

Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications as well as putting forward layer-dependent proximity effects in bilayer graphene as a way to create versatile topological states of matter., The authors were supported by the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 881603 (Graphene Flagship) and No. 824140 (TOCHA, H2020-FETPROACT-01-2018). ICN2 is funded by the CERCA Programme/Generalitat de Catalunya, and is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706).

In this work, we systematically studied the rectifying properties of molecular junction based on asymmetric tunneling and hopping charge transport in a single electronic state model using Landauer formula and Marcus theory. We first analyzed the asymmetric I-V characteristics and revealed distinct physical origins of the rectification under the two types of transports. We found significant difference in I-V characteristics of the two and the hopping transport can afford a much higher rectification ratio than tunneling. Next, the effect of key physical parameters on rectification performance under tunneling and hopping, like asymmetric factor, energy barrier, temperature and molecule-electrode coupling et al, were extensively evaluated, which provided a theoretical baseline for molecular diode design and performance modulation. At last, we further analyzed representative experimental results using the two models. We successfully reproduced the experimental results by adjusting the model parameters and revealed the coexistence of the tunneling and hopping processes in the ferrocene based molecular diode. The model method thus can work as powerful tool in mechanism analysis for the molecular rectification study.

We calculated a spin-polarized conductance in the almost unexplored nanostructure "high temperature ferromagnetic insulator/ graphene/ ferroelectric film" with a special attention to the impact of electric polarization rotation in a strained multiaxial ferroelectric film. The rotation and value of polarization vector are controlled by a misfit strain. We proposed a phenomenological model, which takes into account the shift of the Dirac point due to the proximity of ferromagnetic insulator and uses the Landauer formula for the conductivity of the graphene channel. We derived analytical expressions, which show that the strain-dependent ferroelectric polarization governs the concentration of two-dimensional charge carriers and Fermi level in graphene in a self-consistent way. We demonstrate the realistic opportunity to control the spin-polarized conductance of graphene by a misfit strain ("strain engineering") at room and higher temperatures in the nanostructures CoFeO4/graphene/PZT and Y3Fe5O12/graphene/PZT. Obtained results open the possibilities for the applications of ferromagnetic/graphene/ferroelectric nanostructures as non-volatile spin filters and spin valves., 21 pages, including 5 figures and a supplement at 5 pages with 1 figure

We consider the disorder-induced correction to the minimal conductance of an anisotropic two-dimensional Dirac node or a three-dimensional Weyl node. An analytical expression is derived for the correction $\delta G$ to the conductance of a finite-size sample by an arbitrary potential, without taking the disorder average, in second-order perturbation theory. Considering a generic model of a short-range disorder potential, this result is used to compute the probability distribution $P(\delta G)$, which is compared to the numerically exact distribution obtained using the scattering matrix approach. We show that $P(\delta G)$ is Gaussian when the sample has a large width-to-length ratio, and study how the expectation value, the standard deviation, and the probability of finding $\delta G < 0$ depend on the anisotropy of the dispersion., Comment: 10+ pages, 6 figures

A three-terminal refrigerator based on resonant-tunneling quantum wells is proposed. With the help of the Landauer formula, the expressions for the cooling rate and the coefficient of performance (COP) are derived. The working regions of the refrigerator are determined and the three-dimensional projection graphs of the cooling rate and the COP varying with the positions of the two energy levels are plotted. Moreover, the influence of the bias voltage, the asymmetric factor, and the temperature difference on the optimal performance parameters is analyzed in detail. Finally, the performance characteristics of the refrigerator in the case of negative temperature difference are discussed.

The conductance of bulk metal--insulator--metal junctions is evaluated by the Landauer formula using an \textit{ab initio} electronic structure calculated using a plane-waves basis set within density-functional theory (DFT) and beyond, i.e.\ including exact non-local exchange using hybrid functional (HSE) or many-body $G_0W_0$ and COHSEX quasiparticle (QP) schemes. We consider an Ag/MgO/Ag heterostructure model and we focus on the evolution of the zero-bias conductance as a function of the MgO film thickness. Our study shows that the correction of the electronic structure beyond semi-local density functionals goes in the right direction to improve the agreement with experiments, significantly reducing the zero-bias conductance. This effect becomes more evident at larger MgO thickness, that is in increasing tunneling regime. We also observe that the reduction of the conductance seems more related to the correction of wavefunctions rather than energies, and thus not directly related to the correction of the band-gap of bulk MgO. $G_0W_0$ and HSE both provide a correct band-gap in agreement with experiments, but only HSE gives a significant reduction of the conductance. COHSEX, while overestimating the band-gap, gives a reduction of the conductance very close to HSE., Comment: 11 pages, 12 figures

Resistive non-volatile memories based on oxides (OxRAM) are recently acquiring a wide interest for their performances, which make them promising candidates as storage memories to replace flash technology, and as embedded memories for neural network applications. Nevertheless, emerging OxRAM devices still present some drawbacks, like non-uniformity of switching parameters and switching failures. Overcoming these drawbacks requires a deeper comprehension of the OxRAM working principles, so far not completely understood. This can be achieved by means of textit{ab initio} simulations. Hence this work presents a careful characterization of HfO₂, which is within the most promising materials to build OxRAM devices, by means of accurate quasi-particle (QP) calculations. A study of the electronic transport properties in OxRAM devices is also of primary importance. However, this requires a robust and reliable theoretical framework to compute the conductance of bulk metal/insulator junctions. The standard approach, based on density functional theory, Green function formalism, and Landauer formula, has some limitations and reliability issues. This work proposes a more reliable approach based on QP calculations, which provide a more accurate electronic structure to compute the conductance, and largely tests this new method on different junctions mimicking OxRAM devices., Les mémoires résistives non volatiles basées sur les oxydes (OxRAM) acquièrent récemment un grand intérêt pour leurs performances, ce qui en fait des candidats prometteurs comme mémoire de stockage pour remplacer la technologie flash, et comme mémoires intégrées pour les applications réseau de neurones. Néanmoins, les dispositifs OxRAM émergents présentent encore certains inconvénients, comme la non-uniformité des paramètres de commutation et les défaillances de commutation. Surmonter ces inconvénients exige une compréhension plus profonde des principes de fonctionnement de l’OxRAM, jusqu’à présent pas complètement compris. Ceci peut être réalisé au moyen de simulations textit{ab initio}. Ce travail présente donc une étude approfondie de HfO₂, qui fait partie des matériaux les plus prometteurs pour la construction de dispositifs OxRAM, au moyen de calculs précis des états de quasi-particules (QP). Une étude des propriétés du transport électronique dans les dispositifs OxRAM est également de première importance. Toutefois, cela nécessite un cadre théorique solide et fiable afin de calculer la conductance des jonctions métal/isolant. L’approche standard, basée sur la théorie fonctionnelle de la densité, le formalisme de la fonction de Green et la formule de Landauer, a quelques limites et soucis de fiabilité. Ce travail propose une approche plus fiable basée sur les calculs QP, qui fournissent une structure électronique plus précise pour calculer la conductance, et teste en grande partie cette nouvelle méthode sur différentes jonctions imitant les dispositifs OxRAM.

In this paper, we investigate the transmission spectrum, current–voltage ( ${I}$ – ${V}$ ) characteristics and dielectric function of the zigzag MoS2 nanoribbon with and without a uniaxial tensile strain. By considering only the nearest neighbor atoms, we will first calculate the band structure for this material using the tight-binding method. Then, we present the transmission spectrum and the ${I}$ – ${V}$ characteristics by employing nonequilibrium Green’s function formalism in conjunction with the Landauer formula. Due to the presence of edge states, in the zigzag nanoribbons, this material demonstrates a metallic behavior. We also study the aforementioned parameters in the presence of the strain in the range of 10%–20%. Results indicate that applying a tensile strain of the order of 10% opens up a direct gap within the energy bands. This gap increases upon increasing the strain. Furthermore, the current increases with increase in the tensile strain as well as the number of atoms at the ribbon’s edge. Our numerical simulations also predict possible transitions between subbands. Strain intensifies the amplitude of the dielectric function at lower energies. These results can be instrumental for the design of nanoscale photonic devices based on the nanoribbon MoS2.

We present a novel and comprehensive quantum analytical modeling of a sub-20 nm Dual Metal Double Gate (DMDG) Tunnel Field Effect Transistor (TFET) for the first time in literature. Owing to structural confinement at sub-20 nm regime, the energy states at channel are quantized and carrier propagation is regulated by quantum transport. We address such quantization aspects (viz. subband quantization, bandgap shifting, tunneling through barrier etc.) and incorporate them in analytical modeling using self-consistent solution of Schrodinger-Poisson's equation. As a result of work function difference at gate, we observe creation of quantum well, followed by a tunneling barrier, along the channel. Energy states in the quantum well are derived from Schrodinger equation, whereas, transmission coefficients are derived for each tunneling barrier. Finally, current density is obtained using ‘Landauer formula for quantum transport’. We methodically study the effects of structural confinement on device performances and observe significant shift from classical counterpart. Moreover, we note that quantization in DMDG TFET can be optimized that will lead to superior device performance. The results are verified with simulation data in each occasion to substantiate analytical models.

Recently, the long-range spin-selective transport in chiral molecules has been investigated for bio-spintronics. The experimental results for a natural metalloprotein molecule suggested a high spin selectivity. I performed first-principle calculations of electron spin transport in a natural metalloprotein molecule based on the Landauer formula. A gold–metalloprotein–gold device model was used to confirm the high spin polarization. There was a relatively large spin density at some amide groups in the helical peptide structures. Furthermore, a large spin density of iron atoms enhanced the spin density of the neighboring coordinated atoms, resulting in spin polarization in the whole molecule.

We theoretically study a controllable spatial spin converter and spin valve by using a Y-shaped even-chain zigzag graphene nanoribbon (ZGR) junction with Rashba spin orbit coupling (SOC) and strain. By calculating the spin-dependent conductance spectra of different tunneling terminals through the multi-terminal Landauer formula, we find that the spin up electron can flip its spin orientation, and convert to spin down one on the left electrode, the same spin converting phenomena can be inhibited on the right terminal. The above spin flipping and its valve phenomena are derived from the interactions of the Rashba SOC, strain and magnetization layout. When the strain's orientation is along (perpendicular) to the zigzag chain's direction, the valley valve effect of the even-chain ZGR is remained, the Rashba SOC takes little effect on the spatial spin switching, one can get 100% polarized spin up (down) electrons at different terminals of the Y-shaped ZGR due to the valley valve effect. When the strain is changed to other direction, the valley valve effect is partly destroyed, Rashba SOC can enhance the spin flipping conductance and break the ON/OFF transport states of spin valve. Our investigations might be useful in designing a multi-parameter controllable spin valve and spin detector based on a multi-terminal graphene nanoribbon junction.

An implementation of the Landauer approach utilizing the ballistic quantum transport package Kwant to calculate thermoelectric transport properties is presented. Incoherent scattering is included by an approach suggested by Buttiker, where scattering is mimicked by virtual contacts (Buttiker probes). In this paper we present the implementation and provide a simple validation by comparing results to the Boltzmann transport equation (BTE) for bulk CdTe and a simple short period superlattice. The electronic structure, serving as a base for fitting a tight-binding model, is calculated from first-principles. From there, the electronic structure on a dense k-point grid is generated and passed to the BTE routines, while the transmission coefficients in the Landauer approach are calculated from Green’s functions based on the tight-binding model. Our results show good agreement between the results from the Buttiker and the BTE calculations, which indicates a successful initial implementation. We discover significant performance bottlenecks tied to the density of the Buttiker probes and as such the implementation needs additional optimization to be viable for production work.

We generalize the Landauer formula to describe the dissipative electron transport through a superconducting point contact. The finite-temperature, linear-in-bias, dissipative DC conductance is expressed in terms of the phase- and energy-dependent scattering matrix of the Bogoliubov quasiparticles in the quantum point contact. The derived formula is also applicable to hybrid superconducting-normal structures and normal contacts, where it agrees with the known limits of Andreev reflection and normal-state conductance, respectively., v2: 5+6 pages, 2+1 figures; Corresponds to published version

Recent electronic transport experiments using metallic contacts attached to proteins identified some &ldquo, stylized facts&rdquo, which contradict conventional wisdom that increasing either the spatial distance between the electrodes or the temperature suppresses conductance exponentially. These include nearly temperature-independent conductance over the protein in the 30 to 300 K range, distance-independent conductance within a single protein in the 1 to 10 nm range and an anomalously large conductance in the 0.1 to 10 nS range. In this paper, we develop a generalization of the low temperature Landauer formula, which can account for the joint effects of tunneling and decoherence and can explain these new experimental findings. We use novel approximations, which greatly simplify the mathematical treatment and allow us to calculate the conductance in terms of a handful macroscopic parameters, instead of the myriads of microscopic parameters describing the details of an atomic level quantum chemical computation. The new approach makes it possible to get predictions for the outcomes of new experiments without relying solely on high performance computing and can distinguish important and unimportant details of the protein structures from the point of view of transport properties.

Poor heat dissipation has become the bottleneck that limits the further development of electronics, which lies in the enhancement of interface thermal conductance (ITC). In this paper, the ITC and spectral characteristics of Si/Ge interfaces with mass-graded interlayers are studied through non-equilibrium molecular dynamics simulation. For Si/Ge interface with exponentially mass-graded interlayer, the ITC is 1.73 times larger than that of pure case. More interestingly, the ITC shows a non-monotonic dependence on the number of layers and a double scale behavior when the thickness of each layer increases. To clarify the underlying physical mechanism, spectral phonon transmission function is calculated, and ITC contributed by elastic and inelastic processes is quantified through the Landauer formula. It is revealed that the elastic ITC and inelastic ITC show quite different behaviors with each other when changing the thickness of each layer and number of layers, which is responsible for the abnormal results. The findings here emphasize the mutual control of elastic and inelastic phonon processes at interfaces.

We explore a model of armchair graphene nanoribbons tuned by functionalizing the edge states. Edge modifications are modeled by changing the electronic energy of the edge states in specific periodic patterns. The model can be considered to mimic a controlled doping process with different elements. The band structure, density of states, conductance, and local density of states are calculated, using the tight binding approach, Green’s function methodology, and the Landauer formula. The results show interesting behaviors, which are considerably different from the properties of the perfect nanoribbons. The hybridization of conducting bands with non-conducting bands, which appear perfectly flat in the perfect ribbon, opens up and modifies gaps in conductance near the Fermi level. One particular pattern of edge functionalization causes a strong, symmetric, and systematic band gap change about the Fermi level, modifying the electronic characteristics in the energy dispersion, density of states, local density of states, and conductance.

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

We report the conductance calculation of metallic nanowires of different metals under the application of a tensile force. The elongation induced by the tensile force was simulated by means of the canonical Monte Carlo method combined with the embedded atom method to compute the energy of the system. We studied nanowires composed of Ag, Au, Pt and Cu. The conductance was calculated by means of the Landauer formula and the non-equilibrium Green function formalism. As previously verified experimentally and using other simulation techniques, the conductance is quantized. In addition to this, we have found that there is a strong correlation between the magnitude of the conductance and the width of the nanowire at its thinnest point. Conductance histograms were analyzed for all the different metals.

In this paper, we propose a method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in mesoscopic systems. The method is based on the recursive scattering matrix method (RSMM) that permits us to find the scattering matrix of a system from the scattering matrices of its subsystems. Following ideas of automatic differentiation, we determine expressions for the sum, product, inverse, and diagonalization of a matrix Taylor expansion, and use them into the RSMM to find Taylor series of scattering matrices. The method is validated by obtaining the transmission function of atomic chains with site defects and graphene nanoconstrictions. Finally, an analysis of convergence radius and error estimations of these Taylor expansions is presented., Comment: 3 figures

We derive the exact steady-state solutions for the simplest model systems of resonant tunneling and tunneling with destructive quantum interference from the driven Liouville-von Neumann (DLvN) approach. Under the finite-state lead condition (the two electrodes have finite states), we analyze the asymptotic behavior of the steady-state current in the two limits of electronic relaxation. Under the infinite-state lead condition, the steady-state solutions of the two model systems can be cast as Landauer-type current formulas. According to the formulas, we show that the transmission functions near the resonant peak and the antiresonant dip can be significantly influenced by electronic relaxation in the electrodes. Moreover, under intermediate and strong electronic relaxation conditions, we analytically show that the steady-state current of the DLvN approach dramatically deviates from the Landauer current when destructive quantum interference occurs. In the regime of zero electronic relaxation, our results are reduced to the Landauer formula, indicating that the DLvN approach is equivalent to the Landauer approach when the leads have infinite states without any electronic relaxation.

Transverse magnetoresistance in a ferromagnetic/nonmagnetic/ferromagnetic trilayer originated from charge-spin conversion by anomalous Hall effect is investigated theoretically. Solving the spin diffusion equation in bulk and using the spin-dependent Landauer formula at the ferromagnetic/nonmagnetic interface, an analytical formula of the transverse resistivity is obtained. The charge-spin conversion by the anomalous Hall effect contributes to the magnetoresistance in a manner proportional to the square of the spin anomalous Hall angle. The angular dependence of the magnetoresistance is basically identical to that of planar Hall effect, but has an additional term which depends on the relative angle of the magnetizations in two ferromagnets., Comment: 10 pages, 1 figure, conference proceeding of MMM 2017