Quantum Transport

We report an ab initio software package MATDCAL for investigating electronic transport properties in nano electronic devices. MATDCAL is based on carrying out real space density functional theory (DFT) within the Keldysh nonequilibrium Green function (NEGF) framework. The code is mainly written in MATLAB, combining with numerically intensive part in Java for efficiency. In order to realize parallelization in MATLAB, we have implemented a C-interface in MATLAB to link to MPI. MATDCAL is the first MATLAB-based electronic package for nanoelectronics research that is based on atomistic first principles. We report some implementation issues using MATLAB for large scale physics computation. Several examples will be given on quantum transport analysis of nano-scale devices.

This paper aims to introduce high-performance quaternary NAND and NOR gates that utilize basic binary gates, incorporating a multi-VDD approach and carbon nanotube field-effect transistors (CNTFETs). Furthermore, these gates are designed based on tri-state configurations to facilitate their integration into logic units. The proposed circuits show significant improvements in power consumption, delay, and area utilization compared to previous studies. Notably, when compared to the best prior work, the new circuits achieve approximately a 30% enhancement in power-delay product (PDP). Additionally, three efficient quaternary logic units (QLUs) are developed using these advanced quaternary gates. To support the quaternary multiplexers employed, a quaternary decoder is also introduced to decode the selector lines. Simulations are conducted using HSPICE software with a 32nanometer library file for CNTFETs to evaluate the performance of the designed gates and logic units.

Efficient atomistic simulators are required for full band treatments in strongly quantum confined systems, and for simulation of transport in emerging materials and devices such as graphene. Here we present an efficient transmission matrix based approach to ballistic quantum transport calculation for full three-dimensional, nearest-neighbor tight-binding based atomistic simulations. The method is then used to demonstrate how band-to-band tunneling increases the leakage current in OFF state in field-effect transistors with low band gap semiconductors such as InSb as channel material.

This paper extends the two-boundary obstruction programme into an explicit four-
dimensional Schrödinger benchmark and asks a narrower question than the companion
reduced-testbed paper: when a four- dimensional quasiperiodic model is compared
against matched roughness nulls, does the obstruction decomposition distinguish the
quasiperiodic case by scalar defect magnitude or by nodal morphology? Forward and
backward histories are generated by split-step Schrödinger propagation for free, barrier,
and quasiperiodic configuration-space models, and the four-dimensional obstruction
field
˜
Dnum
α = (A+ B) + αΞi + (1−α)Ξf

is evaluated on those histories. The first result is algebraic: the full reconstruction
remains at machine precision in four dimensions, with relative residuals of order 10−15
.
The second result is comparative: in a 100-seed matched-null ensemble at α= 0.50, the
quasiperiodic case does not exceed the nulls in obstruction-only residual or active nodal
fraction. The surviving signal is instead topological morphology. Relative to matched
roughness, the quasiperiodic benchmark yields fewer nodal-sheet components, a lower
node-normalized fragmentation index, and a lower threshold-persistence component
count. A larger-lattice 204 check using the actual nodal-overlap mask confirms the same
direction while rejecting an axis-spanning interpretation for the original localized-state
setup: the strict x- and w-spanning metrics remain zero for both the reference and all
24 larger-lattice nulls. A broader boundary-state scan then shows that spanning can be
induced by sufficiently broad face-to-face states, but that most overlap-mask spanning is
geometry-driven and reproduced by matched nulls. One limited candidate does survive
a dedicated 50-null follow-up: for a broad face-to-face x-state under the interference
mask, the quasiperiodic reference shows weak but nonzero strict spanning persistence
and larger continuous span scores than the null ensemble. A final cubical-homology

check then shows that this surviving spanning candidate is not handle-rich: it spans
through a comparatively simple foreground with lower b1 + b2 + b3 than the matched
null mean. The bounded conclusion is therefore not that quasiperiodicity amplifies
scalar obstruction in four dimensions, but that in this exploratory configuration-space
benchmark it is associated primarily with reduced nodal-sheet fragmentation and, under
one specific broadened boundary geometry, with limited interference-mask spanning
relative to matched roughness, without evidence of excess topological redundancy.

We present a geometry-first formulation of quantum transport in two-boundary wave systems and develop a unifying obstruction framework separating negotiable mismatch from irreducible nodal constraints. Using a power-family density interpolating between initial and final boundary conditions, we show that the log-transport defect admits an exact decomposition into geometric, reweighting, and boundary-localized terms. We prove that at the self-dual point this defect reduces to a purely geometric obstruction, and we identify Cantor-gap obstruction as the fundamental mechanism underlying hard transport failure in interference-dominated and aperiodic geometries. The framework is representation-independent, analytically controlled, and numerically testable, and it situates transport obstruction alongside universality structures familiar from quantum chaos, quasicrystals, and singular-continuous spectra.

We prove the exact obstruction decomposition proposed by Barker (2026) for the logtransport defect Dα of a two-boundary power-family density ρα ∝ ρ α i ρ 1-α f. The proof is performed entirely within the self-dual dτ-model, in which the gamma function admits the integral representation Γ(z) = ∞-∞ exp zτ-e τ dτ defined on a quasicrystalline lattice generated by the generalized dual method (GDM). This integral provides the saddle-point measure for the two-boundary wave field in the Landaulevel realization of the Berry-Keating Hamiltonian H = xp. Onsager's reciprocal relations applied to the symmetrized velocity v = (u i + u f)/2 and velocity difference δu = u i-u f yield Barker's decomposition as an identity: Dα = A + B + αΞ i + (1-α)Ξ f , where A =-1

This paper develops a reduced transport-obstruction testbed designed to stress the
obstruction decomposition introduced in the companion admissibility manuscript. The
goal is not to simulate quantum measurement in full, but to determine whether the
same decomposition remains diagnostically useful when failure modes are deliberately
separated. A phase-adaptive dual-vortex braid evolves against a deformable background
under six conditions, including a no-crisis control: amplitude attenuation, smoothed
phase null, phase-jitter projector failure, memory wipe, and phase-jitter plus memory
wipe. Across a 20-seed ensemble and an α sweep {0.10,0.20,0.35,0.50,0.65,0.80,0.90},
the full field (A+B)+αΞi+(1−α)Ξf reconstructs the numerically computed transport
defect to machine precision, with worst residuals of order 10−15. Uniform amplitude
attenuation remains essentially invisible to the normalized diagnostic, while phase-jitter
failure produces the largest immediate control-subtracted defect shock and memory wipe
produces the strongest sustained post-crisis deviation. A second normalization by sector
control norms reveals selective excitation: phase corruption is A-dominated, memory
wipe is Ξi-dominated, and the combined crisis inherits both. Control-subtracted sector
maps show that these distinctions are not merely scalar; they have spatial morphology.
Finally, a boundary-swap control shows that the memory signature exchanges Ξi ↔Ξf
under boundary-label exchange, while the phase-jitter signature remains A-dominated.
Thereducedtestbedthereforesupportsaboundedbutsubstantiveclaim: theobstruction
decompositionisnotmerelyexact; itisdiagnosticallygeometry-sensitive, sector-resolved,
and role-aware.

Recent measurements of spatial charge and spin correlations in a strongly interacting two-dimensional Fermi gas have revealed a nonlocal dip in the pair-correlation function below unity, a feature that lies beyond standard mean-field BCS theory and is reproduced by auxiliary-field quantum Monte Carlo (AFQMC). Motivated by the Two-Mode-Field Membrane Theory (TMFMT) and its N-mode extension (NMFMT), we derive a minimal effective pair-field model in which the superconducting/superfluid order parameter is supplemented by a nonlocal inter-pair interaction generated by coupled longitudinal-transverse membrane modes. This yields a closed-form pair-correlation ansatz consisting of a short-range pairing peak and a nonlocal dip term. Using the official Zenodo data accompanying the experiment, we compare this TMFMT/NMFMT-inspired form directly against the published pair-correlation data of Extended Data Fig. S6 and against a BCS-like local baseline. We find that the TMFMT/NMFMT-inspired model outperforms the BCS-like baseline on the key dip observables in five of seven interaction panels, reproduces the experimentally observed g pp < 1 dip in five of seven panels, whereas the BCS-like baseline reproduces it in none, and yields lower mean reduced χ 2 both on the full curves and on the dip region. The results support the view that a nonlocal inter-pair channel is a natural and empirically relevant extension beyond mean-field BCS, while also identifying the interaction regime where the present minimal formulation becomes insufficient.

PubMed [31] is a service of the National Library of Medicine [32] (NLM), USA that includes over 21 million citations for biomedical literatures from MEDLINE, life science journals, and online books. MEDLINE is the NLM's premier bibliographic database and forms the largest component of PubMed containing over 18 million citations dating back to the mid-1960's, covering all fields related to biomedicine . In MEDLINE, the records are indexed with Medical Subject Headings [34] (MeSH) -a NLM's controlled vocabulary thesaurus containing sets of terms naming descriptors in a hierarchical structure that permits searching at various levels of specificity. Until now, PubMed is the richest and most updated source of information about biological data despite its unstructured nature [8]. The result of a PubMed search is a list of citations (including authors, title, source, and often an abstract) to journal articles and an indication of free electronic full-text availability. In addition to this, PubMed provides other services including search filters for clinical queries, links to many other sites providing full-text articles and other related resources and citation matchers. Given a set of query terms, PubMed can identify research articles containing those terms quite efficiently . In spite of these efforts, there is an increasing demand for intelligent Information Retrieval (IR) that requires analyzing the contextual relationship among query terms and judging the relevance of a document in the perspective of this relationship. For example, a simple query containing the string "Alzheimer" roughly translates to the requirement "list all those documents that contain information about Alzheimer disease" for which a simple pattern matching technique based on the occurrence of the query terms in a document is sufficient to decide whether it is relevant to the query or not. However, a more complex query in this domain can be expressed as "metabolic ailments causes Alzheimer disease", which translates to the requirement "list all those documents that contain information about the metabolic ailments that causes Alzheimer disease." This is a much more complex query and requires contextual analysis of the query terms. As observed by Bernstein et al. [9], relating the entities in a query with a specific verb restricts the context of the concepts within text to a large extent. Hence, it is important that the relationships among the biomedical entities present in a text are also extracted and interpreted correctly. Although, PubMed does not support contextual queries, it motivates the upsurge of interest in biomedical text mining to facilitate various degrees of automation in analyzing biological literature like Named Entity Recognition (NER), document classification, terminology extraction, relationship extraction and hypothesis generation [8]. Though, namedentity recognition, document classification and terminology extraction from biomedical text documents have gained reasonable success, reasoning about contents of a text document, however, needs more than identification of the entities present in it. Context of the entities in a document can be inferred from an analysis of the inter-entity relations present in the document. Despite the fact that in addition to the development of many biomedical entity recognizers (e.g., ABNER [23], GENIA tagger [27], etc.) a number of approaches have been proposed to identify biological relations from texts [10, 20, 21, 22,, but most of them focus on mining a fixed set of biological relations occurring with a set of predefined tags. Thus, one of the pre-requisites for the success of these methods is the availability of tagged corpora in which biological entities are already marked. This is far from the reality -as most of the existing textual databases including PubMed do not perform annotations before storing scientific literatures. Moreover, each system is tuned to work with a pre-determined set of relations and does not address the problem of relation extraction in a generic way.

We discuss the general form of the transmission spectrum through a molecular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green function properties into practical graphical rules for assessing beforehand the possible existence of antiresonances in an energy range for a given choice of connecting sites. The analysis is exemplified with a benzene molecule under a hypothetical local gate, which allows one to continuously tune the on-site energy of single atoms, for various connection topologies and gate positions.

We discuss the general form of the transmission spectrum through a molecular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green function properties into practical graphical rules for assessing beforehand the possible existence of antiresonances in an energy range for a given choice of connecting sites. The analysis is exemplified with a benzene molecule under a hypothetical local gate, which allows one to continuously tune the on-site energy of single atoms, for various connection topologies and gate positions.

The Mo framework identifies a geometric invariant C = L^3/T^2 constructed from operationally resolvable spacetime intervals. Previous work established that closure behaves as a conserved spacetime throughput transported along congruence flows, obeying the continuity equation ∇µ(Cu^µ) = 0. In this report we derive a dynamical evolution equation for the closure field itself. Using the Raychaudhuri focusing equation, we show that the logarithmic closure field Ψ = lnC obeys a covariant evolution law driven by shear, vorticity, and spacetime curvature. This relation provides a natural field equation for closure transport in curved spacetime and establishes a dynamical link between spacetime geometry and the closure invariant.

Conceptualization, theory/method development, and implementation are always of great importance and interesting tasks to explore a new dimension in science and technology, which is highly solicited for various functional-driven potential applications (e.g., electronic devices, charge storage devices). Numerous experimental and theoretical studies urge the necessity of a new theory or method to quantify the exact value of charge and energy transport calculations (e.g., mobility, conductivity and quantum capacitance, etc.) through the appropriate processes and methods. With this motivation, the entropy-ruled charge dynamics method has been recently proposed, which unifies the band and hopping transport mechanism via the quantum-classical transition analogy. Here, the energy (in terms of chemical potential) scaled entropy has a direct proportion with the density of states (DOS), and hence, it is termed as DOS proportion. This proportion principally acts as a key descriptor for charge transport (CT) calculations in both molecular and materials systems, which is directly connected with all CT quantities like mobility, conductivity, current density, etc. In this perspective, the breakdown of electron–hole symmetrical transport is discussed, and the possibility of electron–hole symmetrical-to-asymmetrical transition has been addressed with respect to the correlation effect between the total entropy and the chemical potential of a given system. Importantly, the charge disorder-associated Coulombic potential formalism is proposed, and its impact on the DOS proportion is described. The inverse symmetrical behavior between the energy gap and electronic states coupling (i.e., strength of orbital level interactions) is discussed, which helps to provide the charge relaxation information about any ordered and disordered molecular/material systems. Besides that, this perspective explains a unique nature of the entropy-ruled method for the entire transport range from delocalized band to localization (or hopping) transport at different physical limits. The validity and limitations of Einstein’s relation and Boltzmann approach for mobility calculation are discussed with suitable thermodynamic conditions for disordered molecules and periodic systems. Finally, the futuristic scope and expected progress are addressed for correlated electron dynamical systems and devices. It is well-noted that the new DOS proportion and related entropy-ruled transport formalism are fundamentally more important for nurturing semiconducting science and technology toward a new era.

The absorption and emission spectra of transitions between a localized level and a two-dimensional electron gas, subjected to a weak magnetic field, are calculated analytically. Adopting the Landau level bosonization technique developed in previous papers, we find an exact expression for the relative intensities of spectral lines. Their envelope function, governed by the interaction between the electron gas and the core hole, is reminescent of the famous Fermi edge singularity, which is recovered in the limit of a vanishing magnetic field.

We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylinders or rectangles. Under OBCs the long time transition probabilities (LPs) also display asymmetries for certain graphs, as a function of their particular sizes. Interestingly, these effects do not show up in the marginal distributions, obtained by summing the LPs along one direction.

The problem of resonant tunneling through a quantum dot weakly coupled to spinless Tomonaga-Luttinger liquids has been studied. We compute the linear conductance due to sequential tunneling processes upon employing a master equation approach. Besides the previously used lowest-order golden rule rates describing uncorrelated sequential tunneling processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects can be important. Focusing mainly on the temperature dependence of the peak conductance, we discuss the relation of these findings to previous theoretical and experimental results.

Anisotropy of the transport properties (electrical resistivity, ρ(T), thermoelectric power, S(T), and thermal conductivity, κ(T)) of the Al76Co22Ni2 (Y-Al–Ni–Co), o-Al13Co4 and T-Al72.5Mn21.5Fe6.0 complex metallic alloys was investigated experimentally. These compounds belong to the class of approximants in decagonal quasicrystals phases with stacked-layer crystallographic structure and enabled us to study the evolution of transport properties with increasing structural complexity and the unit cell size. For Y-Al–Ni–Co and o-Al13Co4, the anisotropic electronic transport coefficients were analyzed theoretically by Boltzmann transport theory and ab initio calculated anisotropic Fermi surface. The non-metallic anisotropic electrical resistivity of the T-Al72.5Mn21.5Fe6.0 may be analyzed in a semi-quantitative way by the theory of quantum transport of slow charge carriers.

A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in the other one, and vice versa. We apply this duality relation to investigate transport and rectification in ratchet potentials: From the linear mobility we infer ground-state delocalization for weak dissipation. We report reversals induced by adiabatic driving and temperature in the ratchet current and its dependence on the potential shape.

Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of antenna structures where the light is captured and inner structures (reaction centers) where the excitation is transferred. Antennae often display distinguished coherent features: their eigenstates can be separated, with respect to the transfer of excitation, in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In absence of disorder superradiant states have an enhanced coupling strength to the RC, while subradiant ones are basically decoupled from it. Disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. We consider the problem of finding the maximal excitation transfer efficiency as a function of the RC energy and the disorder strength, first in a paradigmatic threelevel system and then in a realistic model for the light-harvesting complex of purple bacteria. Specifically, we focus on the case in which the excitation is initially on a subradiant state, showing that the optimal disorder is of the order of the superradiant coupling. We also determine the optimal detuning between the initial state and the RC energy. We show that the efficiency remains high around the optimal detuning in a large energy window, proportional to the superradiant coupling. This allows for the simultaneous optimization of excitation transfer from several initial states with different optimal detuning.

Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of antenna structures where the light is captured and inner structures (reaction centers) where the excitation is transferred. Antennae often display distinguished coherent features: their eigenstates can be separated, with respect to the transfer of excitation, in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In absence of disorder superradiant states have an enhanced coupling strength to the RC, while subradiant ones are basically decoupled from it. Disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. We consider the problem of finding the maximal excitation transfer efficiency as a function of the RC energy and the disorder strength, first in a paradigmatic three-level system and then in a realistic model for the light-harvesting complex of ...

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: i) weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: i) weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.

We report measurements of resistance oscillations in micron-scale antidots in both the integer and fractional quantum Hall regimes. In the integer regime, we conclude that oscillations are of the Coulomb type from the scaling of magnetic field period with the number of edges bound to the antidot. Based on both gate-voltage and field periods, we find at filling factor ν = 2 a tunneling charge of e and two charged edges. Generalizing this picture to the fractional regime, we find (again, based on field and gate-voltage periods) at ν = 2/3 a tunneling charge of (2/3)e and a single charged edge.

We discuss the universal spin dynamics in quasi one-dimensional systems including the real spin in narrow-gap semiconductors like InAs and InSb, the valley pseudospin in staggered single-layer graphene, and the combination of real spin and valley pseudospin characterizing single-layer transition metal dichalcogenides (TMDCs) such as MoS2, WS2, MoSe2, and WSe2. All these systems can be described by the same Dirac-like Hamiltonian. Spin-dependent observable effects in one of these systems thus have counterparts in each of the other systems. Effects discussed in more detail include equilibrium spin currents, current-induced spin polarization (Edelstein effect), and spin currents generated via adiabatic spin pumping. Our work also suggests that a long-debated spin-dependent correction to the position operator in single-band models should be absent.

When a single photon traverses a cloud of 2-level atoms, the average time it spends as an atomic excitation-as measured by weakly probing the atoms-can be shown to be the spontaneous lifetime of the atoms multiplied by the probability of the photon being scattered into a side mode. A tempting inference from this is that an average scattered photon spends one spontaneous lifetime as an atomic excitation, while photons that are transmitted spend zero time as atomic excitations. However, recent experimental work by some of us [PRX Quantum 3, 010314 (2022)] refutes this intuition. We examine this problem using the weak-value formalism and show that the time a transmitted photon spends as an atomic excitation is equal to the group delay, which can take on positive or negative values. We also determine the corresponding time for scattered photons and find that it is equal to the time delay of the scattered photon pulse, which consists of a group delay and a time delay associated with elastic scattering, known as the Wigner time delay. This work provides new insight into the complex and surprising histories of photons travelling through absorptive media.

In an optical superlattice of triple wells, containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species, yet avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the inter-species overlap during passage can be tuned, making possible controlled large-scale interaction-induced change of internal states.

In an optical superlattice of triple wells, containing two mutually interacting atom species in adjacent wells, we show that one species can be transported through the positions of the other species, yet avoiding significant overlap and direct interaction. The transfer protocol is optimized to be robust against missing atoms of either species in any lattice site, as well as against lattice fluctuations. The degree and the duration of the inter-species overlap during passage can be tuned, making possible controlled large-scale interaction-induced change of internal states.

Electrons moving in graphene behave as massless Dirac fermions, and they exhibit fascinating low-frequency electrical transport phenomena. Their dynamic response, however, is little known at frequencies above one terahertz (THz). Such knowledge is important not only for a deeper understanding of the Dirac electron quantum transport, but also for graphene applications in ultrahigh speed THz electronics and IR optoelectronics. In this paper, we report the first measurement of high-frequency conductivity of graphene from THz to mid-IR at different carrier concentrations. The conductivity exhibits Drude-like frequency dependence and increases dramatically at THz frequencies, but its absolute strength is substantially lower than theoretical predictions. This anomalous reduction of free electron oscillator strength is corroborated by corresponding changes in graphene interband transitions, as required by the sum rule. Our surprising observation indicates that many-body effects and Dirac fermion-impurity interactions beyond current transport theories are important for Dirac fermion electrical response in graphene.

We investigate the quantum walk of two interacting bosons of different mass in a one dimensional lattice. By varying the inter-particle interaction strength we show distinct features in the quantum walk of two particles for different initial states. When the walkers are initially on the same site, both the heavy and light particles perform independent particle quantum walks for small interaction. However, stronger interactions lead to the quantum walk of the repulsively bound pair of atoms. For a different initial state when the walkers are a few sites apart initially, the heavy particle performs quantum walk almost independently and the light particle shows reflected and transmitted components across the heavy particle for small interactions. After a critical interaction strength, the light particle wave function ceases to penetrate through the heavy particle. However, when the quantum walkers are initially kept at the edges of the lattice, then the interaction facilitates the comp...

High transmissivity, ferromagnet-superconductor thin film nanocontacts are studied experimentally. Compared to nonmagnetic metal-superconductor contacts, Andreev reflection is strongly suppressed due to the spin polarization of conduction electrons in the ferromagnet. This effect is used to measure both the transparency of the interface and spin polarization of the direct current in the ferromagnet in contrast to the spin polarization of the tunneling current previously measured in ferromagnet-insulatorsuperconductor systems. [S0031-9007(98)

A semi-classical electrodynamical model is derived to describe the electrical transport along graphene, based on the modified Boltzmann transport equation. The model is derived in the typical operating conditions predicted for future integrated circuits nano-interconnects, i.e., a low bias condition and an operating frequency up to 1 THz. A generalized non-local dispersive Ohm's law is derived, which can be regarded as the constitutive equation for the material. The behavior of the electrical conductivity is studied with reference to a 2D case (the infinite graphene layer) and a 1D case (the graphene nanoribbons). The modulation effects of the nanoribbons' size and chirality are highlighted, as well as the spatial dispersion introduced in the 2D case by the dyadic nature of the conductivity.