Barrier parameters and superconducting gap structure of the etched surface of Y−Ba−Cu−O by scanning tunnelling spectroscopy

Summary Using a scanning tunnelling microscope, the tunnelling currentvs. voltage is measured between a gold tip and the chemically etched (001) surface of YBa₂Cu₃O _x crystals at room temperature. The tunnelling barrier height and thickness are derived by modelling the system in the normal state as a conventional N-I-N junction. TheI(V) andG(V) curves are computed for the same junction in the superconducting state (N-I-S junction). The predicted gap structure for a single BCS-Dynes-like gap is simple and has low zero-bias conductance. The complexG(V) spectra measured belowT _c on the etched junctions with ∼ 50% zero-bias conductance suggest a possible multilayer contribution in the unit cell. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

The observer-based synchronization and parameter estimation of a class of chaotic system via a single output

The conductance of a single molecule transport junction comprising anthracene molecular junction (AMJ) with fullerene as alligator clips was investigated using ab-initio density functional theory (DFT) in the Landauer–Imry regime of coherent tunnelling transport. In our previous research, we have already calculated the electrical transport properties of aromatic molecules with thiol, amine, hydroxyl and selenol end groups concluding the exceptional assistance in the formation of robust molecular junctions. In this article, we have presented the suitability of fullerene anchoring in coupling anthracene molecule with gold electrodes. AMJ with boron-20 (B-20) and C-20 alligator clips exhibited strongest conduction in contrast to nitrogen, oxygen, fluorine and neon alligator clips.     

Negative tunnelling magnetoresistance in spin filtering magnetic junctions with spin-orbit coupling

We present theoretical calculations of spin transport in spin filtering magnetic tunnelling junctions based on the Landauer-Buttiker formalism and taking into account the spin-orbit coupling(SOC).It is shown that spin-flip scattering induced by SOC is stronger in parallel alignment of magnetization of the ferromegnet barrier(FB) and the ferromagnetic electrode than that in antiparallel case.The increase of negative tunnelling magnetoresistance with bias is in agreement with recent experimental observation.     

Transport properties of poly(GACT)-poly(CTGA) deoxyribonucleic acid: A ladder model approach

In this paper, based on the tight-binding Hamiltonian model and within the framework of a generalized Green’s function technique, the electronic conduction through the poly(GACT)-poly(CTGA) DNA molecule in SWNT/DNA/SWNT structure has been numerically investigated. In a ladder model, we consider DNA as a planar molecule containing M cells and four further sites (two base pair sites and two backbone sites) in each cell, sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT) as the electrodes. Having relied on Landauer formalism, we focussed on studying the current-voltage characteristics of DNA, the effect of the coupling strength of SWNT/DNA interface and the role of tube radius of nanotube contacts on the electronic transmission through the foregoing structure. Finally, a characteristic time was calculated for the electron transmission, which measures the delay caused by the tunnelling through the SWNT/DNA interface. The results clearly show that the calculated characteristic time and also the conductance of the system are sensitive to the coupling strength between DNA molecule and nanotube contacts.     

The electron transport characters in a nanostructure with the periodic magnetic-electric barriers

This paper detailedly studies the transmission probability, the spin polarization and the conductance of the ballistic electron in a nanostrueture with the periodic magnetic-electric barriers These observable quantities are found to be strongly dependent not only on the magnetic configuration, the incident electron energy and the incident wave vector, but also on the number of the periodic magnetic-electric barriers The transmission coefficient and the spin polarization show a periodic pattern with the increase of the separation between two adjacent magnetic fields, and the resonance splitting increases as the number of periods increases. Surprisingly, it is found that a polarization can be achieved by spin-dependent resonant tunnelling in this structure, although the average magnetic field of the structure is zero.     

The electron transport characters in a nanostructure with the periodic magnetic-electric barriers

This paper detailedly studies the transmission probability, the spin polarization and the conductance of the ballistic electron in a nanostructure with the periodic magnetic-electric barriers. These observable quantities are found to be strongly dependent not only on the magnetic configuration, the incident electron energy and the incident wave vector, but also on the number of the periodic magnetic-electric barriers. The transmission coefficient and the spin polarization show a periodic pattern with the increase of the separation between two adjacent magnetic fields, and the resonance splitting increases as the number of periods increases. Surprisingly, it is found that a polarization can be achieved by spin-dependent resonant tunnelling in this structure, although the average magnetic field of the structure is zero.     

On the calculation of the magnetoresistance of tunnel junctions with parallel paths of conduction

At the interfaces between the metallic electrodes and barrier in magnetic tunnel junctions it is possible for localized states to form which are orthogonal to the itinerant states for the junction, as well as resonant states that can form at the interfaces. These states form highly conducting paths across the barrier when their orbitals point directly into the barrier; these paths are in addition to those formed by the itinerant states across the entire junction. Most calculations of transport in magnetic tunnel junctions are made with the assumptions that the transverse momentum of the tunnelling electrons is conserved, in which case the itinerant electron states remain orthogonal to localized states. In principle it is possible to include diffuse scattering in both the bulk of the electrodes and the barrier so that the transverse momentum is not conserved, as well as the processes that couple localized states at the electrode-barrier interface to the itinerant states in the bulk of the electrodes. However, including these effects leads to lengthy calculations. Therefore, to assess the conduction across the barrier through the localized states that exist in parallel to the itinerant states we propose an approximate scheme in which we calculate the conductance of only the barrier region. While we do not take explicit account of either of the effects mentioned above, we do calculate the tunnelling through all the states that exist at the electrode-barrier interfaces by placing reservoirs directly across the barriers. To calculate the current and magnetoresistance for magnetic tunnel junctions (the junction magnetoresistance (JMR)) we have used the lattice model developed by Caroli et al. The propagators, density of states and hopping integrals entering the expressions for the current are determined by using the spin polarized scalar-relativistic screened Korringa-Kohn-Rostoker method that has been adapted to layered structures. By using vacuum as the insulating barrier we have determined with no adjustable parameters the JMR in the linear response region of tunnel junctions with fcc Co(100), fccNi(100) and bcc Fe(100) as electrodes. The JMR ratios that we find for these metal/vacuum/metal junctions are comparable with those measured with alumina as the insulating barrier. For vacuum barriers we find that tunnelling currents have minority- spin polarization whereas the tunnelling currents for th se electrodes have been observed to be positively (majority) polarized for alumina barriers and minority polarized for SrTiO 3 barriers. In addition to determining the JMR ratios in linear response we have also determined how the magnetoresistance of magnetic tunnel junctions varies with a finite voltage bias applied across the junction. In particular we have found how the shape of the potential barrier is altered by the applied bias and how this affects the current. Comparisons with data as they become available will eventually determine whether our approximate scheme or the ballistic Landauer-Büttiker approach is better able to represent the features of the electronic structure that control tunnelling in magnetic tunnel junctions.     

Tunneling through a disordered potential barrier

Tunnelling through a weakly disordered potential barrier is studied analytically. A perturbative approach is developed to calculate all statistical moments of the tunnelling transmission coefficient, and its probability distribution function. It is shown that on average disorder enhances the tunnelling conductance, resistance, and the coherent component of the transmitted field.On leave from the Institute of Low-Temperature Physics and Engineering, Kharkov 310164, Ukraine.     

Extension to arbitrary barriers of the Büttiker-Landauer characteristic barrier interaction times

In a series of papers Büttiker and Landauer used various approaches to derive characteristic times describing the interaction of particles with a rectangular barrier (more general barriers were treated only within the WKB approximation). We generalize their results to arbitrary barriers and present calculated characteristic times for a selection of frequently used barrier shapes. We find that, even for a rectangular barrier, two of the approaches lead to corresponding characteristic times that can be quite different, particularly at low energy. Moreover, the identification of one of the characteristic times with the well known “dwell” time is shown not to hold in general, although it is certainly correct for a rectangular barrier.     

The Büttiker-Landauer model generalized

Büttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V ₀(x)+V ₁(x)cos t. In the process, we confirm that Büttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.This paper is dedicated to E. G. D. Cohen.     

Electron transport through SWNT/<Emphasis Type="Italic">trans</Emphasis>-PA/SWNT structure (the role of solitons): A t-matrix technique

Using a tight-binding model and a transfer-matrix technique, we numerically investigate the effects of the coupling strength and the role of solitons on the electronic transmission through a system in which trans-polyacetylene (trans-PA) molecule is sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT). We rely on Landauer formalism as the basis for studying the conductance properties of this system. Our calculations show that the solitons play an important role in the response of this system causing a large enhancement in the conductance. Also our results suggest that the conductance is sensitive to the CNT/molecule coupling strength.      

Enhanced spin polarization in an asymmetric magnetic graphene superlattice

The authors investigate the spin-resolved transport through an asymmetrical magnetic graphene superlattice (MGS) consisting of the periodic barriers with abnormal one in height. To quantitatively depict the asymmetrical MGS, an asymmetry factor has been introduced to measure the height change of the abnormal barrier. It is shown that the spin filter effect is strongly enhanced by the barrier asymmetry both in the Klein and the classical tunneling regimes. In the presence of abnormal barrier, the conductance with certain spin direction is suppressed with respect to different tunneling regimes, and thus high spin polarization with opposite sign can be achieved.     

Tunnelling through randomly inhomogeneous barriers as a special problem of the scattering theory

The tunnelling of electrons through an inhomogeneous delta barrier is considered. The strength of the barrier is defined as a function oscillating around a constant mean value along a plane. Owing to deviations from this value, the tunnelling through such a delta barrier has to be interpreted as a scattering. A simple model is discussed when circular windows of a given radius b representing themselves delta barriers of a given strength γ₀ are embedded in a homogeneous delta barrier defined with another strength . When the centers of the windows are distributed randomly in the barrier plane, the potential energy of the electrons is a random function of two space coordinates. The perpendicular incidence is discussed with emphasis on the angular probability density of the tunnelled electrons. The derivation of the angular probability density proves that three basic quantum-mechanical phenomena can be described by one simple formula: tunnelling, diffraction and scattering.     

Electronic transport for armchair graphene nanoribbons with a potential barrier

We theoretically investigate the electronic transport properties through a rectangular potential barrier embedded in armchair-edge graphene nanoribbons (AGNRs) of various widths. Using the Landauer formula and Dirac equation with the continuity conditions for all segments of wave functions at the interfaces between regions inside and outside the barrier, we calculate analytically the conductance and Fano factor for the both metallic and semiconducting AGNRs, respectively. It is shown that, by some numerical examples, at Dirac point the both types of AGNRs own a minimum conductance associated with the maximum Fano factor. The results are discussed and compared with the previous relevant works.     

Landauer–Büttiker and Thouless Conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.     

Co-tunneling of the charge through a 2-D electron island

A double barrier Single Electron Transistor is realized in two dimensions by confining the 2-D electron gas of a GaAs/GaAlAs heterojunction to a small island by means of Schottky gates. Two gates provide adjustable tunnel barriers and a central gate controls the electron number in the island. The island has small single-particle energy level spacing and forms a metallic island. Periodic conductance oscillations characteristic of Coulomb blockade are observed when the central gate voltage is varied. The ability to vary the tunnel conductance allows us to study the basic physics of the Coulomb blockade: our results show that the quantum charge fluctuation mechanism which limits the tunneling blockade at low temperature is of second order in tunnel barrier transparencies in agreement with the charge Macroscopic Quantum Tunneling (q-MQT) or co-tunneling model.     

Spin-flip effect on electrical transport in magnetic quantum wire systems

We investigate the spin-flip effect on electronic transport in a nanostructure composed of two nonmagnetic (NM) leads separated by a periodic spacer. The spacer is composed of one-dimensional heterostructure formed by a sequence of magnetic (A) and nonmagnetic (B) sites periodically juxtaposed (as in a typical periodic quantum dot (QD)). The calculations are based on the tight-binding model and transfer matrix method, which compute the current–voltage characteristic within the Landauer–Büttiker formalism. Our main goal is to assess the contribution of the spin-flip scattering to the transport properties of such systems. The spin-dependent transport behavior can be controlled via a gate magnetic field and an applied voltage in the ballistic regime. Our results show that the conductance strongly depends on the configurations of the magnetic QD. The application of the predicted results may be useful in designing spin-valve devices, such as spin-polarized molecular transistors.     

Tunnelling through two barriers

Recent theoretical studies of the tunnelling through two opaque barriers claim that the transit time is independent of the barrier widths and of the separation distance between the barriers. Such a result is based on the use of the stationary phase method and the hypothesis of a single transmitted wave packet. In this Letter, we propose an alternative treatment based on a multiple peaks decomposition of the transmitted wave. We observe, that if multiple reflections are allowed for correctly (infinite peaks) the transit time between the barriers appears exactly as expected.     

Spin-polarization and magnetoresistance in graphene-based resonant-tunnelling structures

Spin-dependent transport of relativistic electrons through graphene based double barrier (well) structures with ferromagnetic electrodes have been theoretically investigated. Electron transmission with different spin states is strongly influenced by the incident wave vector, the height (depth) of the barrier and the separation between them. When the angle of the incident electrons is varied from zero to ±π/2, spin polarization varies from zero to 100% with characteristic oscillations that indicate spin anisotropy. Due to Klein tunnelling, spin-polarization is always zero for normal incident electrons; high spin-polarization only occurs at large incident angles. Because the resonance features in the spin-dependent transmission result from resonant electron states in wells or hole states in barriers, the conductance can reach e²/h in this resonant-tunnelling structure.     

Calculating thermopower due to fluctuation-assisted tunnelling with application to carbon nanotube ropes

We show how Sheng's theory of fluctuation-assisted tunnelling can be used to calculate thermopower due to the presence of quantum mechanical tunnelling barriers. For a hole-like situation, this calculated thermopower behaviour increases approximately linearly with increasing temperature (commencing from zero in the zero temperature limit) until a knee is reached, after which the thermopower continues to increase linearly but with a reduced slope. In Sheng's theory, the amplitude for the barrier fluctuations increases with increasing temperature and the knee occurs when the thermal fluctuations become comparable to the magnitude of the tunnelling barriers. Interestingly, this thermopower behaviour compares quite favourably with that measured for systems of metallic single-walled carbon nanotubes (SWCNs) and, in particular, the knee seen in the temperature dependence of the carbon nanotube thermopower data at T∼100 K arises naturally in our calculation. For a system of carbon nanotubes, tunnelling barriers could occur either between individual carbon nanotubes or else due to defects within the carbon nanotubes.