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Topological materials usually possess protected gapless states in either the boundary or bulk, exhibiting various properties such as spin-momentum locking, Klein tunneling, Fermi arcs and so on. Database searches using symmetry data at high-symmetry points have catalogued thousands of topological materials revealing a magnitude of band nodes (BNs) at high-symmetry points or lying within high-symmetry lines/planes. A complete mapping from symmetry data (namely, representation of little group) in any BN to the k ⋅ p model characterizing low-energy Hamiltonian around the BN (and from the k ⋅ p model to concrete BN, inversely), is expected to complete the characterization of all BNs and gapless states. Here we first review recent progress on classifying BNs by systematically and automatically constructing k ⋅ p models based on recently completed tabulation of all irreducible (co-)representation matrices of little groups of the 1651 magnetic space groups. As one indispensable input in constructing a symmetry-allowed and generic k ⋅ p model, the expansion order, has been carefully and systematically truncated for any BN to a reasonable nonzero integer, by comparing the emanating nodal structure (ENS, including nodal point, nodal line and nodal surface) near the BN obtained by the explicitly constructed k ⋅ p model and that by pure symmetry analysis using compatibility relations (CRs). Owing to the progress, we are able to summarize all 25 different configurations of ENS near BN required by CRs, provide a complete mapping from k ⋅ p model to its realization around BN, and the corresponding ENS by CRs in an accessible file, and also reveal the protection mechanism of additional nodal lines that escape conventional analysis by CRs and is only predictable by constructing k ⋅ p model. The symmetry-based classification results on all BNs could facilitate large-scale materials prediction and hold promise for realizing topological semimetals suitable for device applications. [ABSTRACT FROM AUTHOR]

In light of the significance of non-commutative quaternionic algebra in modern physics, this study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing quaternionic wave function, we rewrite the Klein–Gordon equation in extended quaternionic form that includes scalar and the vector fields. Because quaternionic fields are non-commutative, the quaternionic Klein–Gordon equation provides three separate sets of the probability density and probability current density of relativistic particles. We explore the significance of these probability densities by determining the reflection and transmission coefficients for the quaternionic relativistic step potential. Furthermore, we also discuss the quaternionic version of the oscillatory, tunnelling, and Klein zones for the quaternionic step potential. The Klein paradox occurs only in the Klein zone when the impacted particle's kinetic energy is less than 0 − m 0 c 2 . Therefore, it is emphasized that for the quaternionic Klein paradox, the quaternionic reflection coefficient becomes exclusively higher than value one while the quaternionic transmission coefficient becomes lower than zero. [ABSTRACT FROM AUTHOR]

This paper focuses on additional inspections concerning the fermionic sector of the Standard Model Extension (SME). In this context, our main effort in this contribution is to investigate effects of Lorentz-symmetry violation (LSV) on the Klein Paradox, the Zitterbewegung and its phenomenology in connection to Condensed Matter Physics, Atomic Physics, and Astrophysics. Finally, we discuss a particular realization of LSV in the Dirac equation, considering an asymmetry between space and time due to a scale factor present in the linear momentum of the fermion, but which does not touch its time derivative. We go further and extend the implications of this asymmetry in the situation the scale factor becomes space–time dependent to compute its influence on the kinematics of the Compton effect with the extended dispersion relation for the fermion that scatters the photon. • Additional inspections concerning the fermionic sector of the SME. • Effects of LSV on the Klein Paradox, the Zitterbewegung and its phenomenology. • Dirac equation with a space and time asymmetry due to a scale factor in the momentum. • The implications of the Compton effect with a space-time dependent scale factor. [ABSTRACT FROM AUTHOR]

We theoretically investigate the electronic transport and Klein tunneling in AA-stacked bilayer graphene (AA-BLG) encapsulated by dielectric materials. Using the four-band continuum model, we evaluate the transmission and reflection probabilities along with the respective conductances. We find that the interlayer mass-term difference induced by the dielectric materials opens a gap in the energy spectrum and couples the upper and lower Dirac cones in AA-BLG. This cone coupling induces an inter-cone transport that is asymmetric with respect to the normal incidence in the presence of the asymmetric mass-term. The energy spectrum of the gapped AA-BLG exhibits electron-hole asymmetry that is reflected in the associated intra- and inter-cone transport channels. We also find that even though Klein tunneling exists in gated and biased AA-BLG, it is precluded by the interlayer mass-term difference and instead Fabry-Pérot resonances appear. [ABSTRACT FROM AUTHOR]

Incorporating relativistic physics into quantum tunneling can lead to exotic behavior such as perfect transmission through Klein tunneling. Here, we probed the tunneling properties of spin-momentum-locked relativistic fermions by designing and implementing a tunneling geometry that uses nanowires of the topological Kondo insulator candidate samarium hexaboride. The nanowires are attached to the end of scanning tunneling microscope tips and used to image the bicollinear stripe spin order in the antiferromagnet Fe1.03Te with a Neel temperature of about 50 kelvin. The antiferromagnetic stripes become invisible above 10 kelvin concomitant with the suppression of the topological surface states in the tip. We further demonstrate that the direction of spin polarization is tied to the tunneling direction. Our technique establishes samarium hexaboride nanowires as ideal conduits for spin-polarized currents. [ABSTRACT FROM AUTHOR]

In this work, we investigate the transport properties of devices made of graphene strained heterochannels. Due to the effects of local strain on the band structure, the Klein tunneling is strongly suppressed and transport gaps can appear in the unstrained/strained graphene junctions. The gap regions can be modulated in k-space and in energy by strain and doping engineering, respectively. We show that these effects can be exploited to achieve a strong negative differential conductance (NDC) in single gate-induced barrier structures and in p-n junctions. When the local strain is suitably applied, the peak-to-valley ratio (PVR) of the current-voltage characteristics can be as high as a few hundred. The dependence of NDC effect on structure parameters is investigated systematically. In particular, a strong NDC is obtained in single barrier structures with large strained region, while the PVR is not strongly sensitive to the transition length in p-n junctions. [ABSTRACT FROM AUTHOR]

In this paper, we calculate tree-level currents of created particles in strong background electric fields in 4D QED for various initial states. Namely, we do that in pulse background for initial vacuum and thermal states at past infinity. In both cases, we find that the current grows linearly with the length of the pulse with coefficients of proportionality containing the characteristic Schwinger's factor. For the constant electric field background, we calculate the current for several different initial states. We observe that in such a case the current is either zero or linearly divergent. We explain the reason for such a behavior and compare the situation in ordinary and scalar QED. Finally, we calculate the current in two-dimensional situation in the presence of such settings when the so-called Klein paradox can be observed. [ABSTRACT FROM AUTHOR]

The problem of conduction electron scattering by inhomogeneous crystal lattice strains is addressed using a tight-binding formalism and the differential geometric treatment of deformations in solids. In this approach, the relative positions of neighboring atoms in a strained lattice are naturally taken into account, even in the presence of crystal dislocations, resulting in a fully covariant Schrcodinger equation in the continuum limit. Unlike previous work, the developed formalism is applicable to cases involving purely elastic strains as well as discrete and continuous distributions of dislocations-in the latter two cases, it clearly demarcates the effects of the dislocation strain field and core. It also differentiates between elastic and plastic strain contributions, respectively. The electrical resistivity due to the strain field of edge dislocations is then evaluated and the resulting numerical estimate for Cu shows good agreement with reported experimental values. This indicates that the electrical resistivity of edge dislocations in metals is not entirely due to the core, contrary to current models. Application to the study of strain effects in constrained quantum systems is also discussed. [ABSTRACT FROM AUTHOR]

Tunneling plays an essential role in many branches of physics and has found important applications. It is theoretically proposed that Klein tunneling occurs when, under normal incidence, quasiparticles exhibit unimpeded penetration through potential barriers independent of their height and width. We created a phononic heterojunction by sandwiching two types of artificial phononic crystals with different Dirac point energies. The direct observation of Klein tunneling as shown by the key feature of unity transmission is demonstrated. Our experiment reveals that Klein tunneling occurs over a broad band of acoustic frequency. The direct observation of Klein tunneling in phononic crystals could find applications in signal processing, supercollimated beams, and communications. [ABSTRACT FROM AUTHOR]

This work considers the creation of electron-positron pairs from intense electric fields in vacuum, for arbitrary temporal field variations. These processes can be useful to study quantum vacuum effects with ultra-intense lasers. We use the quantized Dirac field to explore the temporal Klein model. This model is based on a vector potential discontinuity in time, in contrast with the traditional model based on a scalar potential discontinuity in space. We also extend the model by introducing a finite time-scale for potential variations. This allows us to study the transition from a singular electric field spike, with infinitesimal duration, to the opposite case of a static field where the Schwinger formula would apply. The present results are intrinsically non-perturbative. Explicit expressions for pair-creation as a function of the potential time-scales are derived. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox model, in contrast with the time symmetry breaking of the temporal Klein model.

We study the interconversion between photons and phonons coupled via radiation pressure in artificial Dirac materials realized by a honeycomb array of optomechanical cells. In particular, we analyze the chiral tunneling of (photon-phonon) polaritons through an oscillating planar barrier. While a static barrier accommodates constructively interfering optical or mechanical waves leading to photon or phonon transmission, an oscillating barrier allows for inelastic scattering that causes sideband excitations and interference effects which, in turn, may suppress or revive the light-sound interconversion. [ABSTRACT FROM AUTHOR]

It is pointed out that the authors of the paper Li et al (2020 New J. Phys. 22 113019) have misinterpreted the Dirac equation by not taking into account that it describes not only electrons but also positrons.

The main purpose of the paper Li et al (2020 New J. Phys. 22 113019) is to determine the common properties of electronic waves and electromagnetic waves. The electronic Maxwell’s equations are identical to the Dirac equation, describing both electrons and positrons.

We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model (with an arbitrary nonlinearity and in arbitrary dimension) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and qudit states in the theory of quantum computing. We show the relation of ±2wi eigenvalues of the linearization at a solitary wave, Bogoliubov SU(1; 1) symmetry, and the existence of bi-frequency solitary waves. We show that the spectral stability of these waves reduces to spectral stability of usual (one-frequency) solitary waves. [ABSTRACT FROM AUTHOR]

Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes, the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn′n- or npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case, the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in. [ABSTRACT FROM AUTHOR]

Due to Klein tunneling, electrostatic confinement of electrons in graphene is not possible. This hinders the use of graphene for quantum dot applications. Only through quasi-bound states with finite lifetime has one achieved to confine charge carriers. Here, we propose that bilayer graphene with a local region of decoupled graphene layers is able to generate bound states under the application of an electrostatic gate. The discrete energy levels in such a quantum blister correspond to localized electron and hole states in the top and bottom layers. We find that this layer localization and the energy spectrum itself are tunable by a global electrostatic gate and that the latter also coincides with the electronic modes in a graphene disk. Curiously, states with energy close to the continuum exist primarily in the classically forbidden region outside the domain defining the blister. The results are robust against variations in size and shape of the blister which shows that it is a versatile system to achieve tunable electrostatic confinement in graphene. [ABSTRACT FROM AUTHOR]

We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms, such as those arising from electromagnetic fields, we develop some abstract discretization theory and provide estimates in fractional order Sobolev spaces for finite element systems. Eigenmode convergence is proved, as well as optimal convergence orders, assuming a flat background metric on a periodic domain. [ABSTRACT FROM AUTHOR]

Neutron cross section calculations for 136Ce(n, 2n)135Ce, 138Ce(n, 2n)137Ce, 140Ce(n, 2n)139Ce, 142Ce(n, 2n)141Ce, 142Nd(n, 2n)141Nd, 144Nd(n, 2n)143Nd, 146Nd(n, 2n)145Nd, 148Nd(n, 2n)147Nd, and 150Nd(n, 2n)149Nd were done in the incident energy range from 10 to 20 MeV. The calculations were performed using three codes TALYS-1.6 for two-component Exciton model, EMPIRE-3.2 Malta for Exciton model, and ALICE/ASH for the Geometry-Dependent Hybrid (GDH) model. The results of model calculations were compared with the available experimental data and also with the evaluated data in the TENDL-2015 (based on the modified TALYS code), ENDF/B-VII.1 libraries. The calculated cross section data were compared with the available experimental data obtained from EXFOR and also compared with semiempirical formulas around 14-15 MeV. The results of model calculation were found to be in good agreement with the experimental data given in literature and semiempirical data around 14-15MeV. [ABSTRACT FROM AUTHOR]

The results of measurements of the differential cross section for elastic deuteron-proton scattering at the energy of 700 MeV per nucleon that were performed at the internal target station of the nuclotron at the Joint Institute for Nuclear Research (JINR, Dubna) are presented. These data were obtained at angles in the range between 70° and 120° in the c.m. frame. The angular dependence obtained in this way is compared with world-averaged data at similar energies and with the results of theoretical calculations performed within the relativistic theory of multiple scattering. [ABSTRACT FROM AUTHOR]

Weyl fermions are characterized by definite helicity, a relation between orientation of the spin and momentum. We investigate controlling helicity utilizing helicity-dependent dynamics due to separation between the Weyl points. We study transport properties of a multilayer structure formed by piece-wise constant scalar and vector potentials and separations between the Weyl points. We show that the transmission spectrum is determined by a relation between the electron momentum and momenta corresponding to Klein tunneling, when the barrier is fully transparent regardless of its width. The helicity dependence of the “Klein momenta” is shown to yield a helicity filtering effect. [ABSTRACT FROM AUTHOR]

Electron-electron interactions are the fastest processes in materials, occurring on femtosecond to attosecond timescales, depending on the electronic band structure of the material and the excitation energy. Such interactions can play a dominant role in light-induced processes such as nano-enhanced plasmonics and catalysis, light harvesting, or phase transitions. However, to date it has not been possible to experimentally distinguish fundamental electron interactions such as scattering and screening. Here, we use sequences of attosecond pulses to directly measure electron-electron interactions in different bands of different materials with both simple and complex Fermi surfaces. By extracting the time delays associated with photoemission we show that the lifetime of photoelectrons from the d band of Cu are longer by ∼100 as compared with those from the same band of Ni. We attribute this to the enhanced electron-electron scattering in the unfilled d band of Ni. Using theoretical modeling, we can extract the contributions of electron-electron scattering and screening in different bands of different materials with both simple and complex Fermi surfaces. Our results also show that screening influences high-energy photoelectrons (≈20 eV) significantly less than low-energy photoelectrons. As a result, high-energy photoelectrons can serve as a direct probe of spin-dependent electron-electron scattering by neglecting screening. This can then be applied to quantifying the contribution of electron interactions and screening to low-energy excitations near the Fermi level. The information derived here provides valuable and unique information for a host of quantum materials. [ABSTRACT FROM AUTHOR]

Tunneling through a potential barrier of height V 0 in a two-dimensional system with a band structure consisting of three bands with a flat band intersecting the touching apices of two Dirac cones is studied. Results of the transmission coefficient at various incident angles, conductivity, shot noise, and Fano factor in this pseudospin-1 Dirac–Weyl system are presented and contrasted with those in graphene which is typical of a pseudospin-1/2 system. The pseudospin-1 system is found to show a higher transmission and suppressed shot noise in general. Significant differences in the shot noise and Fano factor due to the super Klein tunneling effect that allows perfect transmission at all incident angles under certain conditions are illustrated. For Fermi energy E F = V 0 / 2 , super Klein tunneling leads to a noiseless conductivity that takes on the maximum value 2 e 2 D k F / ( π h ) for 0 ≤ E F ≤ V 0 . This gives rise to a minimum Fano factor, in sharp contrast with that of a local maximum in graphene. For E F = V 0 , the band structure of pseudospin-1 system no longer leads to a quantized value of the conductivity as in graphene. Both the conductivity and the shot noise show a minimum with the Fano factor approaching 1/4, which is different from the value of 1/3 in graphene. [ABSTRACT FROM AUTHOR]

Artificial lattices have been employed in a broad range of two-dimensional systems, including those with electrons, atoms, and photons, in the quest for massless Dirac fermions with high flexibility and controllability. Establishing triangular or hexagonal symmetry, from periodically patterned molecule assembly or electrostatic gating as well as from moiré pattern induced by substrate, has produced electronic states with linear dispersions from two-dimensional electron gas (2DEG) residing in semiconductors, metals, and graphene. Different from the commonly studied isotropic host systems, here we demonstrate that massless Dirac fermions with tunable anisotropic characteristics can, in general, be generated in highly anisotropic 2DEG under slowly varying external periodic potentials. In the case of patterned few-layer black phosphorus superlattices, the new chiral quasiparticles exist exclusively in certain isolated energy window and inherit the strong anisotropic properties of pristine black phosphorus. These states exhibit asymmetric Klein tunneling, in which the transmission probability of the wave packets with normal incidence is no longer unity and can be tuned and controlled. In general, the direction of wave packet incidence for perfect transmission and that of the normal incidence are different, and the difference can reach more than 50° under an appropriate barrier orientation in black phosphorus superlattices. Our findings provide insight into the understanding and possible utilization of these novel emergent chiral quasiparticles. [ABSTRACT FROM AUTHOR]

Solution of the Schrödinger equation, which describes resonant transitions between three quantum levels in large-signal and high-frequency electric fields, is generalized to the case of the detuning of frequencies and energies from those exactly resonant for asymmetric three-barrier resonance-tunneling structures with thin high barriers. The dependence of the shape of the resonance levels on the amplitude and frequency of electric fields is studied. It is shown that the number of regions of absolute transparency can be as large as four depending on the microwave-field amplitude. [ABSTRACT FROM AUTHOR]

Hermitian monogenic functions are the null solutions of two complex Dirac type operators. The system of these complex Dirac operators is overdetermined and may be reduced to constraints for the Cauchy datum together with what we called the Hermitian submonogenic system (see [8], [9]). This last system is no longer overdetermined and it has properties that are similar to those of the standard Dirac operator in Euclidean space, such as a Cauchy-Kowalevski extension theorem and Vekua type solutions. In this paper, we investigate plane wave solutions of the Hermitian submonogenic system, leading to the construction of a Cauchy kernel. We also establish a Stokes type formula that, when applied to the Cauchy kernel provides an integral representation formula for Hermitian submonogenic functions. [ABSTRACT FROM AUTHOR]

First we introduce the notion of parallel normal Jacobi operator for real hypersurfaces in the complex quadric [ABSTRACT FROM AUTHOR]

Graphene consists in a single-layer carbon crystal where 2pz electrons display a linear dispersion relation in the vicinity of the Fermi level, conveniently described by a massless Dirac equation in 2 + 1 spacetime. Spin-orbit effects open a gap in the band structure and offer perspectives for the manipulation of the conducting electrons spin. Ways to manipulate spin-orbit couplings in graphene have been generally assessed by proximity effects to metals that do not compromise the mobility of the unperturbed system and are likely to induce strain in the graphene layer. In this work we explore the U(1) × SU(2) gauge 1elds that result from the uniform stretching of a graphene sheet under a perpendicular electric field. Considering such deformations is particularly relevant due to the counter-intuitive enhancement of the Rashba coupling between 30-50% for small bond deformations well known from tight-binding and DFT calculations. We report the accessible changes that can be operated in the band structure in the vicinity of the K points as a function of the deformation strength and direction. [ABSTRACT FROM AUTHOR]

We investigate the tunneling transport for electrons on the surface of a topological insulator (TI) through an electrostatic potential barrier. By using the 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 transmission probability and conductance for the system. It is demonstrated that, the Klein paradox can also been observed in the system same as in graphene system. Interestingly, the conductance reaches the minimum value when the incident electron energy is equal to the barrier strength. Moreover, with increasing barrier width, the conductance turns up some tunneling oscillation peaks, and larger barrier strength can cause lower conductance, shorter period but larger oscillation amplitude. The oscillation amplitude decreases as the barrier width increases, which is similar as that of the system consisting of the compressive uniaxial strain applied on a TI, but somewhat different from that of graphene system where the oscillation amplitude is a constant. The findings here imply that an electrostatic barrier can greatly influence the electron tunneling transport of the system, and may provide a new way to realize directional filtering of electrons. [ABSTRACT FROM AUTHOR]

We show that the cubic Dirac equation with zero mass is globally well posed for small data in the scale invariant space Hn-1/2 (Rn) for n=2, 3. The proof proceeds by using the Fierz identities to rewrite the equation in a form where the null structure of the system is readily apparent. This null structure is then exploited via bilinear estimates in spaces based on the null frame spaces of Tataru. We hope that the spaces and estimates used here can be applied to other nonlinear Dirac equations in the scale invariant setting. Our work complements recent results of Bejenaru-Herr who proved a similar result for n=3 in the massive case. [ABSTRACT FROM AUTHOR]

Recently, it attracts much attention to study spin-resolved transport properties in graphene with Rashba spin-orbit coupling (RSOC). One remarkable finding is that Klein tunneling in single layer graphene (SLG) with RSOC (SLG + R for short below) behaves as in bi-layer graphene (BLG). Based on the effective Dirac theory, we reconsider this tunneling problem and derive the analytical solution for the transmission coefficients. Our result shows that Klein tunneling in SLG + R and BLG exhibits completely different behaviors. More importantly, we find two new transmission selection rules in SLG + R, i.e., the single band to single band ( S → S ) and the single band to multiple bands ( S → M ) transmission regimes, which strongly depend on the relative height among Fermi level, RSOC, and potential barrier. Interestingly, in the S → S transmission regime, only normally incident electrons have capacity to pass through the barrier, while in the S → M transmission regime the angle-dependent tunneling becomes very prominent. Using the transmission coefficients, we also derive spin-resolved conductance analytically, and conductance oscillation with the increasing barrier height and zero conductance gap are found in SLG + R. The present study offers new insights and opportunities for developing graphene-based spin devices. [ABSTRACT FROM AUTHOR]

Bound state solutions of the Dirac equation for the pseudoharmonic potential with spin and pseudo-spin symmetry are studied in this paper. To obtain the exactly normalized bound state wave function and energy expressions we have used the Laplace transform approach. [ABSTRACT FROM AUTHOR]

Scattering of a ballistic electron by the quantum-dot spin qubits fixed in a graphene nanoribbon is investigated theoretically. Two simple cases are investigated in details: scattering from a static quantum dot and scattering from two static quantum dots located at a fixed distance from each other. For the first case, it is shown that the Klein tunneling in a graphene sheet leads to a final entangled state for the reflected and/or transmitted electrons. The amount of the generated entanglement through the scattering process is a function of the incident angle for the ballistic electrons. For the second case, it is shown that the created correlation between the quantum dots is a periodic function of their distance. For frontal incident electrons in both cases, there is not any reflection and the Klein tunneling effect leads to a final well-correlated state for the scattering system. [ABSTRACT FROM AUTHOR]

Graphene's linear dispersion relation and the attendant implications for bipolar electronics applications have motivated a range of experimental efforts aimed at producing p-n junctions in graphene. Here we report electrical transport measurements of graphene p-n junctions formed via simple modifications to a PbZr0.2Ti0.8O3 substrate, combined with a self-assembled layer of ambient environmental dopants. We show that the substrate configuration controls the local doping region, and that the p-n junction behavior can be controlled with a single gate. Finally, we show that the ferroelectric substrate induces a hysteresis in the environmental doping which can be utilized to activate and deactivate the doping, yielding an "on-demand" p-n junction in graphene controlled by a single, universal backgate. [ABSTRACT FROM AUTHOR]

We study the transport properties in a ferromagnetic/nonmagnetic/ferromagnetic (FNF) silicene junction in which an electrostatic gate potential, U, is attached to the nonmagnetic region. We show that the electrostatic gate potential U is a useful probe to control the band structure, quasi-bound states in the nonmagnetic barrier as well as the transport properties of the FNF silicene junction. In particular, by introducing the electrostatic gate potential, both the spin and valley conductances of the junction show an oscillatory behavior. The amplitude and frequency of such oscillations can be controlled by U. As an important result, we found that by increasing U, the second characteristic of the Klein tunneling is satisfied as a result of the quasiparticles chirality which can penetrate through a potential barrier. Moreover, it is found that for special values of U, the junction shows a gap in the spin and valley-resolve conductance and the amplitude of this gap is only controlled by the on-site potential difference, Δz. Our findings of high controllability of the spin and valley transport in such a FNF silicene junction may improve the performance of nano-electronics and spintronics devices. [ABSTRACT FROM AUTHOR]

We consider QED with strong external backgrounds that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can create particles from the vacuum, the Klein paradox being closely related to this process. We describe a canonical quantization of the Dirac field with x-electric potential step in terms of adequate in- and out-creation and annihilation operators that allow one to have consistent particle interpretation of the physical system under consideration and develop a nonperturbative (in the external field) technics to calculate scattering, reflection, and electron-positron pair creation. We resume the physical impact of this development. [ABSTRACT FROM AUTHOR]