anti-Klein Tunneling Research Articles

Effect of a perpendicular magnetic field on bilayer graphene under dual gating

By studying the impact of a perpendicular magnetic field B on AB-bilayer graphene (AB-BLG) under dual gating, we yield several key findings for the ballistic transport of gate U∞. Firstly, we discover that the presence of B leads to a decrease in transmission. At a high value of B, we notice the occurrence of anti-Klein tunneling over a significant area. Secondly, in contrast to the results reported in the literature, where high peaks were found with an increasing in-plane pseudomagnetic field applied to AB-BLG, we find a decrease in conductivity as B increases. However, it is worth noting that in both cases, the number of oscillations decreases compared to the result in the study where no magnetic field was present (B=0). Thirdly, at the neutrality point, we demonstrate that the conductivity decreases and eventually reaches zero for a high value of B, which contrasts with the result that the conductivity remains unchanged regardless of the value taken by the in-plane field. Finally, we consider the diffusive transport with gate U∞=0.2γ1 and observe two scenarios. The amplitude of conductivity oscillations increases with B for energy E less than U∞ but decreases in the opposite case E>U∞.

Direct Evidence of Klein and Anti-Klein Tunneling of Graphitic Electrons in a Corbino Geometry.

Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hall bar magnetic focusing setups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular "edgeless" Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or monolayer graphene which show instead a sharpened collimation of transmission paths. The local maxima on the bilayer magnetoconductance plots migrate to higher fields with increasing doping density. These experimental results are in good agreement with detailed numerical simulations and analytical predictions.

Chirality-2 fermion induced anti-Klein tunneling in a two-dimensional checkerboard lattice

Chirality-2 fermion induced anti-Klein tunneling in a two-dimensional checkerboard lattice

Magnetic field effect on tunneling through triple barrier in AB bilayer graphene

We investigate electron tunneling in AB bilayer graphene through a triple electrostatic barrier of heights Ui(i=2,3,4) subjected to a perpendicular magnetic field. By way of the transfer matrix method and using the continuity conditions at the different interfaces, the transmission probability is determined. Additional resonances appear for two-band tunneling at normal incidence, and their number is proportional to the value of U4 in in the case of U2<U4. However, when U2>U4, anti-Klein tunneling increases with U2. The transmission probability exhibits an interesting oscillatory behavior when U3>U2=U4 and U3<U2=U4. For fixed energy E=0.39γ1, increasing barrier widths increases the number of oscillations and decreases Klein tunneling. The interlayer bias creates a gap for U2<U3<U4 and U3>U2=U4. In the four-band tunneling case, the transmission decreases in T++, T+− and T−− channels in comparison with the single barrier case. It does, however, increase for T−+ when compared to the single barrier case. Transmission is suppressed in the gap region when an interlayer bias is introduced. This is reflected in the total conductance Gtot in the region of zero conductance. Our results are relevant for electron confinement in AB bilayer graphene and for the development of graphene-based transistors.

Photoinduced Klein tunneling in semi-Dirac material

The two-dimensional semi-Dirac model is characterized by the anisotropic energy dispersion, which is quadratic in one direction and linear along the orthogonal direction. We investigated the transport properties of the light irradiated n−p junction along the quadratic dispersion direction based on semi-Dirac materials. It is shown that the out-of-plane component of the pseudospin can be activated by the light irradiation. For the large light field, the out-of-plane component of the pseudospin is dominant, leading to the transition from the perfect normal reflection (anti-Klein tunneling) to the approximately perfect normal transmission (Klein tunneling) in the junction.

Dirac fermion optics and directed emission from single- and bilayer graphene cavities

High-mobility graphene hosting massless charge carriers with linear dispersion provides a promising platform for electron optics phenomena. Inspired by the physics of dielectric optical micro-cavities where the photon emission characteristics can be efficiently tuned via the cavity shape, we study corresponding mechanisms for trapped Dirac fermionic resonant states in deformed micro-disk graphene billiards and directed emission from those. In such graphene devices a back-gate voltage provides an additional tunable parameter to mimic different effective refractive indices and thereby the corresponding Fresnel laws at the boundaries. Moreover, cavities based on single-layer and double-layer graphene exhibit Klein- and anti-Klein tunneling, respectively, leading to distinct differences with respect to dwell times and resulting emission profiles of the cavity states. Moreover, we find a variety of different emission characteristics depending on the position of the source where charge carriers are fed into the cavites. Combining quantum mechanical simulations with optical ray tracing and a corresponding phase-space analysis, we demonstrate strong confinement of the emitted charge carriers in the mid field of single-layer graphene systems and can relate this to a lensing effect. For bilayer graphene, trapping of the resonant states is more efficient and the emission characteristics do less depend on the source position.

Transport properties in gapped bilayer graphene

We investigate transport properties through a rectangular potential barrier in AB-stacked bilayer graphene (AB-BLG) gapped by dielectric layers. Using the Dirac-like Hamiltonian with a transfer matrix approach we obtain transmission and reflection probabilities as well as the associated conductance. For two-band model and at normal incidence, we find extra resonances appearing in transmission compared to biased AB-BLG, which are Fabry-P\'erot resonance type. Now by taking into account the inter-layer bias, we show that both of transmission and anti-Klein tunneling are diminished. Regarding four band model, we find that the gap suppresses transmission in an energy range by showing some behaviors look like "Mexican hats". We examine the total conductance and show that it is affected by the gap compared to AA-stacked bilayer graphene. In addition, we find that the suppression in conductance is more important than that for biased AB-BLG.

Chiral oscillations in electronic transport through graphene nanoribbons induced by pseudospin filters

We show here that the application of potential barriers that induce contributions of hyperboloid subbands (pseudospin filters) in graphene nanoribbons locally breaks the chiral symmetry of the Dirac state, in the sides of the barrier, with the consequent transition from Klein to anti-Klein behavior. With the increased filter potential applied, resonances of Fabry-P\'erot type with line widths that are decreasing are generated in the conductance, which is associated with a pseudospin precession located on the sides of the barrier. Interestingly, throughout this process the chiral symmetry of the state is conserved, and pseudospin oscillations (opposite) that increase in intensity are observed on the sides of the filter. This is associated with a gradual loss of the electron-hole correlation, with the increased filter potential, which ends with the formation of a transport gap when the electron-hole symmetry is completely broken. This is an example of how the chiral symmetry can evolve and still be conserved, during a tunneling process. All this leads to the generation of energy gaps, associated with anti-Klein tunneling, which can be controlled using certain spatial configurations of the applied filters. The inclusion of a new type of asymmetry (roughness in the filters) makes it possible to recover Klein's tunneling in the region of induced gaps. The interaction of the hyperboloid subbands with the Dirac band can be observed in density-of-states maps using the pseudospin filters, following the behavior of the van Hove singularities as a function of the filter potential.

Anti-Klein tunneling in topoelectrical Weyl semimetal circuits

Topoelectrical (TE) circuits consisting of capacitors and inductors can be designed to exhibit various Weyl semimetal (WSM) phases in their admittance dispersion. We consider a TE heterojunction circuit consisting of a central region sandwiched by source and drain regions. The energy flux transmission across the heterojunction can be tuned to exhibit perfect transmission near normal incidence (Klein tunneling) for one valley and perfect reflection (anti-Klein tunneling) for the other valley by controlling the WSM phases of the heterojunction. Perfect valley-polarized transmission occurs when the dispersion tilt to Fermi velocity ratio in the source region is reciprocal to that in the central barrier region. This unusual flux transmission is ascribed to two factors, i.e., perfect pseudospin (sublattice) polarization at normal incidence and complete decoupling of one of the sublattice polarizations at the critical velocity ratio. The emergence of anti-Klein tunneling by design in TE circuits suggests a possible realization of the effect in real WSM materials.

Enhancement of the Fano-resonance response in bilayer graphene single and double barriers induced by bandgap opening

Abstract Fano resonances in bilayer graphene arise due to the coupling between extended and discrete electrons states, and represent an exotic phenomenon in graphene akin to Klein and anti-Klein tunneling, atomic collapse and negative refraction to mention a few. The hallmark of these resonances is identifiable in the conductance curves of bilayer graphene barrier structures. Furthermore, the Fano line-shape can be presented in the conductance by reducing the angular range in the computation of the transport properties. In this work, we explore the possible consequences that bandgap opening in the band structure of bilayer graphene can have over Fano resonances. We have used a four-band Hamiltonian to taking into account the mentioned band structure modifications. The hybrid matrix method and the Landauer–Buttiker formalism have been implemented to obtain the transmittance and the conductance, respectively. We find that the signatures of the Fano resonances on the conductance are enhanced by the opening of the bandgap. In fact, the Fano profile is manifested in the conductance without the need of reducing the angular range. This enhancement results from the improvement of the chirality matching between extended and discrete states induced by the bandgap opening. The main characteristics of the impact of the bandgap opening on the transmission and transport properties of single and double barriers are presented. So, the bandgap opening far from hamper the Fano resonance response promotes it and can be used as modulation parameter to prove the exotic phenomenon of Fano resonances in bilayer graphene barrier structures.

Barrier tunneling of quasiparticles in double-Weyl semimetals

We investigate barrier tunneling of quasiparticles in double-Weyl semimetals. Being the anisotropic dispersion, it exhibits different scattering properties for different barrier orientations. We discuss two cases. In the first case where the barrier is perpendicular to linear momentum direction, we show that the incoming quasiparticles can fully pass through the barrier at normal incidence. This is known as Klein tunneling, a familiar phenomenon in the Graphene. The full transmission also occurs for some other special angles determined by the resonance condition between the barrier width and the wave vector in the barrier. In the second case where the barrier is perpendicular to quadratic momentum direction, the incoming quasiparticles can be fully reflected by the barrier at normal incidence, which is known as anti-Klein tunneling. As the energy of incident quasiparticles changes, it induces a transition from Klein tunneling to anti-Klein tunneling. When the band gap is opened, it has impact on the chirality and Berry phase. So the transmission coefficient is also changed.

Pseudospin-dependent Zitterbewegung in monolayer graphene

We propose a spintronic device based on a narrow nanoribbon patterned from a monolayer graphene (MLG) sheet, embedded between a film of hexagonal boron nitride and a SiO2 substrate, all comprised under a three top-gated structure, to explore spin-dependent quantum transport of Dirac fermions. We developed a theoretical procedure for describing the pseudospin-related effects and the dynamics of Dirac fermions represented by a one-dimensional Gaussian wave packet (1DGWP), which is electrostatically confined in the device. The free-space 1DGWP time evolution follows expected features. Meanwhile, due to the weak breakdown of the real-spin degeneracy, the 1DGWP barely splits inside the under-barrier region governed by the extrinsic Rashba spin–orbit interaction (SOI-R). Most importantly, departing from the pristine MLG, we have found evidence of trembling antiphase oscillations in the probability density time-distribution for each sublattice state, which we have called the pseudospinorial Zitterbewegung effect (PZBE). The PZBE appears modulated with robust transient character and with a decay time in the femtosecond scale. Interestingly, several features of the PZBE become tunable, even its complete disappearance at the vicinity of the Dirac points or at a symmetric pseudospin configuration. For the proposed quasi-1D MLG device, we have captured evidence of the familiar Klein tunneling and the unusual anti-Klein tunneling, whose interplay for 2D MLG under tunable SOI-R was reported recently.

From Klein to anti-Klein tunneling in graphene tuning the Rashba spin–orbit interaction or the bilayer coupling

We calculate the transmission coefficient for a particle crossing a potential barrier in monolayer graphene with Rashba spin–orbit coupling and in bilayer graphene. We show that in both cases one can go from Klein tunneling regime, characterized by perfect normal transmission, to anti-Klein tunneling regime, with perfect normal reflection, by tuning the Rashba spin–orbit coupling for a monolayer or the interplane coupling for a bilayer graphene. We show that the intermediate regime is characterized by a non-monotonic behavior with oscillations and resonances in the normal transmission amplitude as a function of the coupling and of the potential parameters.

Tuning Anti-Klein to Klein Tunneling in Bilayer Graphene.

We show that in gapped bilayer graphene, quasiparticle tunneling and the corresponding Berry phase can be controlled such that they exhibit features of single-layer graphene such as Klein tunneling. The Berry phase is detected by a high-quality Fabry-Pérot interferometer based on bilayer graphene. By raising the Fermi energy of the charge carriers, we find that the Berry phase can be continuously tuned from 2π down to 0.68π in gapped bilayer graphene, in contrast to the constant Berry phase of 2π in pristine bilayer graphene. Particularly, we observe a Berry phase of π, the standard value for single-layer graphene. As the Berry phase decreases, the corresponding transmission probability of charge carriers at normal incidence clearly demonstrates a transition from anti-Klein tunneling to nearly perfect Klein tunneling.

Visualization and Control of Single-Electron Charging in Bilayer Graphene Quantum Dots.

Graphene p-n junctions provide an ideal platform for investigating novel behavior at the boundary between electronics and optics that arise from massless Dirac Fermions, such as whispering gallery modes and Veselago lensing. Bilayer graphene also hosts Dirac Fermions, but they differ from single-layer graphene charge carriers because they are massive, can be gapped by an applied perpendicular electric field, and have very different pseudospin selection rules across a p-n junction. Novel phenomena predicted for these massive Dirac Fermions at p-n junctions include anti-Klein tunneling, oscillatory Zener tunneling, and electron cloaked states. Despite these predictions there has been little experimental focus on the microscopic spatial behavior of massive Dirac Fermions in the presence of p-n junctions. Here we report the experimental manipulation and characterization of massive Dirac Fermions within bilayer graphene quantum dots defined by circular p-n junctions through the use of scanning tunneling microscopy-based (STM) methods. Our p-n junctions are created via a flexible technique that enables realization of exposed quantum dots in bilayer graphene/hBN heterostructures. These quantum dots exhibit sharp spectroscopic resonances that disperse in energy as a function of applied gate voltage. Spatial maps of these features show prominent concentric rings with diameters that can be tuned by an electrostatic gate. This behavior is explained by single-electron charging of localized states that arise from the quantum confinement of massive Dirac Fermions within our exposed bilayer graphene quantum dots.

Hybrid matrix method for stable numerical analysis of the propagation of Dirac electrons in gapless bilayer graphene superlattices

Gapless bilayer graphene (GBG), like monolayer graphene, is a material system with unique properties, such as anti-Klein tunneling and intrinsic Fano resonances. These properties rely on the gapless parabolic dispersion relation and the chiral nature of bilayer graphene electrons. In addition, propagating and evanescent electron states coexist inherently in this material, giving rise to these exotic properties. In this sense, bilayer graphene is unique, since in most material systems in which Fano resonance phenomena are manifested an external source that provides extended states is required. However, from a numerical standpoint, the presence of evanescent-divergent states in the eigenfunctions linear superposition representing the Dirac spinors, leads to a numerical degradation (the so called Ωd problem) in the practical applications of the standard Coefficient Transfer Matrix (K) method used to study charge transport properties in Bilayer Graphene based multi-barrier systems. We present here a straightforward procedure based in the hybrid compliance-stiffness matrix method (H) that can overcome this numerical degradation. Our results show that in contrast to standard matrix method, the proposed H method is suitable to study the transmission and transport properties of electrons in GBG superlattice since it remains numerically stable regardless the size of the superlattice and the range of values taken by the input parameters: the energy and angle of the incident electrons, the barrier height and the thickness and number of barriers. We show that the matrix determinant can be used as a test of the numerical accuracy in real calculations.

Destruction of anti-Klein tunneling induced by resonant states in bilayer graphene

The anti-Klein tunneling at normal incidence is a typical property of bilayer graphene. We study the resonant tunneling through multiple electrostatic barriers in bilayer graphene, and find that a line-type resonance with perfect transmission caused by quasibound states can occur at normal incidence, leading to the destruction of anti-Klein tunneling. The line-type resonance presents -fold splitting in n-barrier, while the Fabry–Pérot resonance shows n-fold splitting, because they originate from different resonant states. The electronic states, the transmission region, and the features of both resonances are limited by the longitudinal wave vectors, which can be effectively controlled by adjusting the barrier height and barrier width.

Fabry-Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling.

We report the experimental observation of Fabry-Pérot interference in the conductance of a gate-defined cavity in a dual-gated bilayer graphene device. The high quality of the bilayer graphene flake, combined with the device's electrical robustness provided by the encapsulation between two hexagonal boron nitride layers, allows us to observe ballistic phase-coherent transport through a 1-μm-long cavity. We confirm the origin of the observed interference pattern by comparing to tight-binding calculations accounting for the gate-tunable band gap. The good agreement between experiment and theory, free of tuning parameters, further verifies that a gap opens in our device. The gap is shown to destroy the perfect reflection for electrons traversing the barrier with normal incidence (anti-Klein tunneling). The broken anti-Klein tunneling implies that the Berry phase, which is found to vary with the gate voltages, is always involved in the Fabry-Pérot oscillations regardless of the magnetic field, in sharp contrast with single-layer graphene.

Klein paradox for a pn junction in multilayer graphene

Charge carriers in single and multilayered graphene systems behave as chiral particles due to the particular lattice symmetry of the crystal. We show that the interplay between the meta-material properties of graphene multilayers and the pseudospinorial properties of the charge carriers result in the occurrence of Klein and anti-Klein tunneling for rhombohedral stacked multilayers. We derive an algebraic formula predicting the angles at which these phenomena occur and support this with numerical calculations for systems up to four layers. We present a decomposition of an arbitrarily stacked multilayer into pseudospin doublets that have the same properties as rhombohedral systems with a lower number of layers.

Directional quantum transport in graphyne p-n junction

Graphyne, a newly proposed allotrope of carbon, has a structure which is topologically equivalent to that of a strongly distorted graphene [B. G. Kim and H. J. Choi, Phys. Rev. B 86, 115435 (2012)]. The energy gap between the valence and conduction bands is due to the symmetry breaking caused by there being three topologically inequivalent hoping elements. The valleyless fermionic transport properties of γ-graphyne are different from those of graphene since the two valleys are merged together in this carbon allotrope. The transmission and conductance of the electrons in γ-graphyne are found to be directionally dependent. Klein tunneling is predicted if the tunneling is in the y-direction. If the tunneling is in the x-direction, perfect back reflection (anti Klein tunneling) is predicted if the tunneling is at normal incidence. The consequences of these directional transport properties on the performances of p-n junctions fabricated with this carbon allotrope are studied. This work reveals the advantages of building p-n junctions based on γ-gaphyne.