Klein Tunneling Research Articles

Experimental observation of super-Klein tunneling in phononic crystals

We numerically and experimentally report the acoustic analogue of the super-Klein tunneling in a heterojunction of phononic crystals formed with Willis scatterers that exhibit pseudospin-1 Dirac cones. Pseudospin-1 Dirac cones are characterized by a triple states degeneracy in the band structure where two linear bands intersect with a flatband. The scattering properties of pseudospin-1 quasiparticles comprise an unity transmission through one potential barrier at its center frequency for all incident angles, which is called the super-Klein tunneling. In addition, the unity transmission does not depend on the barrier width. The Super-Klein tunneling differs from the conventional Klein tunneling, which consists of perfect transmission only under normal incidence through a potential barrier of any width. The Klein tunneling is predicted in pseudospin-1/2 systems like graphene, which are characterized by a two states degeneracy with two intersecting linear band. This direct observation in this acoustic analogue may have important implications in the exploration of the rich physics of pseudospin-1 quasiparticles.

Identifying Klein tunneling signatures in bearded Su-Schrieffer-Heeger lattices from bent flat bands

Identifying Klein tunneling signatures in bearded Su-Schrieffer-Heeger lattices from bent flat bands

Re-assessing special aspects of Dirac fermions in presence of Lorentz-symmetry violation

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.

New Resolution of Klein Paradox by Modified Dirac Equations

New Resolution of Klein Paradox by Modified Dirac Equations

Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems

There have been many studies on the ground state of phononic crystals, but few studies on the nature of the excited state. In this paper, we introduce the asymmetric Klein tunneling method in phononic systems, which enables selective direction and control of elastic waves by inducing polarization through an external field in an artificial barrier. Using tight-binding theory, we systematically studied phononics in a super-honeycomb structure, demonstrating the anisotropic transition properties of excited state phonons through a matrix model involving the ground state’s s-type and the first excited state’s p-type wave functions. Additionally, we exploit the thermal sensitivity of epoxy to achieve localized thermal field-induced distortion of the bottom flat band, forming a tiled Dirac cone, and thereby creating a reconfigurable polarized artificial barrier in the elastic wave system. Elastic waves propagate in these systems with topological charge conservation. Combining this with the theoretical of excited-state phonons, we demonstrate asymmetric Klein tunneling with directional selectivity in the elastic wave carriers, and systematically investigate the performance of this tunneling. Furthermore, we design a four-port elastic waveguide based on the principle of asymmetric tunneling, which achieves exceptional directional selectivity of elastic wave signals by adjusting the polarization direction of barriers at the junctions. These studies not only extend the application of Klein tunneling in elastic wave systems but also open new research avenues for the study of elastic wave devices controlled by various external fields, showing direct application potential in elastic wave signal processing.

Dirac fermions collimation in heterostructures based on tilted Dirac cone materials

This paper aims to theoretically analyze the behavior of Dirac fermions in a tilted Dirac cone material, particularly those interacting with a barrier potential. Our results show that the degree of tilt in the y-direction can lead to different collimations of Dirac fermion beams relative to the Fermi and confinement surfaces. We have highlighted a range of results, including the conical geometry by illustrating the active surfaces and their geometric parameters in reciprocal space. To study the transmission probability, we have conducted numerical analyses, considering various system configurations and different external and internal physical parameters to characterize the fermionic transport behavior in a proposed heterostructure. Additionally, we examined the transmission of Dirac fermions in relation to the refractive indices and refraction between the different media constituting the system, discussing the tunneling effect and the Klein paradox in relation to various physical parameters. Our findings lay the groundwork for the development of controllable electronic devices using Dirac fermion collimation, governed by the tilt parameter, enabling precise manipulation and enhanced functionality.

Klein tunneling and Fabry-Perot resonances in the α - T 3 bilayer with aligned stacking

This paper investigates the quantum tunneling effect on the α − T 3 bilayer with aligned stacking. An effective model is constructed to describe the properties around the triple band crossings for stacking with a vertical alignment of sites in the bilayer system. Focusing on these band crossings, it is found that while the energy spectrum remains gapless throughout, it is characterized by flat energy bands. Subsequently, the transmission coefficient, T, for Dirac quasi-electrons across a rectangular potential barrier is calculated, alongside the relationship between the transmission rate and the coupling parameter α. It is observed that super-tunnel phenomena occur at certain values of the quasiparticle energy, where the transmission is perfect regardless of the angle of incidence on the barrier, with α = 1. Furthermore, it is found that for a wide range of parameter values, the transmittance evolves monotonically and exponentially with increasing alpha. The paper also highlights the occurrence of the Klein paradox in the system, where quasiparticles approaching the barrier with zero-angle incidence exhibit ideal quantum transparency.

P T-symmetric photonic lattices with type-II Dirac cones.

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons and, more specifically, for mimicking the Klein tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the P T-symmetric photonic lattices with type-II Dirac cones for the first time to our knowledge. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the P T symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with P T symmetry only decays because of diffraction, whereas in the P T symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.

On Klein tunneling of low-frequency elastic waves in hexagonal topological plates

Incident particles in the Klein tunnel phenomenon in quantum mechanics can pass a very high potential barrier. Introducing the concept of tunneling into the analysis of phononic crystals can broaden the application prospects. In this study, the structure of the unit cell is designed, and the low frequency (< 1 kHz) valley locked waveguide is realized through the creation of a phononic crystal plate with a topological phase transition interface. The defect immunity of the topological waveguide is verified, that is, the wave can propagate along the original path in the cases of impurities and disorder. Then, the tunneling phenomenon is introduced into the topological valley-locked waveguide to analyze the wave propagation, and its potential applications (such as signal separators and logic gates) are further explored by designing phononic crystal plates. This research has broad application prospects in information processing and vibration control, and potential applications in other directions are also worth exploring.

Transport properties in ABC-ABA-ABC trilayer graphene junctions

Trilayer graphene (TLG) consists of three layers of graphene arranged in a particular stacking order. In the case of ABC-ABA-ABC stacking, the layers are arranged in an A-B-C sequence, followed by an A-B-A sequence, and again an A-B-C sequence. This stacking arrangement introduces specific electronic properties and band structures due to the different stacking configurations. We focus on elucidating the transport properties of a p-n-p junction formed with ABC-ABA-ABC stacking TLG. Employing the transfer matrix method and considering continuity conditions at the junction boundaries, we establish transmission and reflection probabilities, along with conductance. Notably, electron transport through the ABC-ABA-ABC junction exhibits Klein tunneling, resulting in substantial conductance even in the absence of a potential barrier V 0. This effect arises from the effective barrier induced by our specific stacking, facilitating the passage of a maximal number of electrons. However, the presence of V 0 diminishes Klein tunneling, leading to conductance minima. Furthermore, our findings highlight that interlayer bias δ induces a hybridization of the linear and parabolic bands of ABA-TLG within the junction, reducing resonances. In cases where δ ≠ 0 and V 0 ≠ 0, we observe a suppression of the gap, contrary to the results obtained in ABC tunneling studies where a gap exists.

Transport properties of the resonant tunneling structures based on the pseudospin-1 Dirac–Weyl fermions

Transmission, conductivity, and shot noise are investigated in multi-barrier resonant tunneling structures based on the pseudospin-1 Dirac–Weyl model. Super Klein tunneling, perfect transmission plateau, and resonant tunneling collectively contribute to the transport properties. While resonant tunneling occurs when the energy of the passing quasiparticle coincides with the discrete quasibound energy level of the multi-barrier structure and is widely observed in parabolic and Dirac-cone-shape dispersive materials, super Klein tunneling and perfect transmission plateau are unique in pseudospin-1 systems and barrier-structure independent. As a result, the conductivity and shot noise in pseudospin-1 resonant-tunneling multi-barrier structures demonstrate remarkably different properties from their counterparts of both parabolic-dispersion semiconductors and pseudospin-1/2 Dirac–Weyl materials, typically graphene. It is found that the zero conductivity minimum remains for multi-barrier structures and the relative shot noise indicated by the Fano factor in the three-barrier system is larger than that in the double-barrier system when the Klein tunneling effect weakens.

Klein Tunneling in β12 Borophene.

Motivated by the recent observation of Klein tunneling in 8-Pmmn borophene, we delve into the phenomenon in β12 borophene by employing tight-binding approximation theory to establish a theoretical mode. The tight-binding model is a semi-empirical method for establishing the Hamiltonian based on atomic orbitals. A single cell of β12 borophene contains five atoms and multiple central bonds, so it creates the complexity of the tight-binding model Hamiltonian of β12 borophene. We investigate transmission across one potential barrier and two potential barriers by changing the width and height of barriers and the distance between two potential barriers. Regardless of the change in the barrier heights and widths, we find the interface to be perfectly transparent for normal incidence. For other angles of incidence, perfect transmission at certain angles can also be observed. Furthermore, perfect and all-angle transmission across a potential barrier takes place when the incident energy approaches the Dirac point. This is analogous to the "super", all-angle transmission reported for the dice lattice for Klein tunneling across a potential barrier. These findings highlight the significance of our theoretical model in understanding the complex dynamics of Klein tunneling in borophene structures.

Photon scattering by an electric field in noncommutative spacetime

As is known, the existence of a small noncommutativity between coordinates would generate nonlocal self-interactions in the electromagnetic theory. To explore some consequences of this effect on the propagation of photons we consider Moyal space half-filled with a static and homogeneous electric field and analyze electromagnetic fluctuations on top of this step-like background. Both the localization of photons and the possibility of photon production by strong electric fields are addressed. Several aspects of the Klein paradox in this setup are discussed as well.

Transit‐Time Instability Mechanism in Lateral Graphene n+‐i‐n‐i‐n+ Structure with Transverse Terahertz Pasmonic Resonant Cavity

The terahertz (THz) plasmonic instability in the lateral graphene structure (LGS) with the n+‐i‐n‐i‐n+ junction in its graphene channel (GC) is analyzed. The i‐regions in the LGS n+‐i‐n‐i‐n+ GC plays the role of the transit spaces of the electrons emitted from the n+‐regions (the emitters) and collected by the gated n‐region (collector) and the side contact to the latter. The interband Zener–Klein tunneling (ZKT) in the i‐regions also contributes to the currents received by the n‐region. Simultaneously, the n‐region constitutes the transverse resonant plasmonic cavity, in which the plasmons with the wave vector directed perpendicular to the electron propagation direction are excited. The plasmonic instability in the LGSs is associated with the transit‐time negative dynamic conductance of the i‐regions supported by the plasmonic resonances in the n‐region. The self‐excitation of plasmonic oscillations associated with the instability in the LGS with sub‐micrometer i‐regions and supplied with a proper antenna can lead to the emission of THz radiation. The LGS can form periodic arrays, which can serve as an active distributed antenna.

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.

Quantum Limit for the Emittance of Dirac Particles Carrying Orbital Angular Momentum

In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules for a relativistic particle in a cylindrical box, which emulates the volume occupied by a beam of particles with a non-trivial aspect ratio. We apply our results to the evaluation of the quantum limit for emittance in particle accelerators. The developed theory allows the description of quantum beams carrying Orbital Angular Momentum (OAM). We demonstrate how the degeneracy pressure is such to increase the phase–space area of Dirac particles carrying OAM. The results dramatically differ from the classical evaluation of phase–space areas, that would foresee no increase in emittance for beams in a coherent state of OAM. We discuss the quantization of the phase–space cell’s area for single Dirac particles carrying OAM, and, finally, provide an interpretation of the beam entropy as the measure of how much the phase–space area occupied by the beam deviates from its quantum limit.

Massive Klein tunneling in topological photonic crystals

Klein’s paradox refers to the transmission of a relativistic particle through a high potential barrier. Although it has a simple resolution in terms of particle-to-antiparticle tunneling (Klein tunneling), debates on its physical meaning seem lasting partially due to the lack of direct experimental verification. In this article, we point out that honeycomb-type photonic crystals (PhCs) provide an ideal platform to investigate the nature of Klein tunneling, where the effective Dirac mass can be tuned in a relatively easy way from a positive value (trivial PhC) to a negative value (topological PhC) via a zero-mass case (PhC graphene). Specifically, we show that analysis of the transmission between domains with opposite Dirac masses—a case hardly be treated within the scheme available so far—sheds new light on the understanding of the Klein tunneling.

Super Klein tunneling in phononic Lieb lattices

Super Klein tunneling in phononic Lieb lattices

Bound-in-continuum-like corner states in the type-II Dirac photonic lattice

Dirac points are special points in the energy band structure of various materials, around which the dispersion is linear. If the corresponding Fermi surface is projected as a pair of crossing lines—or touching cones in two dimensions, the Dirac point is known as the type-II; such points violate the Lorentz invariance. Until now, thanks to its unique characteristics, the Klein tunneling is successfully mimicked and the topological edge solitons are obtained in the type-II Dirac photonic lattices that naturally possess type-II Dirac points. However, the interplay between these points and corner states is still not investigated. Here, we report both linear and nonlinear corner states in the type-II Dirac photonic lattice with elaborate boundaries. The states, classified as in-phase and out-of-phase, hide in the extended bands that are similar to the bound states in the continuum (BIC). We find that the nonlinear BIC-like corner states are remarkably stable. In addition, by removing certain sites, we establish the fractal Sierpiński gasket structure in the type-II Dirac photonic lattice, in which the BIC-like corner states are also demonstrated. The differences between results in the fractal and nonfractal lattices are rather small. Last but not least, the corner breather states are proposed. Our results provide a novel view on the corner states and may inspire fresh ideas on how to manipulate/control the localized states in different photonic lattices.

150 Gbps THz Chipscale Topological Photonic Diplexer.

Photonic diplexers are being widely investigated for high data transfer rates in on-chip communication. However, dividing the available spectrum into nonoverlapping multicarrier frequency sub-bands has remained a challenge in designing frequency-selective time-invariant channels. Here, an on-chip topological diplexer is reported exhibiting terahertz frequency band filtering through Klein tunneling of topological edge modes. The silicon topological diplexer chip facilitates two high-speed channels with quadrature amplitude modulation (QAM) over a broad bandwidth of 12.5 GHz each. These channels operate at carrier frequencies of 305 and 321.6 GHz, achieving a combined diplexer capacity of 150 Gbits-1. To ensure minimal interference between adjacent channels, a guard band is implemented. Topologically protected edge modes suppress the frequency selective fading of the broadband signals and hold promise for diverse integrated photonic applications spanning terahertz and telecommunication realms, including the design of lossless topological multiplexers, interconnects, antennas, and modulators for the sixth to X generation (6G to XG) wireless.