Fermions In Graphene Research Articles

Lorentzian quantum wells in graphene: The role of shape invariance in zero-energy-state trapping

Confining Dirac fermions in graphene using electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope tip can trap zero-energy quasiparticles. The Lorentzian quantum well provides a faithful, exactly solvable approximation for such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free-particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy. Published by the American Physical Society 2024

New Manifestations of the Strong Nuclear Interactions in Solids

The discovery of global macroscopic, including optical, characteristics with the addition of one neutron made crystals LiH, LiD, Diamond, Graphene an excellent model for studying the strong nuclear interaction. New manifestations of strong interaction in solids are measurements of its dependence on the distance between nucleons, finding a neutron - electron binding energy (106 meV), which is in excellent agreement with the prediction of the theory (106,7 meV). Moreover, the creation of mass in massless Dirac fermions in graphene by strong nuclear interaction has been demonstrated for the first time.

Transmission in graphene through a double laser barrier

We study the tunneling behavior of Dirac fermions in graphene subjected to a double barrier potential profile created by spatially overlapping laser fields. By modulating the graphene sheet with an oscillating structure formed from two laser barriers, we aim to understand how the transmission of Dirac fermions is influenced by such a light-induced electric potential landscape. Using the Floquet method, we determine the eigenspinors of the five regions defined by the barriers applied to the graphene sheet. Applying the continuity of the eigenspinors at barrier edges and using the transfer matrix method, we establish the transmission coefficients. These allow us to show that oscillating laser fields generate multiple transmission modes, including zero-photon transmission aligned with the central band ε and photon-assisted transmission at sidebands ε + l ϖ, with l = 0, ± 1, ⋯ and frequency ϖ. For numerical purposes, our attention is specifically directed towards transmissions related to zero-photon processes (l = 0), along with processes involving photon emission (l = 1) and absorption (l = − 1). We find that transmission occurs only when the incident energy is above the threshold energy ε > k y + 2ϖ, with transverse wave vector k y . We find that the variation in distance d 1 separating two barriers of widths d 2 − d 1 suppresses one transmission mode. Additionally, we show that an increase in laser intensity modifies transmission sharpness and amplitude.

Tuned gap in graphene through laser barrier

We study the effect of the energy gap on the transmission of fermions in graphene exposed to linearly polarized light as a laser barrier. We determine the energy spectrum, apply boundary conditions at interfaces, and use the transfer matrix approach to obtain transmissions for all energy modes. We show that when the energy gap increases, the oscillations of transmissions decrease dramatically until they vanish entirely. However, when the barrier width varies, the oscillations become more significant and exhibit sharp peaks. By increasing the incident energy, the laser field suppresses the Fabry–Pérot resonance, and the transmissions move to the right when the energy gap is tuned.

Transmission in Graphene through Tilted Barrier in Laser Field

AbstractThe transmission of Dirac fermions in graphene through a tilted barrier potential in the presence of a laser field of frequency ω is studied. By using Floquet theory, the Dirac equation is solved and then the energy spectrum is obtained. The boundary conditions together with the transfer matrix method allow to determine the transmission probabilities corresponding to all energy bands . By limiting to the central band and the two first side bands , it is shown that the transmissions are strongly affected by the laser field and barrier. Indeed, it is found that the Klein effect is still present, a variety of oscillations are inside the barrier, and there is essentially no transmission across all bands.

Zigzag Edge States in Graphene in the Presence of In‐Plane Electric Field

Herein, the edge states in a finite‐width graphene ribbon and a semi‐infinite geometry subject to a perpendicular magnetic field and an in‐plane electric field, applied perpendicular to a zigzag edge, are explored. To accomplish this, a combination of analytic and numerical methods within the framework of low‐energy effective theory is employed. Both the gapless and gapped Dirac fermions in graphene are considered. It is found that a surface mode localized at the zigzag edge remains dispersionless even in the presence of electric field. This is shown analytically by employing Darwin's expansion of the parabolic cylinder functions of large order and argument.

Robust valley filter induced by quantum constructive interference in graphene with line defect and strain

In this paper, we theoretically investigate the manipulation of valley-polarized currents and the optical-like behaviours of Dirac fermions in graphene with single line defect. After the introduction of a local uniaxial strain, the valley transmission probability increases and transmission plateau emerges in a large angle range. Such phenomenon originates from resonant tunnelling, and the strain act as an antireflective coating for the valley states, analogous to the antireflective coating in an optical device. This indicates that perfect valley polarization can occur in a larger incident angle range compared with solely line defect. Interestingly, in the presence of Anderson disorder, even though the transmission decreases, the valley polarization is still robust. Our theoretical findings may be experimentally observable and valuable for valleytronic applications based on graphene.

Gate-tunable quantum pathways of high harmonic generation in graphene

Under strong laser fields, electrons in solids radiate high-harmonic fields by travelling through quantum pathways in Bloch bands in the sub-laser-cycle timescales. Understanding these pathways in the momentum space through the high-harmonic radiation can enable an all-optical ultrafast probe to observe coherent lightwave-driven processes and measure electronic structures as recently demonstrated for semiconductors. However, such demonstration has been largely limited for semimetals because the absence of the bandgap hinders an experimental characterization of the exact pathways. In this study, by combining electrostatic control of chemical potentials with HHG measurement, we resolve quantum pathways of massless Dirac fermions in graphene under strong laser fields. Electrical modulation of HHG reveals quantum interference between the multi-photon interband excitation channels. As the light-matter interaction deviates beyond the perturbative regime, elliptically polarized laser fields efficiently drive massless Dirac fermions via an intricate coupling between the interband and intraband transitions, which is corroborated by our theoretical calculations. Our findings pave the way for strong-laser-field tomography of Dirac electrons in various quantum semimetals and their ultrafast electronics with a gate control.

Tunneling of electrons in graphene via double triangular barrier in external fields

We study the transmission probability of Dirac fermions in graphene scattered by a triangular double barrier potential in the presence of an external magnetic field. Our system is made of two triangular potential barrier regions separated by a well region characterized by an energy gap. Solving our Dirac-like equation and matching the solutions at the boundaries allowed us to express our transmission and reflection coefficients in terms of transfer matrix. We show in particular that the transmission exhibits oscillation resonances that are a manifestation of the Klein tunneling effect. The strength of the electrostatic field giving rise to the triangular barrier was found to play a key role in controlling the tunneling peaks appearing in the resistance. However, it only slightly modifies the resonances at oblique incidence and leaves Klein paradox unaffected at normal incidence.

The theory for a 2D electron diffractometer using graphene

Electrons near the Fermi level behaving as massless Dirac fermions in graphene in (1+2)-D relativistic spacetime have been confirmed by an experiment. Using this aspect, a myriad of novel and interesting devices can be sought. In this paper, we laid out the theory for using a monolayer graphene sheet as an electron diffractometer, aiming at the determination of surface properties in materials. The key ingredient is the Mott scattering of electrons by screened Coulomb scatterers in (1+2)-D spacetime. The specific array of scatterers provided by a given surface placed in contact with a graphene sheet will induce an angular distribution for the electron scattering events, which can be properly measured through the electric current flowing to external electrodes. It can provide an in situ technique for characterizing quantum dot superlattices with a resolution of a few nanometers.

Group delay time of fermions in graphene through tilted potential barrier

The group delay time of Dirac fermions subjected to a tilting barrier potential along the $ x $-axis is investigated in graphene. We start by finding the eigenspinor solution of the Dirac equation and then relating it to incident, reflected, and transmitted beam waves. This relationship allows us to compute the group delay time in transmission and reflection by obtaining the corresponding phase shifts. We discovered that the barrier width, incident energy, and incident angle can all be used to modify the group delay time, and that the particles travel through the barrier at the Fermi velocity $ v_F $. Our findings also show that the transmission group delay might be controlled, and that gate voltage control could be useful in graphene-based tilting barriers.

Fermions in graphene with magnetic field and time-oscillating potential

We study the Dirac fermions in graphene under a magnetic field and a scalar potential oscillating in time. Using the Floquet theory and resonance approximation, we show that the energy spectrum exhibits extra subbands resulting from the oscillating potential in addition to quantized Landau levels. The magnetic field and potential are discovered to greatly influence the generation of current density in the x and y-directions. Our numerical analysis reveals that the energy spectrum is symmetric and that the current density oscillates with varying amplitudes under various conditions.

Gapless Dirac magnons in CrCl3

Bosonic Dirac materials are testbeds for dissipationless spin-based electronics. In the quasi two-dimensional honeycomb lattice of CrX3 (X = Cl, Br, I), Dirac magnons have been predicted at the crossing of acoustical and optical spin waves, analogous to Dirac fermions in graphene. Here we show that, distinct from CrBr3 and CrI3, gapless Dirac magnons are present in bulk CrCl3, with inelastic neutron scattering intensity at low temperatures approaching zero at the Dirac K point. Upon warming, magnon-magnon interactions induce strong renormalization and decreased lifetimes, with a ~25% softening of the upper magnon branch intensity from 5 to 50 K, though magnon features persist well above TN. Moreover, on cooling below ~50 K, an anomalous increase in the a-axis lattice constant and a hardening of a ~26 meV phonon feature are observed, indicating magnetoelastic and spin-phonon coupling arising from an increase in the in-plane spin correlations that begins tens of Kelvin above TN.

Goos–Hänchen-like shifts of anisotropic Dirac fermions in graphene

The Goos–Hänchen-like (GHL) shift of Dirac fermions passing through a potential barrier for an anisotropic honeycomb lattice is studied. The analytical solution of the GHL shift and numerical results of the lateral shifts for three values of the merging parameter ( δ ) are presented. Then, the effects of the incidence angle and δ on the lateral shifts of anisotropic Dirac electrons are considered. Moreover, we investigate the influence of the uniaxial strain on a critical angle and see that it changes as a function of energy. We also demonstrate that by changing some parameters, more specifically merging parameter, one can obtain the different shifts for graphene under strong uniaxial strain. • Universal Hamiltonian for description deformation uniaxial strain on graphene used. • GHL shift of the transferred beam using the stationary phase method obtained. • The shift calculated for three value of δ which is an effective factor of our study. • We obtained the shifts with minus and plus sign for values of merging parameter. • By tuning various parameters such as δ and energy different shifts can be obtained.

Evidence for Dirac nodal-line fermions in a phosphorous square-net superconductor

The fastest Dirac fermions of 1200 km/s with a nodal loop are discovered here in the superconductor ZrP${}_{2\ensuremath{-}x}$Se${}_{x}$, surpassing the velocity record held by the point-node Dirac fermions in graphene. By using angle-resolved photoemission spectroscopy, the authors demonstrate that nonsymmorphic phosphorous-based square nets provide the hoped-for stage for high Dirac velocity, nodal line, and superconductivity to meet together. This finding should pave the way for future fast and low-loss electronics, and hopefully will lead to discovery of the elusive Majorana fermion.

Form-preserving Darboux transformations for $$4\times 4$$ Dirac equations

Darboux transformation is a powerful tool for the construction of new solvable models in quantum mechanics. In this article, we discuss its use in the context of physical systems described by \(4\times 4\) Dirac Hamiltonians. The general framework provides limited control over the resulting energy operator, so that it can fail to have the required physical interpretation. We show that this problem can be circumvented with the reducible Darboux transformation that can preserve the required form of physical interactions by construction. To demonstrate it explicitly, we focus on distortion scattering and spin-orbit interaction of Dirac fermions in graphene. We use the reducible Darboux transformation to construct exactly solvable models of these systems where backscattering is absent, i.e., the models are reflectionless.

Effect of Magnetic Field on Fermions in Graphene Through Time-Oscillating Potential

Effect of Magnetic Field on Fermions in Graphene Through Time-Oscillating Potential

Dirac Fermions in Graphene with Stacking Fault Induced Periodic Line Defects.

The exploration of carbon phases with intact massless Dirac fermions in the presence of defects is critical for practical applications to nanoelectronics. Here, we identify by first-principles calculations that the Dirac cones can exist in graphene with stacking fault (SF) induced periodic line defects. These structures are width (n)-dependent to graphene nanoribbon and are thus termed as (SF)n-graphene. The electronic properties reveal that the semimetallic features with Dirac cones occur in (SF)n-graphene with n = 3m + 1, where m is a positive integer, and then lead to a quasi-one-dimensional conducting channel. Importantly, it is found that the twisted Dirac cone in the (SF)4-graphene is tunable among type-I, type-II, and type-III through a small uniaxial strain. The further stability analysis shows that (SF)n-graphene is thermodynamic stable. Our findings provide an artificial avenue for exploring Dirac Ffermions in carbon-allotropic structures in the presence of defects.

Spatial and magnetic confinement of massless Dirac fermions

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length lB is larger than the characteristic length of the confined electric potential lV, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement-induced atomic-like shell states by switching on a pi Berry phase of the quasiparticles. When the lB becomes smaller than the lV, the transition from spatial confinement to magnetic confinement occurs and the atomic-like shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed.

Reduction scheme for coupled Dirac systems

We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential term, is discussed in detail for two-dimensional Dirac Hamiltonian. We discuss its possible application in description of Dirac fermions in graphene or bilayer graphene in presence of distortion scattering or spin–orbit interaction. We illustrate the general results on the explicit examples where the involved interactions are non-uniform in space and time.