Planar Dirac Research Articles

Electric and magnetic waveguides in graphene: quantum and classical

Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. We have assumed the displacement symmetry of the system along the y-direction, whose associated constant is k. We have also examined other symmetries relevant to each type of waveguide, magnetic or electric. Waveguides with square profile have been worked out in detail to show up explicitly some of the most interesting features. For example, the classical region of confined motion of the electric case, for a fixed intensity, is bounded between k and −k, while in the magnetic case that region is symmetric in the energy and presents a gap (−k, k). Besides, in the quantum systems we have shown that there are edge states in the magnetic systems but they are missing in electric waveguides. We have also analysed scattering states and resonances which match with bound states for both waveguides. The classical scattering properties are also quite different in both types of waveguides. While the electric system has essentially one type of refraction of the incident electron, the magnetic system is much richer due to the Lorentz force.

A survey on topological solitons in planar nonlinear Dirac models

A survey on topological solitons in planar nonlinear Dirac models

Planar MN4 (M = Zn, Cd) Monolayers: 2D Anisotropic Dirac Semimetals of Ultrahigh Fermi Velocities

Ultrahigh Fermi Velocities It is appealing to seek 2D Dirac materials with unique structures and intriguing properties. In article number 2200326, Xiaodong Lv, Fengyu Li, and co-workers predict planar 2D Dirac ZnN4 and CdN4 monolayers. Their first-principles calculations demonstrate that the two monolayers both exhibit high stability and an anisotropic Dirac cone at the Fermi level. Particularly, these Dirac fermions present ultrahigh Fermi velocities, and the Dirac cone is robust against external strains and electric fields.

Planar MN4 (M = Zn, Cd) Monolayers: 2D Anisotropic Dirac Semimetals of Ultrahigh Fermi Velocities

After the exfoliation of graphene, it is appealing to seek more 2D Dirac materials with unique structures, rich physics, and intriguing properties. Herein, by means of density functional theory (DFT) computations, two planar 2D Dirac transition‐metal nitrides are reported, namely, MN4 (M = Zn, Cd) monolayers. The basal planes of these monolayers can be regarded as tiled by hexagons and pentagons, with tetracoordinated metal and tricoordinated nitrogen as vertices. Besides the demonstrated mechanical, dynamic, and thermal stabilities, the two MN4 monolayers both exhibit an anisotropic Dirac cone at the Fermi level, thus featuring anisotropic Dirac fermions. Particularly, these Dirac fermions present ultrahigh Fermi velocities, which are in the same order of magnitude as that of graphene (106 m s−1). Moreover, the Dirac cone is robust against external strains and electric fields due to the protection of σv(x) and C2z symmetry. Above all, the remarkable electronic properties suggest that MN4 (M = Zn, Cd) monolayers have potential applications as nanoelectronic devices.

Parallel‐plates‐based Dirac Leaky Wave Antennas

In this work, the authors experimentally show Dirac Leaky Wave Antennas (DLWAs) at upper microwave frequencies. For the first time, DLWAs are implemented using simple Parallel plate waveguide (PPW) technology, while yielding desirable radiation features and continuous beam scanning through broadside, as well as extremely low profile, with significant ease of fabrication, making them well suited for Ku band applications such as satellite communication, radar and emerging fifth-generation (5G). A planar Dirac photonic crystal in PPW is shown with a closed bandgap and linear dispersion around broadside. In this work, 1D and 2D PPDLWAs are designed that provide scannable fan and pencil beams, respectively, with a symmetric beamwidth. Phase and attenuation constants are controlled with unit cell dimensions to obtain a directive beam and scanning in a wide range of angles. For the 2D design, an appropriate wideband feeding network is designed that excites the antenna appropriately. The presented PPDLWAs operate with a peak gain of about 13 dB for the fan beam and 22 dB for the pencil beam, in the frequency range from 12 to 16 GHz.

Cascade of phase transitions in a planar Dirac material

We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)×SU(N ) symmetry. In the large-N limit, we find that the U(M) symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of M first-order phase transitions, experiencing M + 1 phases characterized by symmetry breaking U(M)→U(M − k)×U(k) with k ∈ {0, 1, 2, · · · , M}, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as U(3)→U(1)3, U(4)→U(2)×U(1)2, and U(5)→U(2)2×U(1) exist. For a large flavor-singlet mass, the increase of the chemical potential μ brings about M consecutive first-order transitions that separate the low-μ phase diagram with vanishing fermion density from the high-μ region with a high fermion density.

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces* *Project supported by the National Natural Science Foundation of China (Grant No. 11465006).

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N = 2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.

Influence of a Chern-Simons term in the dynamical fermion masses in reduced or pseudo QED

Mixed-dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four dimensional. Here we investigate dynamical breaking of chiral symmetry in the framework of a mixed-dimensional theory that has been successful in describing graphene and other planar Dirac materials and has been dubbed pseudo or reduced quantum electrodynamics. We explore the interplay between the gauge and fermion sectors when a Chern-Simons term is considered and, by exploring the tensor structure of the fermion self-energy, we show that the radiative corrections may induce both a Dirac and a Haldane mass term. Furthermore, by solving the corresponding Schwinger-Dyson equation in a suitable truncation, we nonperturbatively explore the dynamical generation of fermion masses for different values of the electromagnetic coupling and the Chern-Simons coefficient. We also show that for definite parameter values, the contributions from each chirality cancel out and the chiral symmetry may be restored. Possible implications of this result for physical systems, in particular on what concerns the chiral magnetic effect, are discussed.

Synthetic non-Abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems

In planar tilted Dirac cone systems, the tilt parameter can be made space-dependent by either a perpendicular displacement field, or by chemical substitution in certain systems. We show that the symmetric partial derivative of the tilt parameter generates non-Abelian synthetic gauge fields in these systems. The small velocity limit of these gauge forces corresponds to Rashba and Dresselhaus spin-orbit couplings. At the classical level, the same symmetric spatial derivatives of tilt contribute to conservative, Lorentz-type and friction-like forces. The velocity dependent forces are odd with respect to tilt and therefore have opposite signs in the two valleys when the system is inversion symmetric. Furthermore, toggling the chemical potential between the valence and conduction bands reverses the sign of the all these classical forces, which indicates these forces couple to the electric charge of the carriers. As such, these forces are natural extensions of the electric and magnetic forces in the particular geometry of the tilted Dirac cone systems.

Dirac leaky wave antenna for millimetre‐wave applications

Dirac dispersion cones enable remarkable wave phenomena in electronics as well as electromagnetic systems. In this work, the authors experimentally demonstrate for the first time the Dirac leaky wave antennas (DLWAs) at millimetre-wave (mm-wave) frequencies. The demonstrated DLWAs are implemented in the substrate integrated waveguide technology, delivering unprecedented features at high frequencies such as radiation at, and continuous beam scanning through broadside, with ease of fabrication, making these designs well suited for mm-wave applications such as emerging fifth generation and Internet of Things, radar and imaging. It is shown that a planar Dirac photonic crystal can be realised composed of air columns inside a host SIW waveguide, exhibiting a closed bandgap and linear dispersion around broadside. Phase and attenuation constants are controlled to obtain directive beam and scanning in a wide range of angles (from −30° to 20°). The presented DLWAs have a wide impedance bandwidth around 28 GHz with high efficiency, and operate with peak gains of about 16 dBi with <1 dB gain variation throughout the frequency range from 25 to 31 GHz. Several designs have been proposed, and their prototypes were fabricated using standard substrates. Measured results show excellent agreement with the simulated results, validating the proposed concepts.

Review of Electron-Electron Interaction Effects in Planar Dirac Liquids

We review field theory studies devoted to understanding electron–electron interaction effects in condensed matter systems such as planar Dirac liquids, for example, graphene and graphene-like systems, surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. These liquids are characterized by gapless bands, strong electron–electron interactions, and emergent Lorentz invariance deep in the infrared. We address several important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) and also high-energy (particle) physics. In particular, we consider the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation. The resolution of these problems guide us from a thorough examination of the perturbative structure of gauge field theories to the development and application of nonperturbative approaches known from quantum electro/chromo-dynamics to address strong coupling issues.

Review of electron-electron interaction effects in planar Dirac liquids

Дан обзор теоретико-полевых исследований эффектов электрон-электронного взаимодействия в различных системах физики конденсированных состояний, таких как планарные жидкости Дирака, т. е. графен и графеноподобные системы, поверхностные состояния некоторых топологических изоляторов, а также системы с полуцелыми значениями квантового эффекта Холла. Эти жидкости характеризуются бесщелевой зонной структурой, сильными электрон-электронными взаимодействиями и лоренц-инвариантностью, возникающей в глубоко инфракрасном диапазоне. Рассмотрен ряд рассматриваемых в экспериментах важных задач, которые в настоящее время вызывают большой интерес при исследованиях в физике низких энергий (конденсированные состояния), а также в физике высоких энергий (элементарные частицы). Исследовано влияние взаимодействия на свойства переноса и его предположительно решающее значение при потенциально возможной генерации динамической массы. Решение этих проблем и тщательное изучение пертурбативной структуры калибровочных теорий поля требует развития известных из квантовой электро/хромодинамики непертурбативных подходов и позволяет применять их к исследованию систем с сильным взаимодействием.

Novel electronic and planar magnetic properties of two-dimensional surface decorated antimonene

The structural, magnetic and electronic properties of antimonenes decorated by hydrogen and halogen have been systematically investigated by density functional theory. The results indicate that semi-decorated antimonene (SX-Sb) (X = H, F, Cl, Br and I) exhibit quasi-planar magnetism, while fully-decorated antimonene (FX-Sb) is a planar Dirac material. Due to the existence of Dirac-cone-like feature, the electronic properties of FX-Sb monolayer can be effectively tuned by applying an external biaxial strain or an electric field and meanwhile maintain a high carrier mobility. In addition, the ferromagnetic state of SX-Sb monolayer is found to be energetically stable. SF-Sb and SCl-Sb nanosheets are predicted to be room-temperature ferromagnetic. The diverse electronic and magnetic properties of antimonene highlight the potential applications in electronics and spintronics.

Essentially Nonperturbative Vacuum Polarization Effects in a Two-Dimensional Dirac–Coulomb System with Z &gt; Zcr: Vacuum Charge Density

For a planar Dirac–Coulomb system with a supercritical axially symmetric Coulomb source with the charge Z > Zcr,1 and radius R0, we consider essentially nonperturbative vacuum-polarization effects. Based on a special combination of analytic methods, computer algebra, and numerical calculations used in our previous papers to study analogous effects in the one-dimensional “hydrogen atom,” we study the behavior of both the vacuum density ρVP(r) and the total induced charge and also the vacuum-polarization energy EVP. We mainly focus on divergences of the theory and the corresponding renormalization, on the convergence of partial series for ρVP(r) and ɛVP, on the integer-valuedness of the total induced charge, and on the behavior of the vacuum energy in the overcritical region. In particular, we show that the renormalization via the fermion loop with two external legs turns out to be a universal method, which removes the divergence of the theory in the purely perturbative and essentially nonperturbative modes for ρVP and ɛVP. The most important result is that for Z ≫ Zcr,1 in such a system, the vacuum energy becomes a rapidly decreasing function of the source charge Z, which reaches large negative values and whose behavior is estimated from below (in absolute value) as ~ −|ηeffZ3|/R0. We also study the dependence of polarization effects on the cutoff of the Coulomb asymptotic form of the external field. We show that screening the asymptotic value significantly changes the structure and properties of the first partial channels with mj = ±1/2,±3/2. We consider the nonperturbative calculation technique and the behavior of the induced density and the integral induced charge QVP in the overcritical region in detail.

Equivalence between the planar Dirac oscillator and a spin-1/2 fermion embedded in a transverse homogeneous magnetic field

Abstract It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator can be interpreted as a charged particle minimally coupled to a transverse homogeneous magnetic field.

Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state

The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_{3}F_{2}$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\leqslant Z\leqslant68$ are provided in a tabular form. A simple formula for the polarizability of a nonrelativistic two-dimensional hydrogenic atom, reported previously by several other authors, is recovered from our result in the nonrelativistic limit.

Theory of the strain-induced magnetoelectric effect in planar Dirac systems

The magnetoelectric response in inversion-breaking two dimensional Dirac systems induced by strain is analyzed. It is shown that, in the same way that the piezoelectric response in these materials is related to the valley Chern number, the strain-induced magnetoelectric effect is related both to the non trivial Berry curvature and the derivative of the orbital magnetic moment per valley. This phenomenon allows to locally induce and control charge densities by an external magnetic field in strained zones of the sample.

Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: $\mathcal{C}^*=(92-9\pi^2)/(18\pi)$ and the anomalous dimension of the fermion field: $\gamma_{\psi}(\bar{\alpha},\xi) = 2 \bar{\alpha}\,(1-3\xi)/3 -16\,\left( \zeta_2 N_F + 4/27 \right)\, \bar{\alpha}^2 + O(\bar{\alpha}^3)$, where $\bar{\alpha} = e^2/(4\pi)^2$ and $\xi$ is the gauge-fixing parameter.

Relativistic quantum dynamics of a neutral particle in external electric fields: An approach on effects of spin

The planar quantum dynamics of a spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations is obtained directly from the planar Dirac equation with nonminimum coupling. New solutions of this system, in particular, for the Aharonov–Casher effect, are found and discussed in detail. Pauli equation is also obtained by studying the motion of the particle when it describes a circular path of constant radius. We also analyze the planar dynamics in the full space, including the r=0 region. The self-adjoint extension method is used to obtain the energy levels and wave functions of the particle for two particular values for the self-adjoint extension parameter. The energy levels obtained are analogous to the Landau levels and explicitly depend on the spin projection parameter.

Hydrogenated arsenenes as planar magnet and Dirac material

Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.