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The present investigation is an attempt to understand the fermion mass ratios in the framework of QED of charged fermions without a bare mass. Since QED of massless charged fermions is invariant under the dilatation transformation, this symmetry has to be spontaneously broken to obtain massive fermions. In the proposed model we combine a mass-scale normalisation with the renormalisation procedure, assuming the fermion momentum space being a four-dimensional one-shell hyperboloid embedded in a five-dimensional space. The hyperboloid constrains the allowed fermion field solutions. We construct the theory in the conventional way using equal time anti-commutator and the Lagrangian formalism. Starting from the Dyson–Schwinger equation for fermion propagator in the Landau gauge, we derive the fermion mass function and self-reciprocal solutions for the mass ratios, which are independent of any constant.

The time evolution of the mean values of the standard position, velocity and momentum operators, for a relativistic Dirac particle in a one-dimensional box, as well as for a free Dirac particle on a line with a hole, are studied. By considering the cases of free particle, confined particle and particle with a delta function interaction, it is shown that the Ehrenfest-type theorems for these operators are not always valid.

We analyze three different ways of obtaining a spin-free Dirac equation and demonstrate that the resulting spin-free Dirac equations have different eigenvalues and eigenvectors. This means that the conventional division between scalar and spin–orbit relativistic effects is arbitrary and depends on the method of separation.

Investigating the bound state of fermions and extended dyons in non-relativistic as well as in relativistic frameworks, it has been shown that bound state energy eigenvalues are modified from those of fermions and point-like dyons due to the presence of massive fields in non-Abelian gauge theory. These fields play a dominating role in forming the bound state. It has also been shown that an exact solution of Dirac equation for an extended dyon-fermion system cannot be obtained, due to the presence of a term vanishing more rapidly than r−1 in the potential of this system.

We study the self-adjoint extensions of the Dirac operator α ⋅ ( p − B ) + μ 0 β − W \alpha \cdot (p - B) + \mu _{0}\beta - W , where the electrical potential W W contains a Coulomb singularity of arbitrary charge and the magnetic potential B B is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form v ( r ) / r v(r)/r where v v has a limit at 0, then, for any self-adjoint extension of the Dirac operator, removing the singularity results in a Hilbert-Schmidt perturbation of its resolvent.

(1999). Scattering amplitude for dirac operators. Communications in Partial Differential Equations: Vol. 24, No. 1-2, pp. 377-394.

The solution of the Dirac equation is obtained for a relativistic electron in the focusing and periodic electrostatic fields modeling the field at the axis or plane of a crystal.

We consider the contribution offermion–antifermion condensates to the anomalousmagnetic moment of a fermion in a vacuum in which suchcondensates exist. The real part of the condensatecontribution to the anomalous magnetic moment is shown to bezero. A nonzero imaginary part is obtained below thekinematic threshold for intermediatefermion–antifermion pairs. The calculation isshown to be gauge-parameter independent provided a single fermion masscharacterizes both the fermion propagator andcondensate-sensitive contributions, suggestive of adynamically generated fermion mass. The nonzeroimaginary part is then argued to correspond to the kinematicproduction of the intermediatestate Goldstone bosonsanticipated from a chiral-noninvariant vacuum. Finally,speculations are presented concerning the applicability of these results to quark electromagneticproperties.

We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the fermion matrix establishes that its real eigenvalues (and corresponding eigenvectors) play a role similar to the zero eigenvalues (zero modes) of the Dirac operator in continuous background fields. Using numerical techniques we concentrate on studying the real part of the spectrum. These results provide new insights into the behaviour of physical quantities as a function of the topological charge. In particular we discuss fermion determinant, effective action and pseudoscalar densities., 33 pages, 10 eps-figures; reference added

In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. We construct a lattice formulation of the massless Dirac fermion using the overlap formalism. We show that the result is parity invariant in contrast to the formulation using Wilson fermions in the massless limit. This facilitates a non-perturbative study of three-dimensional massless Dirac fermions interacting with a gauge field in a parity-invariant setting with no need for fine-tuning.

The presence of a heavy fermion doublet in the electroweak instanton probably leads to unsuppressed fermion number nonconservation. By calculating numerically the effective potential barrier of electroweak instanton with heavy fermion in Minkowski space by using semiclassical approximation, it is shown that, if the mass of heavy fermion exceeds a critical value [Formula: see text] TeV (for MH = MW), the tunneling by electroweak instanton should be unsuppressed and the heavy fermion decays with fermion number violation. The dependence of critical fermion mass on the Higgs mass is also presented.

The Dirac equation is formulated on (1+{ital D})-dimensional discrete Minkowski space-time. We find that the minimum number of components of the fermion field is 2{sup D{minus}1} in the massless case, which is smaller than 2{sup D+1} of the Kogut-Susskind fermion. There exist no extra poles in the fermion propagator. The action is not Hermitian but the quantization can be performed consistently. In the (1+3)-dimensional massless case the equation describes a single species of Dirac particle in the continuous space-time limit. In the (1+1)-dimensional massless case the equation is the same as the automaton equation by {close_quote}t Hooft and describes a chiral fermion. The time evolution operator is unitary and the norm is conserved. For interacting fermions with gauge fields the evolution operator is not unitary. But in the continuum limit the unitarity will be recovered. The consequences of loosening the unitarity condition on the time evolution operator are discussed. {copyright} {ital 1997} {ital The American Physical Society}

The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulk-edge correspondence of the massless Dirac fermion systems., Comment: 5 pages

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential(graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field controlled Dirac fermion band structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when applying the bi-harmonic laser field which can provide a straightforward experimental test of the predicted phenomena., Comment: 9 pages, 7 figures, version that will appear in Phys. Rev. B

The recent focus on topological insulators is due to the scientific interest in the new state of quantum matter as well as the technology potential for a new generation of THz optoelectronics, spintronics and quantum computations. It is important to elucidate the dynamics of the Dirac fermions in the topologically protected surface state. Hence we utilized a novel ultrafast optical pump mid-infrared probe to explore the dynamics of Dirac fermions near the Dirac point. The femtosecond snapshots of the relaxation process were revealed by the ultrafast optics. Specifically, the Dirac fermion-phonon coupling strength in the Dirac cone was found to increase from 0.08 to 0.19 while Dirac fermions were away from the Dirac point into higher energy states. Further, the energy-resolved transient reflectivity spectra disclosed the energy loss rate of Dirac fermions at room temperature was about 1 meV/ps. These results are crucial to the design of Dirac fermion devices. © 2013 American Chemical Society., This work was supported by the National Science Council of the Republic of China, Taiwan (Contract No. NSC101-2112-M-009-016-MY2, NSC 101-2112-M-009-017-MY2, NSC 102-2112-M-009-006-MY3, NSC101-2009-M-002-007), the Grant MOE ATU Program at NCTU and RFBR Project 12-02-33174 d. The work at BNL was supported by U.S. Department of Energy, under Contract No. DEAC02- 98CH10886.

A single electron transitor may be fabricated using qunatum dots. A good model for the confinement potential of a quantum dot is a parabolic well. Here we consider such a parabolic dot made of graphene. Recently, we found counter intuitively that resonant quasi-boundstates of both positive and negative energies exist in the energy spectrum. The presence of resonant quasi-boundstates of negative energies is a unique property of massless Dirac fermions. As magnetic field B gets smaller the energy width of these states become broader and for sufficiently weak value of B resonant quasi-bound states disappear into a quasi-continuum. In the limit of small B resonant and nonresonant states transform into discrete anomalous states with a narrow probability density peak inside the well and another broad peak under the potential barrier. In this paper we compute the optical strength between resonant quasi-bound states as a function of B, and investigate how the signature of resonant quasi-bound states of Dirac electrons may appear in optical measurements.

We report the first observation of Shubnikov-de Haas (SdH) oscillations and quantized Hall resistance in the multilayered massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ with tilted cones. Holes were injected into the thin crystal fixed on a polyethylene naphthalate (PEN) substrate by contact electrification. The detection of SdH oscillations whose phase was modified by Berry's phase $\pi$ strongly suggested that the carrier doping was successful in this system. We succeeded in detecting the quantum Hall effect (QHE) with the steps which is the essence of two dimensional Dirac fermion systems. The number of effectively doped layers was examined to be two in this device. We reveal that the correlation between effective layers plays an important role in QHE., Comment: 11 pages, 4 figures

The intersection of two ferromagnetic domain walls placed on the surface of topological insulators provides a one-way beam splitter for domain-wall Dirac fermions. Based on an analytic expression for a static two-soliton magnetic texture we perform a systematic numerical study of the propagation of Dirac wave packets along such intersections. A single-cone staggered-grid finite difference lattice scheme is employed in the numerical analysis. It is shown that the angle of intersection plays a decisive role in determining the splitting ratio of the fermion beam. For a non-rectangular intersection, the width and, to a lesser extent, the type of domain walls, e.g. Bloch or N{\'e}el, determine the properties of the splitter. As the ratio between domain-wall width and transverse localization length of the Dirac fermion is increased its propagation behavior changes from quantum-mechanical (wave-like) to classical ballistic (particle-like). An electric gate placed near the intersection offers a dynamic external control knob for adjusting the splitting ratio.

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, a genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined non-locally by Majorana fermions located at two spatially separated vortices., Comment: 32 pages, no figures, v3: published version

The covariant Dirac equation and its solutions show that rotation and acceleration can be used to generate and control spin currents., 8 pages

Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi 2 Te 3 substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi 2 Te 3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi 2 Se 3 , where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi 2 Se 3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.

Topological insulators (TIs) are a unique class of materials characterized by a surface (edge) Dirac cone state of helical Dirac fermions in the middle of bulk (surface) gap. When the thickness (width) of TIs is reduced, however, interaction between the surface (edge) states will open a gap removing the Dirac cone. Using density function theory calculation, we demonstrate the creation of helical Dirac fermions from interfacing two gapped TI films, a single bilayer Bi grown on a single quintuple layer Bi2Se3 or Bi2Te3. The theoretical prediction is directly confirmed by experiment. We further show that the extrinsic helical Dirac fermions consists of predominantly Bi bilayer states, which are created by a giant Rashba effect due to interfacial charge transfer. Our findings provide a promising new method to create novel TI materials by interface engineering., 18 pages and 4 figures

The Dirac equation, which was derived by combining, in a consistent manner, the relativistic invariance condition with the quantum probability principle, has shown its fecundity by explaining the half-integer spin of fermions and predicting antimatter, the first resulting from a wave beat between a particle and its antiparticle. In the previous paper, it was conjectured that the spinning motion of the electron is that of a massless charge vibrating at light speed, and that this internal motion is responsible for the rest mass measured in external motions (inertia) and interactions (gravitation). In this paper, we develop implications of this concept on such basic properties as time, mass, electric charge, and magnetic moment.

Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a number of novel and exotic quantum phenomena in the topological insulators and for their potential applications in spintronics and quantum computations. It is thus essential to understand the electron dynamics of the Dirac fermions, i.e., how they interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling in these topological insulators and found that the electron-disorder interaction is the dominant factor in the scattering process. The Dirac fermion dynamics in Bi2(Te3-xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding the electron dynamics of the Dirac fermions in topological insulators and in engineering their surface state for fundamental studies and potential applications., Comment: 14 Pages, 4 Figures

The persistent current in strictly one-dimensional Dirac systems is investigated within two different models, defined in the continuum and on a lattice, respectively. The object of the study is the effect of a single magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac model, an analytical expression for the persistent current flowing along a ring with a single delta-like magnetic impurity is obtained after regularization of the unbounded negative energy states. The predicted decay of the persistent agrees with the lattice simulations. The results are generalized to finite temperatures. To realize a single Dirac massless fermion, the lattice model breaks the time-reversal symmetry, and, in contrast with the continuum model, a pointlike nonmagnetic impurity can lead to a decay in the persistent current., 18 pages, 14 figures

The inclusion of Dirac fermions in Einstein-Cartan gravity leads to a four-fermion interaction mediated by non-propagating torsion, which can allow for the formation of a Bardeen-Cooper-Schrieffer condensate. By considering a simplified model in 2+1 spacetime dimensions, we show that even without an excess of fermions over antifermions, the nonthermal distribution arising from preheating after inflation can give rise to a fermion condensate generated by torsion. We derive the effective Lagrangian for the spacetime-dependent pair field describing the condensate in the extreme cases of nonrelativistic and massless fermions, and show that it satisfies the Gross-Pitaevski equation for a gapless, propagating mode., Comment: Minor clarifications, typos corrected. Matches version published in PRD

Equations for relativistic particles for arbitrary spin have been of interest since Dirac original work for spin , but they involved either bothersome constraints or start with as many Dirac equations as are required to get the derived spin from its original value. We first show that it is possible to have just one equation involving 's and 's matrices that give possibilities up to for the spin. We then decompose the 's and 's into direct products of ordinary spin matrices and a new type of them that we call sign spin. The problem reduces then to one in terms of the generators of a U(4) group entirely similar to the one in the spin - isospin theory of nuclear physics and hence the name of supermultiplets in the title. Using then the techniques of the latter we discuss the problem of a free particle in a magnetic field for n = 1,2 and 3 or equivalently eigenvalues for spins 0,, 1 and , and the energies are given as solutions of elementary algebraic equations.

The Dirac equation of the fermion in the classical electromagnetic field is used to prove the existence of the Evans-Vigier field from the first principles of relativistic quantum theory.

Scalar and vector interactions, with the scalar interaction coupled to a composite spin-1/2 system so as to cause a shift of its mass, are shown to obey a low-energy theorem which guarantees that the second order interaction is the same as for a point Dirac particle, in which case the second-order interaction comes from z graphs. Off-shell and contact interactions appropriate to the composite system cancel and this is verified in a model of a composite fermion. The low-energy theorem and its generalizations provide a justification for the use of the Dirac equation as it has been used in relativistic nuclear scattering and mean field theories. \textcopyright{} 1996 The American Physical Society.

Three-dimensional (3D) Dirac semimetals are featured by 3D linear energy-momentum dispersion relation, which have been proposed to be a desirable system to study Dirac fermions in 3D space and Weyl fermions in solid-state materials. Significantly, to reveal exotic transport properties of Dirac semimetals, the Fermi level should be close to the Dirac point, around which the linear dispersion is retained. Here we report the magnetotransport properties near the Dirac point in Cd3As2 nanowires, manifesting the evolution of band structure under magnetic field. Ambipolar field effect is observed with the Dirac point at V g = 3.9 V. Under high magnetic field, there is a resistivity dip in transfer curve at the Dirac point, which is caused by the Zeeman splitting enhanced density of state around the Dirac point. Furthermore, the low carrier density in the nanowires makes it feasible to enter into the quantum limit regime, resulting in the quantum linear magnetoresistance being observed even at room temperature. Besides, the dramatic reduction of bulk conductivity due to the low carrier density, together with a large surface to volume ratio of the nanowire, collectively help to reveal the Shubnikov-de Haas oscillations from the surface states. Our studies on transport properties around the Dirac point therefore provide deep insights into the emerging exotic physics of Dirac and Weyl fermions.

The electronic surface-states of a topological insulator in the presence of an in-plane magnetization vortex M(ϕ)=M(cos(Φ+νϕ), sin(Φ+νϕ)) are investigated theoretically. For a general angle of magnetization Φ∈[0,2π) and topological charge ν = 1, the modifications to the zero-mass single Dirac cone dispersion are treated exactly and the spectrum of bound eigenstates which forms in the energy window ±M cos(Φ) is derived. The space-time resolved dynamics of Dirac fermions in the presence of such vortices is studied numerically using a single-cone (2 + 1)D finite-difference scheme. In the continuous spectral region, Φ-dependent scattering of Dirac fermions at the vortex is observed. Depending on the type of vortex ( Φ, ν) and the impact parameter, the propagation direction of the Dirac fermion is changed: the magnetization of the vortex exerts a torque onto the fermion spin which, by momentum-spin locking associated with the helical Dirac states, results in an in-plane rotation of the propagation direction of...

We assume that a single particle of mass m cannot be localized to better than +h/2mc. Using our understanding of finite and discrete measurement accuracy, the single particle transition in 1+1 space-time from (O, O) to (z, t) can then be characterized by a scale factor N and two integers r, 1defined by z = N(r – l)h/mc and ct = N(r + l)h/mc 2. The average velocity over this finite interval is v = fic. The square of the average momentum is p2 = #mc2. We show that the solution of the free particle Dirac equation with these boundary conditions can be derived by assuming that the (unobserved) trajectories connecting the two endpoints are all constructed from Nr steps to the right and NZ steps to the left, with velocity +C or —c respectively; each single step has length h/me. We attribute this Zitterbewegung to the emission and absorption of transverse photons to and from the background radiation, each of which necessarily flips the spin. We assert that the symmetry . ...-. condition on the background radiation that this radiation be undetectable in free particle motion, plus the assumption that the starting and ending spin state must be the same, constitutes the essential requirement for successful single particle mass renormalization in our simple model. We then show that these requirements suffice to determine finite series which uniquely correspond to the (truncated) series . . solution of the corresponding free particle Dirac equation with the same boundary conditions. We sketch how to extend the model to 3+1 dimensions. The connection of oti model to the derivation of Maxwell’s equations from finite and discrete spacetime measurement accuracy is briefly discussed.

Using Hamilton-Jacobi method, we study the Dirac particles emission from Reissner-Nordstrom-Vaidya (RNV) black hole. The Dirac particles are described by Dirac equation in curved spacetime and emission process is defined as tunneling effect. The probability of Dirac particles emission is related to the Hawking temperature and we obtain that this temperature is equal to temperature that derived through spinless particles emission. Furthermore, we also show that the mass of Dirac particles does not affect to the Hawking temperature.

We explore alternative solutions of the Dirac equation on a lattice. In this sector we examine the characteristics of the states and argue that the excitation spectrum is different.

The three-dimensional (3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A 3Bi (A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission (ARPES) measurements on the two cleaved surfaces, (001) and (100), of Na3Bi. On the (001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k x –k y plane and by varying the photon energy to get access to different out-of-plane k z s. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the (100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the (100) plane. We directly observe two isolated 3D Dirac nodes on the (100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ~150 meV before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the 3D Dirac cones, on the possible formation of surface reconstruction of the (001) surface, and on the issue of basic Brillouin zone selection for the (100) surface.

The mechanism of high Tc superconductivity has not been solved completely yet. It was argued by Anderson that the properties of high Tc superconductivity are normal but the normal state properties are not normal. This seems to be true. We approach the subject of high Tc superconductivity viewing it from the normal state. First the ground state of the S=l/2 square lattice Heisenberg antiferromagnet is investigated using a BCS type variational method and a massless Majorana fermion representation for the spin 1/2 operator. Second when a hole is doped, we investigate how the spin gap appears as an elementary excitation of the spin fluctuation, where we use another Majorana fermion representation for an itinerant hole. Third we investigate the situation in which more holes are doped on the square lattice antifer­ romagnet and spin Majorana fermions are exchanged between itinerant holes. Here, the spin gap becomes unstable, and high Tc superconductivity appears instead of the spin gap, where we describe the superconductive gap by a massive Dirac fermion in the Nambu representation instead of a Majorana fermion. We also discuss the noncoexistence of the spin gap and the superconductive gap formed by the holes and seek to determine the critical concentration of holes, that concentration at which the spin gaps disappear and the superconductive gaps replace them. We also examine the phase diagram of the spin gap state and the supercon­ ductive state as a function of the hole concentration and the temperature. The method we adopt is that introduced by Tsvelik,l) who uses the Majorana fermion representation for spins and holes in the Kondo problem and the heavy fermion problem. A Majorana fermion is massless, and, using this representation, we can avoid the use of both the slave boson and fermion to represent the spin operator and their gauge fields. Then we can use the BCS-type variational method for the interaction of the Majorana fermions without using the Gutzwiller projection together with the restriction of the double occupancy of the opposite spins on the same site, as adopted in the modified variational method by Zhang, Gros, Rice and Shiba. 2 l

We have theoretically investigated the spin inelastic scattering of helical electrons off a high-spin nanomagnet absorbed on a topological surface. The nanomagnet is treated as a dynamic quantum spin and driven by the spin transfer torque effect. We proposed a mechanism to electrically manipulate the spin texture of helical Dirac fermions rather than by an external magnetic field. By tuning the bias voltage and the direction of impurity magnetization, we present rich patterns of spin texture, from which important fingerprints exclusively associated with the spin helical feature are obtained. Furthermore, it is found that the nonmagnetic potential can create the resonance state in the spin density with different physics as the previously reported resonance of charge density.

We present novel gamma-ray features that are almost exclusively a consequence of kinematical considerations in one-step cascade processes. These features arise from relativistic effects on final state photons from decaying intermediate states. Depending on the spin of the intermediate state the specific shape of the signal varies: a scalar or Majorana fermion intermediate state produces gamma-ray boxes, whereas a Dirac fermion intermediate state produces gamma-ray triangles. We refer to physical realisations that produce such features. Finally, we illustrate their strong constraining power using data drawn from the Fermi-LAT instrument.

Arguments favouring the existence of a fourth fermion family in the framework of the Standard Model are given. The masses of the fourth family neutrino, charged lepton and down quark are close to each other within an accuracy of the order of a few GeV and lie between 300–700 GeV. Experiments on the search for these particles are discussed.

Fermions are considered in a multidimensional space with two extra dimensions. Fermion Lagrangian contains coupling to a metric of deformed extra space. We show that the point-like defect on a space with topology of sphere leads to fermion interaction with such defect and calculate cross section of a fermion scattering on such defect.

An idea is proposed for realizing a fully spin-polarized Dirac semimetal in frustrated itinerant magnets. We show that itinerant electrons on a triangular lattice exhibit the Dirac cone dispersion with half-metallic behavior in the presence of a three-sublattice ferrimagnetic order. The Dirac nodes have the same structure as those of graphene. By variational calculation and Monte Carlo simulation, we demonstrate that the ferrimagnetic order with the Dirac node spontaneously emerges in a simple Kondo lattice model with Ising anisotropy. The realization will be beneficial for spintronics as a candidate for spin-current generator., 5 pages, 4 figures, accepted for publication in Phys. Rev. Lett

We present a numerical method to compute the Landauer conductance of noninteracting two-dimensional massless Dirac fermions in disordered systems. The method allows for the introduction of boundary conditions at the ribbon edges and accounts for an external magnetic field. By construction, the proposed discretization scheme avoids the fermion doubling problem. The method does not rely on an atomistic basis and is particularly useful to deal with long-range disorder, the correlation length of which largely exceeds the underlying material crystal lattice spacing. As an application, we study the case of monolayer graphene sheets with zigzag edges subjected to long-range disorder, which can be modeled by a single-cone Dirac equation., 11 pages, 10 figures

We use a single site lattice in four dimensions to study the scaling of large $N$ Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to the weak coupling transition defined through the eigenvalues of the folded Wilson loop operator to set a scale. We do not observe perturbative scaling in the region studied in this paper. Instead, we observe that the scale changes very slowly with the bare coupling. The lowest eigenvalue of the overlap Dirac operator is another scale that shows similar behavior as a function of the lattice coupling.

We report electronic transport of Dirac cones when Fe is replaced by Ru, which has an isoelectronic electron configuration to Fe, using single crystals of Ba(Fe${}_{1\ensuremath{-}x}$Ru${}_{x}$As)${}_{2}$. The electronic transport of parabolic bands is shown to be suppressed by scattering due to the crystal lattice distortion and the impurity effect of Ru, while that of the Dirac cone is not significantly reduced due to the intrinsic character of Dirac cones. It is clearly shown from magnetoresistance and Hall coefficient measurements that the inverse of average mobility, proportional to cyclotron effective mass, develops as the square root of the carrier number ($n$) of the Dirac cones. This is the unique character of the Dirac cone linear dispersion relationship. Scattering of Ru on the Dirac cones is discussed in terms of the estimated mean free path using experimental parameters.

We use Monte Carlo simulation to probe the phase structure of a SU(2) gauge theory containing $N_f$ Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional four fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory. The resultant lattice theory is invariant under a set of shift symmetries which correspond to a discrete subgroup of the continuum chiral-flavor symmetry. The pseudoreal character of the representation guarantees that the theory has no sign problem. For the case of $N_f=4$ we observe a crossover in the behavior of the chiral condensate for strong four fermi coupling associated with the generation of a dynamical mass for the fermions. At weak gauge coupling this crossover is consistent with the usual continuous phase transition seen in the pure (ungauged) NJL model. However, if the gauge coupling is strong enough to cause confinement we observe a much more rapid crossover in the chiral condensate consistent with a first order phase transition

We develop an effective bulk model with a topological boundary condition to study the surface states of topological insulators. We find that the Dirac point energy, the band curvature and the spin texture of surface states are crystal face-dependent. For a given face on a sphere, the Dirac point energy is determined by the bulk physics that breaks p-h symmetry in the surface normal direction and is tunable by surface potentials that preserve T symmetry. Constant energy contours near the Dirac point are ellipses with spin textures that are helical on the S/N pole, collapsed to one dimension on any side face, and tilted out-of-plane otherwise. Our findings identify a route to engineering the Dirac point physics on the surfaces of real materials., 4.1 pages, 2 figures and 1 table

In this chapter the Dirac equation is solved for an electron in the presence of a magnetostatic field. To solve the Dirac equation requires a specific choice of gauge for the magnetostatic field, and a specific choice of the spin operator. It is then possible to separate the wavefunction into a gauge- and spin-dependent factor and a reduced wavefunction that satisfies a reduced form of the Dirac equation that is independent of the choice of gauge and spin operator. In generalizing QED to include the magnetic field exactly, the conventional momentum representation for the Feynman amplitudes is not available, because momentum perpendicular to the magnetic field is not conserved. However, the separation of the wavefunction allows an analogous separation of the electron propagator and the vertex functions, with the gauge-independent part closely analogous to the momentum-space representation in the unmagnetized case. The gauge-dependent part (partially) describes the location of the center of gyration of the electron, and how it changes in a QED interaction, and such information is rarely of interest, and is simply ignored when using the reduced theory.

We rederive in a physical manner the Weyl anomaly in two-dimensional space–time by considering the Dirac Sea. It is regularized by some bosonic extra species which are formally negatively counted. In fact, we calculate the trace of the energy–momentum tensor in the Dirac Sea in presence of background gravitational field. It has to be regularized, since the Dirac Sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive bosonic species some of which are to be counted negative in the Dirac Sea. The mass terms in the Lagrangian of the regularization fields have a dependence on the background gravitational field.