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We analyze the effects of Robin-like boundary conditions on different quantum field theories of spin 0, 1/2 and 1 on manifolds with boundaries. In particular, we show that these conditions often lead to the appearance of edge states. These states play a significant role in physical phenomena like quantum Hall effect and topological insulators. We prove in a rigorous way the existence of spectral lower bounds on the kinetic term of different Hamiltonians, even in the case of Abelian gauge fields where it is a non-elliptic differential operator. This guarantees the stability and consistency of massive field theories with masses larger than the lower bound of the kinetic term. Moreover, we find an upper bound for the deepest edge state. In the case of Abelian gauge theories, we analyze a generalization of Robin boundary conditions. For Dirac fermions, we analyze the cases of Atiyah–Patodi–Singer and chiral bag boundary conditions. The explicit dependence of the bounds on the boundary conditions and the size of the system is derived under general assumptions.

The response of fermionic system to external gauge fields is defined by current–current correlation function Π_μν(q, q₀). Transport properties of different physical quantities are determined by zero energy–momentum limit of it. As it is known close to half-filling the physics of graphene is described by (2+1)-dimensional Dirac theory. In this paper, we calculate current–current correlation function in Dirac theory in a presence of chemical potential η and gap m.

In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the Sp(2, 2) group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to an UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i.e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli–Lubanski type operator are also pointed out.

In this research, in a difficult but absolutely precise way of calculation, we show how a very tiny amount of a non-commutative change of quantum space would appear almost as big as a normal physical interaction, namely the Rashba spin-orbit interaction, for relativistic fermions. Hence, in order to show that, we firstly solve a relativistic equation of motion of a Dirac particle, influenced by a typical harmonic energy-dependent interaction for commutative and non-commutative frameworks via the Nikiforov–Uvarov exact approach. Then to study perturbation effects of a spin-orbit interaction, we apply it for both mentioned frameworks, obtaining their energy polynomial relations and discriminant formula to precisely extract all physical-admissible roots of their quartic equations. In this step, we analyze the behaviors of their quartic eigenvalue polynomials in four sections and accurately compare them one by one. Finally, we distinctly show that the magnitude of the physical spin-orbit perturbation appears, almost of the same order of imposing a non-commutative geometry change of framework, as an outstanding result.

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the $Sp(2,2)$ group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

The general formalism of the free Dirac fermions on spatially flat (1+3)-dimensional Friedmann-Lemaître–Robertson–Walker (FLRW) space–times is developed in momentum representation. The mode expansions in terms of the fundamental spinors satisfying the charge conjugation and normalization conditions are used for deriving the structure of the anticommutator matrix-functions and, implicitly, of the retarded, advanced, and Feynman fermion propagators. The principal result is that the new type of integral representation we proposed recently in the de Sitter case can be applied to the Dirac fermions in any spatially flat FLRW geometry. Moreover, the Dirac equation of the left-handed massless fermions can be analytically solved finding a general spinor solution and deriving the integral representations of the neutrino propagators. It is shown that in the Minkowski flat space–time our new integral representation is up to a change of variable just like the usual Fourier representation of the fermion propagators. The form of the Feynman propagator of the massive fermions on a spatially flat FLRW space–time with a scale factor of Milne-type is also outlined.

The results of spectroscopic (magneto-transmission and Raman scattering) studies^1–8 of multilayers of carbon which are thermally decomposed from carbon-terminated surface of silicon carbide, and of thin layers of highly oriented pyrolytic and natural graphite were presented.

Those carbon multilayers on silicon carbide which are not directly affected by the SiC/C interface and which in consequence are nearly charge neutral show the magneto-optical properties identical with the properties characteristic of a single graphite sheet, graphene. Inter Landau level transitions in this multilayer graphene have been studied in a wide spectral range from far-infrared to almost visible region. The dispersion relations of electronic states are found to reflect the form of the Dirac cone with almost perfect electron-hole symmetry and only weak deviations from linearity at high energies. Cyclotron resonance transition in multilayer graphene can be observed in magnetic fields down to 40 mT, and its width is practically independent on temperature up to 300 K. Such parameters as carrier mobility and minimal conductivity as well as the possibility to probe the immediate vicinity of the Dirac point were evaluated and discussed in detail.

For comparison, the magneto-optical properties of thin layers of bulk graphite were also reported. The Dirac like electronic dispersion relations are also found in these systems, but only in the vicinity of the particular (H) point of the Brillouin zone. In general, the measured spectra are, however, more complex and reflect the three-dimensional character of graphene layers with Bernal stacking.

Note from Publisher: This article contains the abstract only.

Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah–Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).

Graphene has brought forward a lot of new physics. One of them is the emergence of massless Dirac fermions in addition to the electrons and these features are new to physics. In this theoretical study, the signatures for quantum scar and the breakdown of universality in graphene are investigated with reference to the presence of these two types of fermions. Taking the graphene quantum dot (QD) potential as the confining potential, the radial part of Dirac equations are solved numerically. Concentrations of the two component eigen-wavefunctions about classical periodic orbits emerge as the signatures for the quantum scar. The sudden variations, in the ratio of the radial wave-functions (large and small components), R(g/f), with mass ratio $\kappa$ are the signatures for breakdown of universality in graphene. The breakdown of universality occurs for the states k = −1 and k = 1, and the state k = −1 is more susceptible to the breakdown of universality.

Wilson–Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the ${\varphi }^4$ field theories that describe low-energy physics of the canonical models, such as Ising, XY, and Heisenberg. Here, I review its application to a class of the Gross–Neveu–Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the ${\varphi }^4$ field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term and which still exhibit critical fixed points in the suitably formulated Wilson–Fisher $ϵ$-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art $ϵ$-expansion, quantum Monte Carlo, large N, and functional renormalization-group calculations can be made.

In this paper, we are discussing the problem of low energy greybody factors for fermions emitted by a Schwarzschild-de Sitter (SdS) black hole. In our study, we are using the analytical methods proposed by Unruh some time ago for determining the greybody factors. We have found that at low energies the greybody factors are constant for a given total angular momentum (similar to what happens in the case of scalar particles reported before in the literature). Also, our results are indicating an enhancement in the energy spectrum if one is increasing the value of the cosmological constant. These results are consistent with numerical calculations performed by S. F. Wu et al., Phys. Rev. D78 (1998) 084010.

In this paper, we study the relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity in $(3+1)$-dimensions, where we work with the curved Dirac equation with minimal coupling in cylindrical coordinates. Using the tetrads formalism of General Relativity, we obtain a second-order differential equation. Solving this differential equation, we obtain a generalized Laguerre equation as well as the relativistic Landau levels for the fermion and antifermion, where such energy levels are quantized in terms of the quantum numbers n, $m_j$ and $m_s$, and explicitly depends on the rainbow functions $f(\epsilon )$ and $g(\epsilon )$, charge parameter $\sigma$, cyclotron frequency ${\omega }_c$, curvature parameter $\alpha$, and on the square rest energy $m_0^2$ and square z-momentum $k_z^2$, respectively. Posteriorly, we study the nonrelativistic limit of the system, where we obtain the nonrelativistic Landau levels. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of Landau levels for the three-rainbow gravity scenarios as a function of the magnetic field B and of the curvature parameter $\alpha$. In addition, we also compared our problem with other works, where we verified that our results generalize several particular cases in the literature.

In the present work, we report on the magneto-transport properties of graphitic based materials (graphene, few-layer graphene, and bulk graphite) in very high magnetic field. Quantum Hall Effect (QHE) has been studied in graphitic systems in very high pulsed magnetic field (up to B = 57 T) and at low temperature (≤ 4 K). Graphene sample shows well-defined Hall resistance plateaus at filling factors v = 2,6,10, etc. Few-layer graphene systems display clear signatures of standard and unconventional QHE. Magneto-transport studies on bulk highly oriented pyrolytic graphite show a charge density wave transition at strong enough magnetic field as well as Hall coefficient sign reversal.

The tunneling effect of two-dimensional Dirac fermions in a constant magnetic field is studied. This can be done by using the continuity equation at some points to determine the corresponding reflexion and transmission coefficients. For this, we consider a system made of graphene as superposition of two different regions where the second is characterized by an energy gap t'. In fact, we treat concrete systems to practically give two illustrations: barrier and diode. For each case, we discuss the transmission in terms of the ratio of the energy conservation and t'. Moreover, we analyze the resonant tunneling by introducing a scalar Lorentz potential where it is shown that a total transmission is possible.