Planar Dirac Fermions in External Electromagnetic Fields

Arxiv preprint arXiv:1008.4901, 2010

2011

The present article discusses magnetic confinement of the Dirac excitations in graphene in presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to 1/r is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in presence of the 1/r (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cut-off Coulomb potential to dictate the excitation spectra of graphene. The spectrum of the graphene excitations in presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.

Physical Review B, 2008

We evaluate the transmission through magnetic barriers in graphene-based nanostructures. Several particular cases are considered: a magnetic step, single and double barriers, and ␦-function barriers. A separate class of magnetic-barrier structures are those with inhomogeneous magnetic-field profiles, such that the average magnetic field vanishes, which can be realized by nanostructured ferromagnetic stripes placed on top of the graphene layer. Quantum bound states that are localized near or in the barrier are predicted for a magnetic step and some structures with finite-width barriers but none for ␦-function barriers. When a bound state is localized close to the barrier edge, it has a nonzero velocity parallel to this edge. The transmission depends strongly on the direction of the incident electron or hole wave vector and gives the possibility to construct a directiondependent wave vector filter. In general, the resonant structure of the transmission is significantly more pronounced for ͑Dirac͒ electrons with linear spectrum than for the usual electrons with a parabolic spectrum.

2017

Physical Review Letters, 2008

We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.

Physical Review B, 2006

We study the problem of Dirac fermion confinement in graphene in the presence of a perpendicular magnetic field B. We show, analytically and numerically, that confinement leads to anomalies in the electronic spectrum and to a magnetic field dependent crossover from √ B, characteristic of Dirac-Landau level behavior, to linear in B behavior, characteristic of confinement. This crossover occurs when the radius of the Landau level becomes of the order of the width of the system. As a result, we show that the Shubnikov-de Haas oscillations also change as a function of field, and lead to a singular Landau plot. We show that our theory is in excellent agreement with the experimental data.

Physical Review B, 2012

We compute the magnetization of graphene in a magnetic field, taking into account for generality the possibility of a mass gap. We concentrate on the physical regime where quantum oscillations are not observed due to the effect of the temperature or disorder and show that the magnetization exhibits non-linear behaviour as a function of the applied field, reflecting the strong non-analyticity of the two-dimensional effective action of Dirac electrons. The necessary values of the magnetic field to observe this non-linearity vary from a few Teslas for very clean suspended samples to 20-30 Teslas for good samples on substrate. In the light of these calculations, we discuss the effects of disorder and interactions as well as the experimental conditions under which the predictions can be observed.

New Journal of Physics, 2009

The properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (δ-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a finite number of barriers. The results are contrasted with those for electrons described by the Schrödinger equation. In addition, a collimation of an incident beam of electrons is obtained along the direction perpendicular to that of the SL. We also highlight the analogy with optical media in which the refractive index varies in space.

A single atomic layer of carbon, graphene, has the low-energy "relativistic-like" gapless quasiparticle excitations which in the continuum approximation are described by quantum electrodynamics in 2+1 dimensions. The Diraclike character of charge carriers in graphene leads to several unique electronic properties which are important for applications in electronic devices. We study the gap opening in graphene following the ideas put forward by P. I. Fomin for investigation of chiral symmetry breaking and particle mass generation in quantum field theory.

arXiv (Cornell University), 2022

In this paper, a simple method is proposed to get analytical solutions (or with the help of a finite numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic fields. In order to decouple the Dirac-Weyl equation we have assumed a displacement symmetry of the system along a direction and some conditions on the magnetic and electric fields. The resulting equations have the natural form to apply the technique of supersymmetric quantum mechanics. The example of an electric well with square profile is worked out in detail to illustrate some of the most interesting features of this procedure.