Gabriela Murguia

Magnetic field barriers in graphene: an analytically solvable model.

We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with a hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum mechanics, and leads to an exactly solvable model. We study in detail the bound-state spectrum. For a narrow barrier the spectrum is characterized by a few bands, except for the zero energy level that remains degenerated. As the width of the barrier increases we can track the bands evolution into the degenerated Landau levels. In the scattering regime a simple analytical formula is obtained for the transmission coefficient, this result allows us to identify the resonant conditions at which the barrier becomes transparent.

The electron propagator in external electromagnetic fields in low dimensions

We study the electron propagator in quantum electrodynamics in one and two spatial dimensions in the presence of external electromagnetic fields. In this case, the propagator is not diagonal in momentum space. We obtain the propagator on the basis of the eigenfunctions of the operator (γ⋅Π)2 in terms of which the propagator acquires a free form. Πμ is the canonical momentum operator and γμ are the Dirac matrices. In two dimensions, we work with an irreducible representation of the Clifford algebra and consider to all orders the effects of an arbitrary magnetic field perpendicular to the plane of motion of the electrons. We then discuss the special cases of a uniform magnetic field and an exponentially damped static magnetic field. These cases are relevant to graphene in the massless limit. We further consider the electron propagator for the massive Schwinger model and incorporate the effects of a constant electric field to all orders.

Planar Dirac Fermions in External Electromagnetic Fields

We study the electron propagator in two spatial dimensions in the presence of external electromagnetic fields, this is, we focus in (2+1)-dimensional quantum electrodynamics (QED), where a third spatial dimension is suppressed. This is not a mere theoretical simplification, and we explain ourselves: back in time, some twenty years ago, it was shown that the low-energy effective theory of graphene in a tight-binding approach is the theory of two species of massless Dirac electrons in a (2+1)-dimensional Minkowski spacetime, each on a different irreducible representation of the Clifford algebra. The isolation of graphene samples in 2004 and 2005, has given rise to the new paradigm of relativistic condensed matter, bringing a new boost, both theoretical and experimental, to the matching of common interests of the condensedmatter and high energy physics communities. Thus, themassless limit of our findings is of direct relevance in this subject. We assume the electrons moving in a magnetic field alone pointing perpendicularly to their plane of motion. We first develop the general case and then, we present a couple of examples: themotion of electrons in a uniformmagnetic field, which is a canonical example to present the Ritusmethod and the case of a static magnetic field which decays exponentially along the x-axis (Murguia et al, 2010; Raya & Reyes, 2010). There are many problems relating electrons in non-uniform magnetic fields of relevance in graphene. In particular, it has been established the possibility to confine quasiparticles in magnetic barriers (DeMartino et al, 2007; Ramezani et al, 2009). This could be feasible creating spatially inhomogeneous, but constant in time, magnetic fields depositing ferromagnetic layers over the substrate of a graphene sample layer (Reijniers et al, 2001). The physical properties of graphene make it a promising novel material to control the transport properties in nanodevices. It has been considered to be used in electronics and spintronics applications, like in single-electron transistors (Ponomarenko et al, 2008; Wu et al, 2008), in the so called magnetic edge states (Park & Sim, 2008), which may play an important role in the spin-polarized currents along magnetic domains, and in quantum dots and antidots magnetically confined. Moreover, the quantum Hall effect in graphene has been observed at room temperature (Novoselov et al, 2007), evidence which confirms the great potential of graphene as the material to be used in carbon-based electronic devices. The effects of the exponentially decaying magnetic field can hardly be considered with other approaches, 13

Free form of the Foldy-Wouthuysen transformation in external electromagnetic fields

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator

Classical limit for the scattering of Dirac particles in a magnetic field

(\gamma \cdot \Pi)^2

Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field

, with

Hard and soft supersymmetry breaking for ?graphinos? in uniform magnetic fields

\Pi^\mu = p^\mu - e A^\mu

Magnetic Edge States in Graphene

. In this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.

FAST TRACK COMMUNICATION: Free form of the Foldy-Wouthuysen transformation in external electromagnetic fields

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0\|sin(\theta/2)|/\hbar 0) is consistent, contrarily to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.

D-wave overlapping band model for cuprate superconductors

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non‐relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non‐perturbative methodology should be applied.