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Graphene nanoribbons (GNRs) are natural waveguides for electrons in graphene. Nevertheless, unlike micron-sized samples, conductance is nearly suppressed in these narrow graphene stripes, mainly due to scattering with edge disorder generated during synthesis or cut. A possible way to circumvent this effect is to define an internal waveguide that isolates specific modes from the edge disorder and allows ballistic conductance. There are several proposals for defining waveguides in graphene; in this manuscript, we consider strain folds and scalar potentials and numerically evaluate these proposals' performance against edge and bulk disorder. Using the Green's function approach, we calculate conductance and the local density of states (LDOS) of zigzag GNRs and characterize the performance of these different physical waveguiding effects in both types of disorder. We found a general improvement in the electronic conductance of GNR due to the presence of the internal waveguiding, with the emergence of plateaus with quasi-ballistic properties and robustness against edge disorder. These findings are up to be applied in modern nanotechnology and being experimentally tested., Comment: 7 pages, 5 figures

We propose and numerically simulate an optoelectronic compact circular polarimeter. It allows for electrical measurement of the degree of circular polarization and light intensity at room temperature for a wide range of incidence angles in a single shot. The device, being based on ${\mathrm{Ga}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$, is easy to integrate into standard electronics and does not require bulky movable parts nor extra detectors. Its operation hinges mainly on two phenomena: the spin-dependent capture of electrons and the hyperfine interaction between bound electrons and nuclei on ${\mathrm{Ga}}^{2+}$ paramagnetic centers in ${\mathrm{Ga}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$. The first phenomenon confers the device with sensitivity to the degree of circular polarization and the latter phenomenon allows one to discriminate the handedness of the incident light.

The detection of light helicity is key to several research and industrial applications from drugs production to optical communications. However, the direct measurement of the light helicity is inherently impossible with conventional photodetectors based on III-V or IV-VI semiconductors, being naturally non-chiral. The prior polarization analysis of the light by a series of often moving optical elements is necessary before light is sent to the detector. A method is here presented to effectively give to the conventional dilute nitride GaAs-based semiconductor epilayer a chiral photoconductivity in paramagnetic-defect-engineered samples. The detection scheme relies on the giant spin-dependent recombination of conduction electrons and the accompanying spin polarization of the engineered defects to control the conduction band population via the electrons' spin polarization. As the conduction electron spin polarization is, in turn, intimately linked to the excitation light polarization, the light polarization state can be determined by a simple conductivity measurement. This effectively gives the GaAsN epilayer a chiral photoconductivity capable of discriminating the handedness of an incident excitation light in addition to its intensity. This approach, removing the need of any optical elements in front of a non-chiral detector, could offer easier integration and miniaturisation. This new chiral photodetector could potentially operate in a spectral range from the visible to the infra-red using (In)(Al)GaAsN alloys or ion-implanted nitrogen-free III-V compounds., Comment: 7 pages, 7 figures

Electromagnetic dressing by a high-frequency field drastically modifies the electronic transport properties on Dirac systems. Here its effects on the energy spectrum of graphene with two possible phases of Kekul\'e distortion (namely, Kek-Y and Kek-O textures) are studied. Using Floquet theory it is shown how circularly polarized light modifies the gapless spectrum of the Kek-Y texture, producing dynamical band gaps at the Dirac point that depends on the amplitude and the frequency of the electric field, and breaks the valley degeneracy of the gapped spectrum of the Kek-O texture. To further explore the electronic properties under circularly polarized radiation, the dc conductivity is studied by using the Boltzmann approach and considering both inter-valley and intra-valley contributions. When linearly polarized light is considered, the band structure of both textures is always modified in a perpendicular direction to the electric field. While the band structure for the Kek-Y texture remains gapless, the gap for the Kek-O texture is reduced considerably. For this linear polarization it is also shown that non-dispersive bands can appear by a precise tuning of the light field parameters thus inducing dynamical localization. The present results suggest that optical measurements will allow to distinguish between different Kekul\'e bond textures., Comment: 14 pages, 5 figures

We analyze the quasienergy-spectrum and the valence to conduction-band transition probabilities of a tilted anisotropic Dirac material subject to linearly and circularly polarized electromagnetic fields. The quasienergy-spectrum is numerically calculated from the monodromy matrix of the Schr\"odinger equation via the Floquet theorem for arbitrarily intense electromagnetic fields. To asses the valence to conduction-band transition times we deduced a Rabi-like formula in the rotating wave approximation. In the strong-field regime the spectrum as a function of the momentum components divides into two very distinctive regions. In the first, located around the Dirac point, the quasi-spectrum is significantly distorted by the field as the electronic parameters are renormalized by electronic-dressing. In the second, all the characteristics of the free carrier spectrum are retained. Linearly polarized light anisotropically deforms the spectrum according to the field polarization direction. Dirac-like points form around the original Dirac point. The quasi spectrum of circularly polarized light, instead, exhibits a gap formation in the Dirac point and has elliptical symmetry. We show that, in contrast to the single-photon resonant transitions that characterize the weak-field regime, the strong-field regime is dominated by multiphoton resonances., Comment: 13 pages, 8 figures

Spin-dependent recombination in GaAsN offers many interesting possibilities in the design of spintronic devices mostly due to its astounding capability to reach conduction band electron spin polarization close to 100% at room temperature. The mechanism behind the spin selective capture of electrons in ${\mathrm{Ga}}^{2+}$ paramagnetic centers is revisited in this paper to address inconsistencies common to most previously presented models. Primarily, these errors manifest themselves as major disagreements with the experimental observations of two key characteristics of this phenomenon: the effective Overhauser-like magnetic field and the width of the photoluminescence Lorentzian-like curves as a function of the illumination power. These features are not only essential to understand the spin-dependent recombination in GaAsN, but are also key to the design of novel spintronic devices. Here we demonstrate that the particular structure of the electron capture expressions introduces spurious electron-nucleus correlations that artificially alter the balance between the hyperfine and the Zeeman contributions. This imbalance strongly distorts the effective magnetic field and width characteristics. In this work we propose an alternative recombination mechanism that preserves the electron-nucleus correlations and, at the same time, keeps the essential properties of the spin selective capture of electrons. This mechanism yields a significant improvement to the agreement between experimental and theoretical results. In particular, our model gives results in very good accord with the experimental effective Overhauser-like magnetic field and width data, and with the degree of circular polarization under oblique magnetic fields.

International audience; The impact of Ga3+ centers in the spin-filtering effect observed in GaAsN samples is investigated through a model based on the master equation approach. Our results, compared with experimental data, show that, Ga3+ are essential to understanding the behavior of the photoluminescence intensity and degree of circular polarization as functions of a Faraday configuration magnetic field. The model presented here takes into account the interplay of Ga2+ and Ga3+ centers, Zeeman and hyperfine interaction. The various processes that drive the spin-filtering effect, as the spin selective capture of conduction band electrons into Ga centers are also considered here.

In this paper, we analyse the quantization of cyclotron orbits for a 2D non-relativistic and spinless charged particle under the influence of a static and uniform magnetic field, the Landau problem. We follow the algebraic approach of rising and lowering operators. The Hamiltonian is expressed in terms of the usual rising and lowering operators of an isotropic quantum oscillator. Through a Bogoliubov transformation, we show that the Hamiltonian may be reduced to the one of a quantum oscillator that accounts for the formation of infinitely degenerate Landau levels. The explicit form of the position-space wave functions of Fock–Darwin states for a vanishing parabolic confinement potential is worked out by applying the techniques of ladder operators and the induction method. To explore the internal dynamics of the electron states, we compute the Fock–Darwin states’ density currents expressing them in terms of the ladder operators. In the supplementary material, we provide the reader with Mathematica algorithm that can help perform some of the calculations exposed in the paper. The charged particle in a magnetic field is used to explore some of the fundamental concepts of quantum mechanics as commuting operators, simultaneous eigenstates, degeneracy, rising and lowering operators, etc. This approach can be used as supplementary material in undergraduate final-year courses like quantum mechanics or solid state physics.

The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schr\"odinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under the normal incidence of linearly polarized waves are obtained for an arbitrarily intense electromagnetic radiation. We applied a set of unitary transformations to reduce the Schr\"odinger equation to an ordinary second-order differential Hill equation with complex coefficients. Through the stability analysis of this differential equation, the weak and strong field regimes are clearly distinguished in the quasi-spectrum. In the weak electric field regime, above a certain threshold given by the field parameters, the spectrum mostly resembles that of free electrons in graphene. Below this threshold, in the strong electric field regime, the spectrum abruptly becomes highly anisotropic and a gap opens up. As an example, we apply the results to the particular case of borophene., Comment: 8 pages, 4 figures

The dynamical-gap formation in an anisotropic tilted Dirac semimetal modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schr\"odinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under normal incidence of elliptically polarized electromagnetic waves are obtained using a nonperturbative approach. In it, the Schr\"odinger equation is reduced to an ordinary second-order differential Mathieu equation. It is shown that the stability conditions of the Mathieu functions are directly inherited by the wave function resulting in a quasiparticle spectrum consisting of bands and gaps determined by dynamical diffraction and resonance conditions between the electron and the electromagnetic wave. Estimations of the electromagnetic field intensity and frequency, as well as the magnitude of the generated gap, are obtained for the $8\text{\ensuremath{-}}Pmmn$ phase of borophene. We provide a simple method that enables us to predict the formation of dynamical gaps of unstable wave functions and their magnitudes. This method can readily be adapted to other anisotropic tilted Dirac semimetals.

We propose an experimental procedure to track the evolution of electronic and nuclear spins in Ga2+ centers in GaAsN dilute semiconductors. The method is based on a pump-probe scheme that enables to monitor the time evolution of the three components of the electronic and nuclear spin variables. In contrast to other characterization methods, as nuclear magnetic resonance, this one only needs moderate magnetic fields ( $B\approx 10$ mT), and does not require microwave irradiation. Specifically, we carry out a series of tests for different experimental conditions in order to optimize the procedure for maximum sensitivity in the measurement of the circular degree of polarization. Based on previous experimental results and the theoretical calculations presented here, we estimate that the method could yield a time resolution of about 10ps.

Similar to nitrogen-vacancy centers in diamond and impurity atoms in silicon, interstitial gallium deep paramagnetic centers in GaAsN have been proven to have useful characteristics for the development of spintronic devices. Among other interesting properties, under circularly polarized light, gallium centers act as spin filters that dynamically polarize free and bound electrons reaching record spin polarizations (close to 100%). Furthermore, the recent observation of the amplification of the spin filtering effect under a Faraday configuration magnetic field has suggested that the hyperfine interaction that couples bound electrons and nuclei permits the optical manipulation of the nuclear spin polarization. Even though the mechanisms behind the nuclear spin polarization in gallium centers are fairly well understood, the origin of nuclear spin relaxation and the formation of an Overhauser-like magnetic field remain elusive. In this work we develop a model based on the master equation approach to describe the evolution of electronic and nuclear spin polarizations of gallium centers interacting with free electrons and holes. Our results are in good agreement with existing experimental observations. In particular, we are able to reproduce the amplification of the spin filtering effect under a circularly polarized excitation in a Faraday configuration magnetic field. In regard to the nuclear spin relaxation, the roles of nuclear dipolar and quadrupolar interactions are discussed. Our findings show that, besides the hyperfine interaction, the spin relaxation mechanisms are key to understand the amplification of the spin filtering effect and the appearance of the Overhauser-like magnetic field. To gain a deeper insight in the interplay of the hyperfine interaction and the relaxation mechanisms, we have also performed calculations in the pulsed excitation regime. Our model's results allow us to propose an experimental protocol based on time-resolved spectroscopy. It consists of a pump-probe photoluminescence scheme with the detection and the tracing of the electron-nucleus flip-flops through photoluminescence measurements.

International audience; We demonstrate the triggering and detection of coherent electron-nuclear spin oscillations related to the hyperfine interaction in Ga deep paramagnetic centers in GaAsN by band-to-band photoluminescence without an external magnetic field. In contrast to other point defects such as Cr4+ in SiC, Ce3+ in yttrium aluminum garnet crystals, nitrogen-vacancy centers in diamond, and P atoms in silicon, the bound-electron spin in Ga centers is not directly coupled to the electromagnetic field via the spin-orbit interaction. However, this apparent drawback can be turned into an advantage by exploiting the spin-selective capture of conduction band electrons to the Ga centers. On the basis of a pump-probe photoluminescence experiment we measure directly in the temporal domain the hyperfine constant of an electron coupled to a gallium defect in GaAsN by tracing the dynamical behavior of the conduction electron spin-dependent recombination to the defect site. The hyperfine constants and the relative abundance of the nuclei isotopes involved can be determined without the need of an electron spin resonance technique and in the absence of any magnetic field. Information on the nuclear and electron spin relaxation damping parameters can also be estimated from the oscillation amplitude decay and the long-time-delay behavior.

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest non-vanishing terms of the wave function near the singularity it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity., Comment: 16 pages, 17 figures, 1 table

We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields., Comment: 17 pages, 3 tables

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail., Comment: 14 pages, 4 figures, misprints and figures corrected

In this paper we introduce an alternative approach to studying the motion of a planar charged particle subject to a static uniform magnetic field. It is well known that an electric charge under a uniform magnetic field has a planar motion if its initial velocity is perpendicular to the magnetic field. Although some constants of motion (CsM), as the energy and the angular momentum, have been widely discussed for this system, others have been neglected. We find that the angular momentum, the generator of the magnetic translations and the magnetic Laplace–Runge–Lenz vector are CsM for this particular system. We show also that these three quantities form an orthogonal basis of vectors. The present work addresses many aspects of the motion of a charged particle in a magnetic field that should be useful for students and tutors of the classical mechanics courses at the senior undergraduate level.