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Experimental and theoretical studies on optical orientation and spin-dependent recombination in a semiconductor in a magnetic field under the normal incidence of circularly polarized radiation onto the sample surface are reviewed. The experiments were carried out on GaAs1 –xNx solid solutions, in which Ga2+ interstitial displacement defects play the role of deep paramagnetic centers responsible for spin-dependent recombination. It is established that, in the investigated materials, the hyperfine interaction of a localized electron with one nucleus of the paramagnetic center remains strong even at room temperature. The theory is compared with an experiment conducted in the steady-state excitation mode and under two-pulse pump-probe conditions. An analytical formula for spin beats in a magnetic field is derived.

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

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.

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.

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.

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.

We develop a model of magnetoresistance oscillations induced by the Hall field in order to study the temperature dependence observed in recent experiments in two dimensional electron systems. The model is based on the solution of the von Neumann equation incorporating the exact dynamics of two-dimensional damped electrons in the presence of arbitrarily strong magnetic and dc electric fields, while the effects of randomly distributed neutral and charged impurities are perturbatively added. Both the effects of elastic impurity scattering as well as those related to inelastic processes play an important role. The theoretical predictions correctly reproduce the experimentally observed oscillations amplitude, provided that the quantum inelastic scattering rate obeys a T 2 temperature dependence, consistent with electron–electron interaction effects.

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.

AbstractExperimental and theoretical studies on optical orientation and spin-dependent recombination in a semiconductor in a magnetic field under the normal incidence of circularly polarized radiation onto the sample surface are reviewed. The experiments were carried out on GaAs_1 –_ x N_ x solid solutions, in which Ga^2+ interstitial displacement defects play the role of deep paramagnetic centers responsible for spin-dependent recombination. It is established that, in the investigated materials, the hyperfine interaction of a localized electron with one nucleus of the paramagnetic center remains strong even at room temperature. The theory is compared with an experiment conducted in the steady-state excitation mode and under two-pulse pump-probe conditions. An analytical formula for spin beats in a magnetic field is derived.

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

In this work we study the microwave photoconductivity of a two-dimensional electron system (2DES) in the presence of a magnetic field and a two-dimensional modulation (2D). The model includes the microwave and Landau contributions in a non-perturbative exact way, the periodic potential is treated perturbatively. The Landau-Floquet states provide a convenient base with respect to which the lattice potential becomes time-dependent, inducing transitions between the Landau-Floquet levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. The total longitudinal conductivity and resistivity exhibit strong oscillations, determined by $\epsilon = \omega / \omega_c$ with $\omega$ the radiation frequency and $\omega_c$ the cyclotron frequency. The oscillations follow a pattern with minima centered at $\omega/\omega_c =j + {1/2} (l-1) + \delta $, and maxima centered at $\omega/\omega_c =j + {1/2} (l-1) - \delta $, where $j=1,2,3.......$, $\delta \sim 1/5$ is a constant shift and $l$ is the dominant multipole contribution. Negative resistance states (NRS) develop as the electron mobility and the intensity of the microwave power are increased. These NRS appear in a narrow window region of values of the lattice parameter ($a$), around $a \sim l_B$, where $l_B$ is the magnetic length. It is proposed that these phenomena may be observed in artificially fabricated arrays of periodic scatterers at the interface of ultraclean $GaAs/Al_xGa_{1-x} As$ heterostructures., Comment: 20 pages, 8 figures

In this work we present a model for the photoconductivity of a two dimensional electron system (2DES) subjected to a magnetic field. The model includes the microwave and Landau contributions in a non-perturbative exact way, Impurity scattering effects are treated perturbatively. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We discuss results related with the recently discovered zero-resistance states. It is found that, in agreement with experiment, negative dissipation can only be induced in very high mobility samples. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the time evolution of wave packets of noninteracting electrons in a two-dimensional periodic system in the presence of magnetic and electric fields. The model includes consistently the coupling between Landau levels as well as the periodic and external field contributions. It is shown that the electric field produces localization along its longitudinal direction, this effect is a physical consequence of the quantization of the energy levels with respect to the longitudinal quasi-momentum. For incommensurate orientations of E relative to the lattice the wave packet becomes localized in both directions.

The optical response of an AlGaN/GaN/(InxGa1−xN)n/GaN/AlGaN heterostructure is obtained from precise, and comparatively simple, transition probability calculations. A comprehensive approach to evaluate these quantities from rigorous expressions of the heterostructure's energy eigenvalues and eigenfunctions is given. Taking full account of the longitudinal quantum wells and the lateral quantum dot confinement, quite precise intraband energy levels and wave functions have been obtained. Photoluminescence results for sectionally constant band-edge profile differ from the experimental measurements by approximately 45 meV. We show that the band-edge modulation arising from charge polarization, is responsible for this difference.

A phenomenological theory to describe the electromagnetic properties of granular superconductors, based on known bulk superconductors expressions and conventional Josephson's junctions tunneling currents, is presented and succesfully used to fit distinct experimental results for the magnetic susceptibility as a function of the temperature and the applied magnetic field of rather different samples., Comment: 6 pages, 6 figures

We investigate Bloch electrons in two dimensions subject to constant electric and magnetic fields. The model that results from our pursuit is governed by a finite difference equation with a quasienergy spectrum that interpolates between a butterfly-like structure and a Stark ladder structure. These findings ensued from the use of electric and magnetic translation operators., 9 pages, 2 figures, Uses REVTEX. Final version, corrected typos

The magnetic-field and temperature behavior of the critical current exponents in poycrystalline YBa2CuxOy (with x = 3,4 and different grain sizes), has been measured in the low magnetic-field region. The critical exponent α of small-grain samples with dominant weak links, increases with increasing the magnetic field and temperature. Except for very low magnetic fields and temperatures far away from Tc, the exponent α becomes larger than 1. For big grain sizes and dominant Josephson-like junctions the critical exponent oscillates between 1/2 and 1.

From careful four probe measurements at different magnetic fields, we deduce the critical transport current density Jc(B) behaviour for polycrystalline Y and Gd-based superconducting samples which, on top of the characteristic Fraunhofer-like “weak-link” gross structure, exhibit anomalous oscillations, due to quantum interference effects in a finite number of current loops in mesoscopic networks of Josephson junctions.

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

Optical and spin properties of individual GaAs droplet dots in AlGaAs barriers are studied in photoluminescence experiments at 4K. First we report strong mixing of heavy hole-light hole states. Using the neutral and charged exciton emission as a monitor we observe the direct consequence of quantum dot symmetry reduction in this strain free system. By fitting the polar diagram of the emission with simple analytical expressions obtained from k•p theory we are able to extract the mixing that arises from the heavy-light hole coupling due to the geometrical asymmetry of the quantum dot. Second we report optical orientation experiments. Circularly polarized optical excitation yields strong circular polarization of the resulting photoluminescence. Optical injection of spin polarized electrons into a GaAs dot gives rise to dynamical nuclear polarization that considerably changes the exciton Zeeman splitting (Overhauser shift). We show that the created nuclear polarization is bistable and present a direct measurement of the build-up time of the nuclear polarization in a single GaAs dot in the order of one second.

Zero resistance differential states have been observed in two-dimensional electron gases (2DEG) subject to a magnetic field and a strong dc current. In a recent work we presented a model to describe the nonlinear transport regime of this phenomenon. From the analysis of the differential resistivity and the longitudinal voltage we predicted the formation of negative differential resistivity states, although these states are known to be unstable. Based on our model, we derive an analytical approximated expression for the Voltage-Current characteristics, that captures the main elements of the problem. The result allow us to construct an energy functional for the system. In the zero temperature limit, the system presents a quantum phase transition, with the control parameter given by the magnetic field. It is noted that above a threshold value ($B>B_{th}$), the symmetry is spontaneously broken. At sufficiently high magnetic field and low temperature the model predicts a phase with a non-vanishing permanent current; this is a novel phase that has not been observed so far., 6 pages, 2 figures

A theoretical and experimental study of the spin-dependent photoconductivity in dilute Nitride GaAsN is presented. The non linear transport model we develop here is based on the rate equations for electrons, holes, deep paramagnetic and non paramagnetic centers both under CW and pulsed optical excitation. Emphasis is given to the effect of the competition between paramagnetic centers and non paramagnetic centers which allows us to reproduce the measured characteristics of the spin-dependent recombination power dependence. Particular attention is paid to the role of an external magnetic field in Voigt geometry. The photoconductivity exhibits a Hanle-type curve whereas the spin polarization of electrons shows two superimposed Lorentzian curves with different widths, respectively related to the recombination of free and trapped electrons. The model is capable of reproducing qualitatively and quantitatively the most important features of photoluminescence and photocurrent experiments and is helpful in providing insight on the various mechanisms involved in the electron spin polarization and filtering in GaAsN semiconductors., Comment: 10 pages, 5 figures

We present a model to describe the nonlinear response to a direct dc current applied to a two-dimensional electron system in a strong magnetic field. The model is based on the solution of the von Neumann equation incorporating the exact dynamics of two-dimensional damped electrons in the presence of arbitrarily strong magnetic and dc electric fields, while the effects of randomly distributed impurities are perturbatively added. From the analysis of the differential resistivity and the longitudinal voltage we observe the formation of negative differential resistivity states (NDRS) that are the precursors of the zero differential resistivity states (ZDRS). The theoretical predictions correctly reproduce the main experimental features provided that the inelastic scattering rate obey a $T^2$ temperature dependence, consistent with electron-electron interaction effects., Comment: 5 pages, 4 figures

high mobility 2DES under the influence of microwave radiation of frequency v at moderate values of the magnetic field exhibits strong oscillations with zero-resistance states sZRSd governed by the ratio v / vc, where vc is the cyclotron frequency. In this work we present a model for the photoconductivity of a 2DES subjected to a magnetic field. The model includes the microwave and Landau contributions in a nonperturbative, exact way, while impurity-scattering effects are treated perturbatively. In our model, the Landau-Floquet states act coherently with respect to the oscillating field of the impurities that in turn induces transitions between these levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We study the effects of both short-range and long-range disorder on the photoconductivity. Our calculation yields a magnetoresistance oscillatory behavior with the correct period and phase. It is found that, in agreement with experiment, negative dissipation can only be induced in very high mobility samples. We analyze the dependence of the results on the microwave power and polarization. For highintensity radiation, multiphoton processes take place predicting negative-resistance states centered at v / vc = 1 2 and v / vc = 3 2 .

The object of the present work is to study the quantum Hall effect through its symmetries and topological aspects. We consider the model of an electron moving in a two-dimensional lattice in the presence of applied in-plain electric field and perpendicular magnetic field. We refer to this as the two dimensional electric-magnetic Bloch problem (EMB). The Hall conductivity quatizations beyond the linear response approximation is analyzed., Comment: 6 pages

This paper discusses the relevance of symmetries and topology in the understanding of quantum Hall effect. We specifically consider a simple model of an electron in a two dimensional periodic potential subject to constant electric and magnetic fields. The work addresses the vanishing of the longitudinal magnetoresistance and the quantization of the Hall conductivity, and also the calculation of non‐perturbative corrections.

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.

In this work, we present a model to describe the nonlinear response to a dc electrical current of a two-dimensional electron system subjected to magnetic and microwave fields. Considering the separation of the electron coordinates into the non-commuting relative and guiding center coordinates, we obtain a unitary transformation that exactly solves the time-dependent Schrodinger equation in the presence of arbitrarily strong electric, magnetic and microwave fields. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We discuss results related to the recently discovered zero-resistance states and to the microwave-induced resistivity oscillations and the Hall-induced resistivity oscillations.