Two dimensional electrons in a lateral magnetic superlattice

Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion

Tunneling transport across electrical potential barriers in Weyl semimetals with tilted energy dispersion is investigated. We report that the electrons around different valleys experience opposite direction refractions at the barrier interface when the energy dispersion is tilted along one of the transverse directions. Chirality dependent refractions at the barrier interface polarize the Weyl fermions in angle-space according to their valley index. A real magnetic barrier configuration is used to select allowed transmission angles, which results in electrically controllable and switchable valley polarization. Our findings may pave the way for experimental investigation of valley polarization, as well as valleytronic and electron optic applications in Weyl semimetals.

Tailoring sample-wide pseudo-magnetic fields on a graphene-black phosphorus heterostructure

Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of developing a valley filter.

Klein tunneling in Weyl semimetals under the influence of magnetic field

Klein tunneling refers to the absence of normal backscattering of electrons even under the case of high potential barriers. At the barrier interface, the perfect matching of electron and hole wavefunctions enables a unit transmission probability for normally incident electrons. It is theoretically and experimentally well understood in two-dimensional relativistic materials such as graphene. Here we investigate the Klein tunneling effect in Weyl semimetals under the influence of magnetic field induced by ferromagnetic stripes placed at barrier boundaries. Our results show that the resonance of Fermi wave vector at specific barrier lengths gives rise to perfect transmission rings, i.e., three-dimensional analogue of the so-called magic transmission angles in two-dimensional Dirac semimetals. Besides, the transmission profile can be shifted by application of magnetic field in the central region, a property which may be utilized in electro-optic applications. When the applied potential is close to the Fermi level, a particular incident vector can be selected by tuning the magnetic field, thus enabling highly selective transmission of electrons in the bulk of Weyl semimetals. Our analytical and numerical calculations obtained by considering Dirac electrons in three regions and using experimentally feasible parameters can pave the way for relativistic tunneling applications in Weyl semimetals.

Magneto-optical properties of ABC-stacked trilayer graphene

The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene.

Voltage-controllable spin beam splitter based on realistic magnetic-barrier nanostructure

We report a theoretical investigation on the Goos-Hänchen (GH) effect of spin electron beams in realistic magnetic-barrier (MB) nanostructures under an applied voltage, which can be experimentally created by lithographic patterning of ferromagnetic (FM) or superconducting films. GH shifts of spin electron beams are calculated numerically for the InAs material system, with the help of the stationary phase method. It is shown that a significant spin polarization effect can be induced by such MB nanostructures with symmetric magnetic field profiles. It also is shown that both magnitude and sign of the spin polarization is closely relative to the electric barrier (EB) produced by a constant voltage applied to the metallic FM stripe of system. These interesting properties may provide an alternative way to spin injection into the semiconductor, and such nanostructures can serve as voltage-tunable spin beam splitters.

Magnetotransport properties of a magnetically modulated two-dimensional electron gas with the spin-orbit interaction

We study the electrical transport properties of a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction in the presence of a constant perpendicular magnetic field (B(0)( ̂z) which is weakly modulated by B1 = B1 cos(qx) ̂z, where B(1) ≪ B(0) and q = 2π/a with a the modulation period. We obtain the analytical expressions of the diffusive conductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and produce beating patterns in the amplitude of the Weiss and Shubnikov-de Haas oscillations. We show that the Rashba strength can be determined by analyzing the beating pattern in the Weiss oscillation. We find a simple equation which determines the Rashba spin-orbit interaction strength if the number of Weiss oscillations between any two successive nodes is known from the experiment. We compare our results with the electrically modulated 2DEG with the Rashba interaction. For completeness, we also study the beating pattern formation in the collisional and the Hall conductivities.

Thermodynamic properties of a magnetically modulated graphene monolayer

The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in the presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their bandwidth oscillates with magnetic field, leading to Weiss-type oscillations in the thermodynamic properties. The effect of magnetic modulation on the thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen oscillations at low and high magnetic fields, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene compared to electrically modulated graphene. On the other hand, the phase remains the same and the amplitude of the oscillation is large when compared with the magnetically modulated two-dimensional electron gas (2DEG). Explicit asymptotic expressions of the density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.

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 band's 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.

Electron dynamics in inhomogeneous magnetic fields

This review explores the dynamics of two-dimensional electrons in magnetic potentials that vary on scales smaller than the mean free path. The physics of microscopically inhomogeneous magnetic fields relates to important fundamental problems in the fractional quantum Hall effect, superconductivity, spintronics and graphene physics and spins out promising applications which will be described here. After introducing the initial work done on electron localization in random magnetic fields, the experimental methods for fabricating magnetic potentials are presented. Drift-diffusion phenomena are then described, which include commensurability oscillations, magnetic channelling, resistance resonance effects and magnetic dots. We then review quantum phenomena in magnetic potentials including magnetic quantum wires, magnetic minibands in superlattices, rectification by snake states, quantum tunnelling and Klein tunnelling. The third part is devoted to spintronics in inhomogeneous magnetic fields. This covers spin filtering by magnetic field gradients and circular magnetic fields, electrically induced spin resonance, spin resonance fluorescence and coherent spin manipulation.

Quantized magnetic confinement in quantum wires

Ballistic quantum wires are exposed to longitudinal profiles of perpendicular magnetic fields composed of a spike and a homogeneous part. An asymmetric magnetoconductance peak as a function of the homogeneous magnetic field is found, comprising quantized conductance steps in the interval where the homogeneous magnetic field and the magnetic barrier have identical polarities, and a characteristic shoulder with several resonances in the interval of opposite polarities. The observations are interpreted in terms of inhomogeneous diamagnetic shifts of the quantum wire modes leading to magnetic confinement.

The magnetoplasmon spectrum of a weakly modulated two-dimensional electron gas system

The magnetoplasmon spectrum of a magnetically modulated two-dimensional electron gas (2DEG) is investigated. We derive the inter- and intra-Landau-band magnetoplasmon spectrum within the self-consistent field approach. The derivation is performed at zero temperature as well as at finite temperature. Results are presented for the inter- and intra-Landau-band magnetoplasmon spectrum as a function of the inverse magnetic field. Magnetic Weiss oscillations are found to occur in the magnetoplasmon spectrum as a result of magnetic modulation. Furthermore, our finite temperature theory facilitates the analysis of effects of temperature on the magnetoplasmon spectrum. The results are compared with those obtained for an electrically modulated 2DEG system. In addition, we derive and discuss the effects of simultaneous electric and magnetic modulations on the magnetoplasmon spectrum of the 2DEG when the modulations are in phase as well as when they are out of phase. Magnetic oscillations are affected by the relative phase of the two modulations and the position of the oscillations depends on the relative strength of the two modulations in the former case while we find complete suppression of Weiss oscillations for a particular relative strength of the modulations in the latter case.

Quantum interference of magnetic edge channels activated by intersubband optical transitions in magnetically confined quantum wires

We investigate the photoresistance of a magnetically confined quantum wire in which microwave-coupled edge channels interfere at two pinning sites in the fashion of a Mach-Zehnder interferometer. The conductance is strongly enhanced by microwave power at B = 0 and develops a complex series of oscillations when the magnetic confinement increases. Both results are quantitatively explained by the activation of forward scattering in a multimode magnetically confined quantum wire. By varying the strength of the magnetic confinement we are able to tune the phase of electrons in the arms of the interferometer. Quantum interferences which develop between pinning sites explain the oscillations of the conductance as a function of the magnetic field. A fit of the data gives the distance between pinning sites as 11 µm. This result suggests that quantum coherence is conserved over a distance three times longer than the electron mean free path.

Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices

We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.

Modulation effects on Landau levels in a monolayer graphene

Magnetoelectronic properties of a single-layer graphene are studied by the Peierls tight-binding model. A new numerical technique is developed to obtain a band-like Hamiltonian matrix. A spatially modulated magnetic field B' could drastically alter the Landau levels due to a uniform magnetic field B. The modulation effects include enhancement in dimensionality, change of energy dispersions, destruction of state degeneracy and creation of band-edge states. The dispersionless Landau levels, those at the Fermi levels excepted, become the 1D parabolic bands. The density of states thus exhibits many pairs of asymmetric prominent peaks. The height, frequency and number of pronounced peaks strongly depend on the modulation strength. These characteristics are hardly affected by the period and direction when B' is much weaker than B. The predicted results could be verified by experimental measurements on magneto-optical absorption spectra.

Magnetic confinement of massless Dirac fermions in graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.

Drastic facilitation of the onset of global chaos

We show that the onset of global chaos in a time periodically perturbed Hamiltonian system may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. We develop the asymptotic theory and verify it in simulations.

Magnetic quantum dot: a magnetic transmission barrier and resonator

We study the ballistic edge-channel transport in quantum wires with a magnetic quantum dot, which is formed by two different magnetic fields B(*) and B0 inside and outside the dot, respectively. We find that the electron states located near the dot and the scattering of edge channels by the dot strongly depend on whether B(*) is parallel or antiparallel to B0. For parallel fields, two-terminal conductance as a function of channel energy is quantized except for resonances, while, for antiparallel fields, it is not quantized and all channels can be completely reflected in some energy ranges. All these features are attributed to the characteristic magnetic confinements caused by nonuniform fields.

Resistance resonance effects through magnetic edge states

We report on the magnetoresistance of a two-dimensional electron gas subjected to an abrupt magnetic field gradient arising from a ferromagnetic stripe fabricated at its surface. A sharp resistance resonance effect is observed at B(p) due to the formation of two types of magnetic edge states that drift in opposite directions perpendicular to the magnetic field gradient for B<B(p) and B>B(p). A semiclassical drift-diffusion model gives a good description of the effects of the magnetic confinement on both the diagonal and off-diagonal components of the resistivity tensor.