Cyclotron Orbit Research Articles

Gyrobunching and wave–particle resonance in the lower hybrid drift instability

We report a first principles study of the coupled evolution of energetic ions, background majority ions, electrons and electromagnetic fields in magnetized plasma during the linear phase of the lower hybrid drift instability. A particle-in-cell code, with one spatial and three velocity space co-ordinates, is used to analyse the evolving distribution of a drifting ring-beam population of energetic protons in physical space and gyrophase angle. This analysis is carried out for bulk plasma parameters that approximate to core conditions in large tokamaks, with an energetic ion distribution that is motivated by observations of ion cyclotron emission and may be relevant to alpha channelling. Resonant energy transfer occurs at the two gyrophase angles at which the instantaneous speed of an energetic proton on its cyclotron orbit precisely matches the phase velocity of the lower hybrid wave along the simulation domain. Electron space-charge oscillations determine the wavelength of the propagating lower hybrid wave, and thereby govern the spatial distribution of gyrobunching of the energetic protons that drive the instability.

Electrostatic modulation of anisotropic magnetotransport in Ar+-irradiated SrTiO3: Effects of boundary scattering

We present low temperature, magnetotransport measurements on a quasi-two-dimensional electron gas created by Ar${}^{+}$-irradiation of SrTiO${}_{3}$. We observe negative (positive) magnetoresistance for fields applied in (out of) the plane of the electron gas. By modulating the mobility $\ensuremath{\mu}$ of the electron gas through an electrostatic field, we find the in-plane magnetoresistance is a function of the cyclotron frequency. The negative in-plane magnetoresistance can be explained by a drop in boundary scattering, which occurs as the cyclotron orbits become smaller than the finite thickness of the electron gas. These results elucidate the critical role boundary scattering plays in the magnetotransport of quasi-two-dimensional electron gases. The implications of these results on recent magnetotransport measurements of LaAlO${}_{3}$/SrTiO${}_{3}$ samples are discussed.

Resonant Cyclotron Acceleration of Particles by a Time Periodic Singular Flux Tube

We study the dynamics of a classical nonrelativistic charged particle moving on a punctured plane under the influence of a homogeneous magnetic field and driven by a periodically time-dependent singular flux tube through the hole. We observe an effect of resonance of the flux and cyclotron frequencies. The particle is accelerated to arbitrarily high energies even by a flux of small field strength which is not necessarily encircled by the cyclotron orbit; the cyclotron orbits blow up and the particle oscillates between the hole and infinity. We support this observation by an analytic study of an approximation for small amplitudes of the flux which is obtained with the aid of averaging methods. This way we derive asymptotic formulas that are afterwards shown to represent a good description of the accelerated motion even for fluxes which are not necessarily small. More precisely, we argue that the leading asymptotic terms may be regarded as approximate solutions of the original system in the asymptotic domai...

Semiclassical quantization of skipping orbits

We propose a simple description of the spectrum of edge states in the quantum Hall regime, in terms of semiclassical quantization of skipping orbits along hard wall boundaries, ${\cal A}=2 \pi (n+\gamma) \ell_B^2$, where ${\cal A}$ is the area enclosed between a skipping orbit and the wall and $\ell_B$ is the magnetic length. Remarkably, this description provides an excellent quantitative agreement with the exact spectrum. We discuss the value of $\gamma$ when the skipping orbits touch one or two edges, and its variation when the orbits graze the edges and the semiclassical quantization has to be corrected by diffraction effects. The value of $\gamma$ evolves continuously from $1/2$ to $3/4$. We calculate the energy dependence of the drift velocity along the different Landau levels. We compare the structure of the semiclassical cyclotron orbits, their position with respect to the edge, to the wave function of the corresponding eigenstates.

Landau levels and edge states in a cylindrical two-dimensional electron gas: A semiclassical approach

The Einstein-Brillouin-Keller (EBK) semiclassical quantization is used to deduce the quantum-mechanical magnetoelectronic structure of a cylindrical two-dimensional electron gas (2DEG). This approach allows for a detailed knowledge of the correspondence between the classical paths, the EBK single-electron energy, and the quantum states. A better understanding is also given by a comparison between the classical motion of electrons in a planar surface and the trajectories on the curved surface of the cylinder. In a channel patterned in a flat 2DEG, under a transverse magnetic field different kinds of orbits are allowed: (i) cyclotron orbits corresponding to flat Landau levels, (ii) edge states which collide with one channel wall, and (iii) traversing trajectories colliding with both channel walls. In a cylindrical 2DEG, different kinds of orbits are allowed, when a magnetic field acts orthogonally to the cylinder axis: (i) cyclotron orbits, (ii) edge states localized on the flanks of the tube, (iii) anomalous edge states weakly localized on the flanks with backward velocity, and (iv) traversing trajectories.

Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects -- such as Berry phase and Maslov index -- occurring at order $\hbar$ in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase -- which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands -- acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the "k-dependent Hamiltonian" H(k), where k is the Bloch wavevector.

Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field

We developed a quantitative theory of transverse magnetoresistance for the two-dimensional electron gas (2DEG) in a quantum well with parabolic confinement potential in the magnetic field in the plane of the free movement of electrons. Our theory is based on the solution of Boltzmann kinetic equation for the components of the tensors of kinetic coefficients, when the perturbing force is directed along the plane of the free movement of electrons, and Titeike's formula for the diagonal component of the conductivity along the direction of confinement, based on the idea of the drift of the centres of cyclotron orbits in the crossed electric and magnetic fields. Numerical calculations have been performed for the 2D electron gas in GaAs/AlxGa1−xAs QWs. It is shown, that the magnetoresistance is negative and equal about 50% in the weak magnetic field case, ωc<<ω0 if the quantum limit ℏ ω0 > k0T is fulfilled.

Very large magnetoresistance in graphene nanoribbons.

Graphene has unique electronic properties1,2 and graphene nanoribbons are of particular interest because they exhibit a conduction band gap, which arises due to size confinement and edge effects3-11. Theoretical studies have suggested that graphene nanoribbons could have interesting magneto-electronic properties with very large magnetoresistance predicted4,12-20. Here we report the experimental observation of a significant enhancement in the conductance of a graphene nanoribbon field-effect transistor in a perpendicular magnetic field. A negative magnetoresistance of nearly 100% was observed at low temperatures, with over 50% remaining at room temperature. This magnetoresistance can be tuned by varying the gate or source-drain bias. We also find that the charge transport in the nanoribbons is not significantly modified by an in-plane magnetic field. The large values of the magnetoresistance we observe may be attributed to the reduction of quantum confinement by the formation of cyclotron orbits and the delocalization effect under the perpendicular magnetic field15-20.

Strain-Induced Pseudo–Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles

Recent theoretical proposals suggest that strain can be used to engineer graphene electronic states through the creation of a pseudo-magnetic field. This effect is unique to graphene because of its massless Dirac fermion-like band structure and particular lattice symmetry (C3v). Here, we present experimental spectroscopic measurements by scanning tunneling microscopy of highly strained nanobubbles that form when graphene is grown on a platinum (111) surface. The nanobubbles exhibit Landau levels that form in the presence of strain-induced pseudo-magnetic fields greater than 300 tesla. This demonstration of enormous pseudo-magnetic fields opens the door to both the study of charge carriers in previously inaccessible high magnetic field regimes and deliberate mechanical control over electronic structure in graphene or so-called "strain engineering."

Correlation-induced single-flux-quantum penetration in quantum rings

Conventionally, the states of a two-dimensional quantum ring in a high magnetic field have a well-defined spatial structure. But Coulomb repulsion between individual orbits causes oscillations in the size of this structure each time a magnetic flux-quantum enters or leaves the system. This effect has now been measured experimentally in semiconducting quantum rings. The confined electronic states of mesoscopic structures in a magnetic field are arranged in Landau levels consisting of spatially discrete eigenstates. These Landau orbits are the quantum mechanical analogue of classical cyclotron orbits. Here we present magnetoconductance oscillations in semiconductor rings, which visualize the spatial discreteness of the Landau orbits in high magnetic fields (typically B>2 T). We will show that these oscillations are caused by the flux-quantized, discrete electronic size of the ring leading to a corresponding modulation of its two-point conductance. The oscillation period is given by the number of flux quanta penetrating the conducting area of the structure. These high-field oscillations are distinctively different from the well-known Aharonov–Bohm effect1, where, most generally, the penetration of individual flux quanta h/e through a nanostructure causes periodic crossings of field-dependent energy levels, which give rise to magneto-quantum oscillations in its conductance2,3,4.

A Tuning Method for Electrically Compensated Ion Cyclotron Resonance Mass Spectrometer Traps

We describe a method for tuning electrically compensated ion cyclotron resonance (ICR) traps by tracking the observed cyclotron frequency of an ion cloud at different oscillation mode amplitudes. Although we have used this method to tune the compensation voltages of a custom-built electrically compensated trap, the approach is applicable to other designs that incorporate electrical compensation. To evaluate the effectiveness of tuning, we examined the frequency shift as a function of cyclotron orbit size at different z-mode oscillation amplitudes. The cyclotron frequencies varied initially by approximately 12 ppm for ions with low z-mode oscillation amplitudes compared with those with high z-mode amplitudes. This frequency difference decreased to approximately 1 ppm by one iteration of trap tuning.

Quasiparticle interference and Landau level spectroscopy in graphene in the presence of a strong magnetic field

We present a calculation of the modulation in the Local Density Of electronic States (LDOS) caused by an impurity in graphene in the presence of external magnetic field. We focus on the spatial Fourier Transform (FT) of this modulation around the impurity. The FT due to the low energy quasiparticles are found to be nonzero over the reciprocal lattice corresponding to graphene. At these lattice spots the FT exhibits well-defined features at wavevectors that are multiples of the inverse cyclotron orbit diameter (see Figure 2) and is cut off at the wavevector corresponding to the energy of observation. Scanning Tunneling Spectroscopy (STS) on graphene and the energy-resolved FT fingerprint obtained therefrom may be used to observe the quasiparticle interference of Dirac particles in graphene in the presence of magnetic field.

Combined Electron Resonance Driven by an All-Oscillating Potential of Patterned Magnets

A novel mechanism is proposed for the phenomenon of combined electron resonance. It is shown that the spatially localized microwave fields of an Fe stripe array mediate the intense electronic transitions involving the changes in both spin and orbital quantum numbers when the electron moves along a cyclotron orbit in a semiconductor (e.g., InGaAs-based) quantum well. This discovery bridges the fields of spintronics and quantum computing, paving the way for conceptually new hybrid devices based on ferromagnetic and semiconductor structured materials.

TRANSPORT IN A BILAYER SYSTEM AT HIGH LANDAU FILLING FACTOR

We have studied Shubnikov de Haas oscillations and the quantum Hall effect in GaAs -double well structures in tilted magnetic fields. We found strong magnetoresistance oscillations as a function of an in-plane magnetic field B∥ at ν = 4N + 3 and ν = 4N + 1 filling factors. At low perpendicular magnetic field B⊥, the amplitude of the conventional Shubnikov-de Haas (SdH) oscillations also exhibits B∥-periodic dependence at fixed values of B⊥. We interpret the observed oscillations as a manifestation of the interference between cyclotron orbits in different quantum wells.

Observing the Quantization of Zero Mass Carriers in Graphene

Application of a magnetic field to conductors causes the charge carriers to circulate in cyclotron orbits with quantized energies called Landau levels (LLs). These are equally spaced in normal metals and two-dimensional electron gases. In graphene, however, the charge carrier velocity is independent of their energy (like massless photons). Consequently, the LL energies are not equally spaced and include a characteristic zero-energy state (the n = 0 LL). With the use of scanning tunneling spectroscopy of graphene grown on silicon carbide, we directly observed the discrete, non-equally-spaced energy-level spectrum of LLs, including the hallmark zero-energy state of graphene. We also detected characteristic magneto-oscillations in the tunneling conductance and mapped the electrostatic potential of graphene by measuring spatial variations in the energy of the n = 0 LL.

Application of electron spectroscopy for studying inverse p-decay at increasing density of neutrino flux due to diffraction

In the present paper, a new method is substantiated for studying the inverseβ-decay with the use of Auger- and photoelectron spectra for the registration of electrons, which appear at the interaction of low-energy (∼ 1 MeV and smaller) electron neutrinos (ve) with a substance. The new method is an alternative to the existing method based on the use of high-energy ve with the energy of ∼ 10 MeV, which form electrons at the interaction with a substance, the energy of which is sufficient for Cherenkov effect to appear. The offered method was realized using a high-sensitive electron magnetic spectrometer with double focusing by a non-uniform magnetic field π□2 with the cyclotron orbit radius of 100 cm, which was built at our institute; the first x-ray electron spectra were obtained on it and the constant of the device was determined.

Magnetoconductance oscillations in graphene antidot arrays

Epitaxial graphene films have been formed on the C-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. Nanoscale square antidot arrays have been fabricated on these graphene films. At low temperatures, magnetoconductance in these films exhibits pronounced Aharonov–Bohm oscillations with the period corresponding to magnetic flux quanta added to the area of a single antidot. At low fields, weak localization is observed and its visibility is enhanced by intervalley scattering on antidot edges. At high fields, we observe two distinctive minima in magnetoconductance, which can be attributed to commensurability oscillations between classical cyclotron orbits and antidot array. All mesoscopic features, surviving up to 70K, reveal the unique electronic properties of graphene.

Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling

We study the effect of the interplay between the Rashba and the Dresselhaus spin-orbit couplings on the transverse electron focusing in two-dimensional electron gases. Depending on their relative magnitude, the presence of both couplings can result in the splitting of the first focusing peak into two or three. This splitting has information about the relative value of spin-orbit couplings and therefore about the shape of the Fermi surface. More interesting, the presence of the third peak is directly related to the tunneling probability (``magnetic breakdown'') between orbits corresponding to the different sheets of the Fermi surface. In addition, destructive interference effects between paths that involve tunneling and those that do not can be observed in the second focusing condition. Such electron paths (orbits) could be experimentally detected using current techniques for imaging the electron flow opening the possibility to directly observe and characterize the magnetic breakdown effect in this system.

Quenching of the Quantum Hall Effect in Multilayered Epitaxial Graphene: The Role of Undoped Planes

We propose a mechanism for the quenching of the Shubnikov-de Haas oscillations and the quantum Hall effect observed in epitaxial graphene. Experimental data show that the scattering time of the conduction electron is magnetic field dependent and of the order of the cyclotron orbit period, i.e., it can be much smaller than the zero field scattering time. Our scenario involves the extraordinary graphene n=0 Landau level of the uncharged layers which is pinned at the Fermi level. We find that the coupling between this n=0 Landau level and the conducting states of the doped plane leads to a scattering mechanism having the right magnitude to explain the experimental data.

Wave packet dynamics in a two-dimensional electron gas with spin orbit coupling: Splitting andzitterbewegung

We study the effect of splitting and Zitterbewegung of one- and two-dimensional electron wave packets in the semiconductor quantum well under the influence of the Rashba spin orbit coupling. Results of our investigations show that the spin orbit interaction induces dramatic qualitative changes in the evolution of spin-polarized wave packet. The initial wave packet with spin polarization splits into two parts, which propagate with unequal group velocity. This splitting appears due to the presence of two branches of electron spectrum corresponding to the stationary states with different chirality. It is also demonstrated that in the presence of external magnetic field $\mathbf{B}$ perpendicular to the electron-gas plane the wave packet splits into two parts, which rotate with different cyclotron frequencies. It was shown that after some periods, the electron density distributes around cyclotron orbit and the motion acquires an irregular character. Our calculations were made for both cases of weak and strong spin orbit couplings.