Cyclotron Orbit Research Articles

Magnetotransport of 2D electrons on liquid helium in the fluid and solid phases

The magnetoconductivity σ(B) in the two-dimensional (2D) nondegenerate electron fluid and 2D solid has been analyzed theoretically and investigated experimentally, from 60 mK to 1.3 K in magnetic fieldsB up to 8 Tesla. In the fluid phase, σ(B) is described by the Drude model in weak to moderately strong classical fields, including the range βB≫1. At higher fields (depending on the density σ(B) is nonmonotonous and diplays a minimum. This behavior is due to many-electron effects, which can be described in terms of cyclotron orbit diffusion controlled by an internal fluctuational electric field. The squared internal field derived from experiments is in good agreement with computer simulations. In the solid phase electron transport becomes strongly non-linear even for weak driving voltagesV 0. Experimentally we determine, from the losses, the effective AC Corbino conductivity at a frequencyf. We find that σ(BαfV 0/B forV 0 below some threshold voltageV c . In this region the Hall velocity υ H approaches the ripplon phase velocityv 1=w(G 1)/G 1 at the first reciprocal lattice vectorG 1 of the electron solid. We suggest that this behaviour is due to to a resonant drag force from the Bragg-Cerenkov radiation of coherent ripplons by the moving crystal.

Quasiclassical calculation of magnetoresistance oscillations of a two-dimensional electron gas in spatially periodic magnetic and electrostatic fields.

A classical approach, relating magnetoresistance oscillations of a two-dimensional electron gas (2DEG) in a weak lateral superlattice to the guiding center drift of cyclotron orbits, is extended to superlattices defined by spatially periodic electrostatic and magnetic fields of arbitrary shape but equal lattice constants. The results are applied to the experimentally relevant situation of modulation fields produced by periodic arrays of magnetized strips or dots on the surface of a heterostructure containing a 2DEG. Magnetic modulation fields of different symmetries, tuned by the orientation of the magnetization, are superimposed on the stress-induced electrostatic modulation and lead to characteristic interference effects on the Weiss oscillations of the magnetoresistance. \textcopyright{} 1996 The American Physical Society.

GHz surface acoustic waves as a probe of composite fermions in two-dimensional electron systems

By providing the low-disorder two-dimensional electron system at submicron dimensions, important new length scales are revealed. Using surface acoustic waves of wavelength λ≲1 μm to measure the 2D electron conductivity, enhanced conductivity is observed at even-denominator filling factors v =½, ¼: this represents measurement of composite fermions' conductivity at a dimension smaller than the quasiparticles' mean free path. At smaller λ we are able to observe geometric resonance of the composite fermions' cyclotron orbit and the ultrasound wavelength. Observation of this resonance allows measurement of the composite fermion Fermi wave vector.

Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands.

We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a DC or AC electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this formalism, the pattern of band splitting, the distribution of Hall conduct- ivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture.

Cyclotron oscillations in a tilted magnetic field: A tool to measure the mean free path of ballistic electrons in high purity GaAs

The mean free path (mfp) of ballistic electrons in high purity GaAs was measured using a novel effect due to the cyclotron motion of ballistic electrons in tilted magnetic fields. Whenever the cyclotron orbit is commensurate with the device length an increase in the collected current is observed, leading to pronounced oscillations. We utilize the fact that the total path length varies as we change the angle of the magnetic field to extract the mfp using a single device. For high purity GaAs with an impurity concentration N a+ N d≈6 × 10 14 cm −3 we measure an mfp of ≈4 μm for electrons below the optical phonon energy. We suggest that the observed mfp is primarily due to impact ionization of neutral donors by the ballistic electrons. The large contrast of the oscillations proves that both injection and collection give preference to the direction normal to the layers and thus, that the momentum component parallel to the layers is conserved during transmission over the barrier.

Two-dimensional electrons in a magnetic superlattice

We report on the motion of two-dimensional electrons in a magnetic field which is periodic on the scale of a few hundred nanometres. Such a system exhibits novel magnetoresistance oscillations that we unambiguously identify as due to a commensurability effect between the period of the magnetic field and the diameter of the cyclotron orbit. We find that a semiclassical picture of electron motion can quantitatively describe all of the observed experimental features. We also propose methods of optimizing the effects of the magnetic modulation in hybrid semiconductor-superconductor devices.

Many-electron magnetoconductivity of 2D electrons on liquid helium

The magnetoconductivity σ(B) of 2D electrons on liquid helium was measured from 0.25 K to 1.30 K in the electron fluid phase in magnetic fieldsB<-8 Tesla. In low fields the Drude model holds even for μB≫ 1. At higher fields σ(B) becomes density dependent. The Drude behaviour and the density dependence are due to many-electron effects where cyclotron orbit diffusion is controlled by internal electric fields. The density and temperature dependence of these internal fields derived from experiments are in good agreement with Monte Carlo simulations.

De Haas-van Alphen Oscillation in Both Normal and Superconducting Mixed States of CeRu2

We have observed the de Haas-van Alphen (dHvA) oscillation in both the normal and superconducting mixed states of CeRu 2 . The dHvA amplitude in the mixed state is extremely reduced for the large cyclotron orbit or the carrier with a large cross-sectional area of the Fermi surface compared to the small one. We have detected three dHvA branches, ranging from 6×10 5 Oe to 2.3×10 7 Oe. The origin of these branches is well explained by the 4 f -itinerant band model.

Edge states in strong electric and magnetic fields in a two-dimensional semiconductor system

A detailed theoretical study of the density of states (DOS) for non-interacting electrons in strong electric and magnetic fields F and B is presented in the presence of a hard well edge in a two-dimensional electron system (2DES). The presence of the edge (taken along the x axis) in the 2DES lifts the x direction degeneracy of each Landau level (LL). Thus, the DOS for non-interacting electrons is observed to be in sharp contrast to the usual δ function peaks centered at each LL with energy E = E N = (N + 1 2 ) h ̷ ω c . Using the Green's function approach, our numerical results show that (i) a strong electric field applied along the x direction will strongly modify the DOS and (ii) the DOS shifts to the higher energy side with increasing parameter α = eFl h ̷ ω c with l the radius of the cyclotron orbit.

Experimental study of the acoustoelectric effects in GaAs-AlGaAs heterostructures

We present the results of a detailed experimental study of the electric current and voltage induced in the 2DEG of a GaAs-AlGaAs heterostructure by a surface acoustic wave (SAW). New results are obtained for these acoustoelectric effects at zero and low (<0.1 T) magnetic fields. At zero magnetic field the acoustoelectric current (voltage) was found to show a non-monotonic temperature dependence with a maximum at 40-50 K. Measurements on high-mobility 2DEGs where the electron mean free path is comparable with the SAW wavelength reveal geometric resonances of the cyclotron orbit with the SAW wavelength. With increasing magnetic field the acoustoelectric effects increase significantly and display rich oscillatory structure. We compare our data for the high-magnetic-field regime with that published in the literature.

Berry phase, hyperorbits, and the Hofstadter spectrum.

We develop a semiclassical theory for the dynamics of electrons in a magnetic Bloch band, where the Berry phase plays an important role. This theory, together with the Boltzmann equation, provides a framework for studying transport problems in high magnetic fields. We also derive an Onsager-like formula for the quantization of cyclotron orbits, and we find a connection between the number of orbits and Hall conductivity. This connection is employed to explain the clustering structure of the Hofstadter spectrum. The advantage of this theory is its generality and conceptual simplicity.

Is There a Magnetic-Field-Induced Breakdown in the Universality of Conductance Fluctuations?

Over the past few years, there have been many reports of the breakdown of universality in conductance fluctuations in mesoscopic systems when a high magnetic field is applied, particularly in the case of quantum wires. Normally, conductance fluctuations are described by a single scaling parameter–the coherence length lφ. The increase in the magnetic coherence length B c is generally attributed to a decrease in lφ which is not observed in the amplitude of the fluctuations. Worse, in high mobility material, the fluctuations seem to increase in amplitude, which is also inconsistent with a decrease in lφ. Here, we argue that (1) the wire behavior is governed by surface scattering, (2) there is a formation of edge states in the high magnetic field, and (3) a breakdown of diffusive transport and transition to quasi-ballistic transport in the edge states in high-mobility material. The transition to high field behavior occurs when the cyclotron orbit at the Fermi surface becomes smaller than the width, so that proper treatment of the amplitude of the fluctuations and of the magnetic correlation length remains in keeping with theoretically expected behavior without loss of universality.

The Magnetic Field Dependent Characteristics of Conductance Fluctuations in Ballistic Quantum Dots

We study magneto-resistance fluctuations in GaAs/AlGaAs, ballistic quantum dots. At low temperatures, and at sufficiently low magnetic fields, the fluctuations obscure any average features in the magneto-resistance. As the magnetic field is increased, such that the cyclotron orbit size becomes much smaller than the dot dimensions, however, a strong decay in their high frequency content is observed. We associate this behaviour with the formation of well defined edge states in the dot, and in order to account for our observations apply a simple model, which considers the flux enclosed by skipping orbits localised at the dot walls.

Highelandau levels and electron correlation

Exact diagonalization of the Hamiltonian is employed to study the ground state of double-layer system in which a higher Landau level in one layer is degenerate with the ground Landau level in the other. It is shown that electrons form bound pairs over a wide range of layer separations and filling factors. The binding is due to the attraction between an electron in the low-density layer and the interior of the larger cyclotron orbit in the high-density layer. Results from exact diagonalization are reinforced by an approach using the analytical model wave functions.

Breakdown of correlated diffusion in quasiballistic quantum wires at high magnetic fields.

We study the universal conductance fluctuations (UCF) observed in the low-temperature magnetoconductance of high-mobility GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wires. As the magnetic field is increased, such that the cyclotron orbit becomes smaller than the wire width, both the amplitude \ensuremath{\delta}g and correlation field ${\mathit{B}}_{\mathit{c}}$ of the fluctuations are found to increase linearly with magnetic field. The linear increase in ${\mathit{B}}_{\mathit{c}}$ is in agreement with the results of recent nonlocal studies of the UCF, and is thought to demonstrate a transition to edge-related transport. Similarly, the increase in \ensuremath{\delta}g is argued to result from a magnetically induced breakdown of correlated diffusion, which occurs as the edge states begin to be resolved. Such a breakdown was not observed in previous studies of dirty wires, in which the electron motion remains diffusive up to very high fields, but is instead thought to result from the quasiballistic nature of the wires we study.

The single-layer/bilayer transition of electron systems in AlGaAs/GaAs/AlGaAs quantum wells subject to in-plane magnetic fields

Equilibrium properties of electrons in double-heterojunction AlGaAs/GaAs/AlGaAs structures are investigated theoretically, using a fully self-consistent numerical method. The transition from single to bilayer electron systems is discussed for structures with varying distance between interfaces as a function of the in-plane magnetic field strength. A phenomenon of separability of the energy dispersion curves in parts corresponding to electrons in either the first or the second layer is analysed in detail. The magnetic-field-induced variation in the effective distance between electron layers is compared to the constant layer separation in standard double-well structures. Because the barrier between interfaces is relatively small and soft, the van Hove singularities in the 2D density of states are expected to be more easily detectable than in double-well systems. The cyclotron mass, proportional to the density of states and characterizing the electron motion in tilted magnetic fields, is calculated as a function of in-plane magnetic field. The separability of the energy spectra resulting in tilted cyclotron orbits is demonstrated on the basis of a classical picture of an electron moving in crossed electric and magnetic fields.

How real are composite fermions?

A new picture of fractional quantum Hall effect (FQHE) in terms of a novel particle called composite fermion has emerged recently. A composite fermion is a composite of two flux quanta which are effectively bound to an electron as a result of electron-electron interaction. A system of electrons at half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field with a distinct Fermi surface. The FQHE is then viewed as the integral quantum Hall effect of composite fermions away ffrom half-filling. in order to test for these new particles, we have studied transport of anti-dot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the anti-dot lattice. At half-filling we observe the same dimensional resonances. This establishes the “semi-classical” behavior of composite fermions.

Anomalous behavior of magneto-quantum oscillations in the organic superconductor κ-(BEDT-TTF)2I3

κ-(BEDT-TTF)2I3 is an extreme case of an electronically two-dimensional (2D) organic metal with a superconducting transition at around 4 K. In magnetic fields up to 27 T the field, angular and the temperature dependence of de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillation amplitudes were investigated. From the temperature dependence of the oscillation amplitudes the cyclotron effective massm* was investigated using Lifshitz-Kosevich formula (LK) and the surprising result is, thatm* appears to be magnetic field dependent as soon as the magnetic field is applied exactly perpendicular to the conducting planes so that the cyclotron orbit lies within those planes (i.e. Θ=0o) but field independent at Θ≠0o. It is shown that the LK formula can satisfactorily be used for the interpretation of all data obtained at Θ≠0o but not in the case where Θ=0o. An explanation of the anomalous data at Θ=0o can furthermore neither be given satisfactorily by the descriptions of magneto-quantum oscillations in 2D electronic systems nor by the occurrence of magnetic interaction effects (MI). Tentatively, the observed smaller oscillation amplitudes in κ-(BEDT-TTF)2I3 at Θ=0o above 12 T and below 1 K compared to the standard LK theory will be discussed in terms of a loss in the number of fermions by the occurrence of quasiparticles with fractional statistics.

Interband Transition Strength and Magneto‐Absorption Spectrum in Type‐I Superlattices in In‐Plane Magnetic Fields

AbstractUsing a simplified parabolic band model approach within the framework of the envelope function approximation, the influence of in‐plane magnetic fields on the electronic and optical properties of type‐I superlattices is studied. The results are in qualitative agreement with experimental facts previously reported, as well as with previous theoretical results obtained using more elaborated and toilsome methods. Furthermore, this approach allows to advance, in a great extent, in the analytical treatment of interband transitions, leading straightforwardly to some general conclusions. The not well understood case of high magnetic field effects (magnetic length comparable with the superlattice period) is studied in detail. There strong variations of the interband transition strengths as function of the cyclotron orbit center position are found, a fact which is directly connected with the broadening and final saturation of the magneto‐absorption spectrum with increasing fields. A consistent explanation of such strong variations is given in terms of magnetic subband mixing.

Observation, manipulation, and uses for magnetron motion in ion cyclotron resonance mass spectrometry

An ion of mass-to-charge ratio, m/q, moving under the combined influence of a static magnetic field, B, and an axial quadrupolar electrostatic potential field undergo three "natural" ("normal mode") motions: cyclotron rotation at frequency ω+, magnetron rotation at frequency ω−, and an axial "trapping" oscillation at frequency ωT. Ordinarily, magnetron motion is unobserved, and considered to be undesirable, because ion-neutral collisions result in radial diffusive loss of ions as they roll "downhill" on the magnetron potential surface. However, azimuthal quadrupolar excitation at the ion cyclotron frequency, ωc = qB/m, converts magnetron motion into cyclotron motion, and (for heavy ions) ion-neutral collisions then shrink the cyclotron orbit, leaving a compact ion packet at or near the center of the ICR ion trap. In this paper, we describe briefly the formal basis for such ion axialization, visualization of magnetron motion, the effect of quadrupolar rf excitation amplitude and duration, and how to achieve ion axialization over a wide range of ion m/q values. Applications of the axialization process include ion remeasurement with high (up to 99%) efficiency; prolonged and efficient ion trapping at high collision gas pressure for cooling of electronically, vibrationally, and/or rotationally "hot" ions; enhanced mass resolving power and peak height-to-noise ratio; and enhanced parent ion selectivity (first stage of MS/MS) and enhanced product ion S/N ratio and mass resolving power (second stage of MS/MS). Moreover, because ions may now be axialized, they need not be formed or injected on-axis, thereby making possible continuous injection of externally formed ions, and/or separation between ion and optical axes for photoionization, photodissociation, photodetachment, and optical spectroscopy of trapped ions.