Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at ν=1/3\nu=1/3

Resonant inelastic light scattering experiments at $\nu=1/3$ reveal a novel splitting of the long wavelength modes in the low energy spectrum of quasiparticle excitations in the charge degree of freedom. We find a single peak at small wavevectors that splits into two distinct modes at larger wavevectors. The evidence of well-defined dispersive behavior at small wavevectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long wavelength modes of the electron liquid.Comment: 4 pages, 4 figure

Transition from Free to Interacting Composite Fermions away from ν\nu=1/3

Spin excitations from a partially populated composite fermion level are studied above and below $\nu=1/3$. In the range $2/7<\nu<2/5$ the experiments uncover significant departures from the non-interacting composite fermion picture that demonstrate the increasing impact of interactions as quasiparticle Landau levels are filled. The observed onset of a transition from free to interacting composite fermions could be linked to condensation into the higher order states suggested by transport experiments and numerical evaluations performed in the same filling factor range.Comment: 4 pages, 5 figures, to appear in PR

Spin-Atomic Vibration Interaction and Spin-Flip Hamiltonian of a Single Atomic Spin in a Crystal Field

We derive the spin-atomic vibration interaction $V_{\rm SA}$ and the spin-flip Hamiltonian $V_{\rm SF}$ of a single atomic spin in a crystal field. We here apply the perturbation theory to a model with the spin-orbit interaction and the kinetic and potential energies of electrons. The model also takes into account the difference in vibration displacement between an effective nucleus and electrons, \Delta {{\boldmath r}}. Examining the coefficients of $V_{\rm SA}$ and $V_{\rm SF}$, we first show that $V_{\rm SA}$ appears for \Delta {{\boldmath r}}$\ne$0, while $V_{\rm SF}$ is present independently of \Delta {{\boldmath r}}. As an application, we next obtain $V_{\rm SA}$ and $V_{\rm SF}$ of an Fe ion in a crystal field of tetragonal symmetry. It is found that the magnitudes of the coefficients of $V_{\rm SA}$ can be larger than those of the conventional spin-phonon interaction depending on vibration frequency. In addition, transition probabilities per unit time due to $V_{\rm SA}$ and $V_{\rm SF}$ are investigated for the Fe ion with an anisotropy energy of $-|D|S_Z^2$, where $D$ is an anisotropy constant and $S_Z$ is the $Z$ component of a spin operator.Comment: 55 pages, 17 figures, to be published in J. Phys. Soc. Jpn. 79 (2010) No. 11, typos correcte

The role of magnetic anisotropy in the Kondo effect

In the Kondo effect, a localized magnetic moment is screened by forming a correlated electron system with the surrounding conduction electrons of a non-magnetic host. Spin S=1/2 Kondo systems have been investigated extensively in theory and experiments, but magnetic atoms often have a larger spin. Larger spins are subject to the influence of magnetocrystalline anisotropy, which describes the dependence of the magnetic moment's energy on the orientation of the spin relative to its surrounding atomic environment. Here we demonstrate the decisive role of magnetic anisotropy in the physics of Kondo screening. A scanning tunnelling microscope is used to simultaneously determine the magnitude of the spin, the magnetic anisotropy and the Kondo properties of individual magnetic atoms on a surface. We find that a Kondo resonance emerges for large-spin atoms only when the magnetic anisotropy creates degenerate ground-state levels that are connected by the spin flip of a screening electron. The magnetic anisotropy also determines how the Kondo resonance evolves in a magnetic field: the resonance peak splits at rates that are strongly direction dependent. These rates are well described by the energies of the underlying unscreened spin states.Comment: 14 pages, 4 figures, published in Nature Physic

Higher-Energy Composite Fermion Levels in the Fractional Quantum Hall Effect

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect

Magnetic Anisotropy of Single Mn Acceptors in GaAs in an External Magnetic Field

We investigate the effect of an external magnetic field on the physical properties of the acceptor hole states associated with single Mn acceptors placed near the (110) surface of GaAs. Crosssectional scanning tunneling microscopy images of the acceptor local density of states (LDOS) show that the strongly anisotropic hole wavefunction is not significantly affected by a magnetic field up to 6 T. These experimental results are supported by theoretical calculations based on a tightbinding model of Mn acceptors in GaAs. For Mn acceptors on the (110) surface and the subsurfaces immediately underneath, we find that an applied magnetic field modifies significantly the magnetic anisotropy landscape. However the acceptor hole wavefunction is strongly localized around the Mn and the LDOS is quite independent of the direction of the Mn magnetic moment. On the other hand, for Mn acceptors placed on deeper layers below the surface, the acceptor hole wavefunction is more delocalized and the corresponding LDOS is much more sensitive on the direction of the Mn magnetic moment. However the magnetic anisotropy energy for these magnetic impurities is large (up to 15 meV), and a magnetic field of 10 T can hardly change the landscape and rotate the direction of the Mn magnetic moment away from its easy axis. We predict that substantially larger magnetic fields are required to observe a significant field-dependence of the tunneling current for impurities located several layers below the GaAs surface.Comment: Non

Anomalous structure in the single particle spectrum of the fractional quantum Hall effect

The two-dimensional electron system (2DES) is a unique laboratory for the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels. Within a Landau level the kinetic energy of the electrons is suppressed, and electron-electron interactions set the only energy scale. Coulomb interactions break the degeneracy of the Landau levels and can cause the electrons to order into complex ground states. In the high energy single particle spectrum of this system, we observe salient and unexpected structure that extends across a wide range of Landau level filling fractions. The structure appears only when the 2DES is cooled to very low temperature, indicating that it arises from delicate ground state correlations. We characterize this structure by its evolution with changing electron density and applied magnetic field. We present two possible models for understanding these observations. Some of the energies of the features agree qualitatively with what might be expected for composite Fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites also generates structure similar to those observed in the experiment. Neither of these models alone is sufficient to explain the observations across the entire range of densities measured. The discovery of this unexpected prominent structure in the single particle spectrum of an otherwise thoroughly studied system suggests that there exist core features of the 2DES that have yet to be understood.Comment: 15 pages, 10 figure

Quantum manipulation via atomic-scale magnetoelectric effects

Magnetoelectric effects at the atomic scale are demonstrated to afford unique functionality. This is shown explicitly for a quantum corral defined by a wall of magnetic atoms deposited on a metal surface where spin-orbit coupling is observable. We show these magnetoelectric effects allow one to control the properties of systems placed inside the corral as well as their electronic signatures; they provide alternative tools for probing electronic properties at the atomic scale