Real-Space Imaging of Alternate Localization and Extension of Quasi Two-Dimensional Electronic States at Graphite Surfaces in Magnetic Fields

We measured the local density of states (LDOS) of a quasi two-dimensional (2D) electron system near point defects on a surface of highly oriented pyrolytic graphite (HOPG) with scanning tunneling microscopy and spectroscopy. Differential tunnel conductance images taken at very low temperatures and in high magnetic fields show a clear contrast between localized and extended spatial distributions of the LDOS at the valley and peak energies of the Landau level spectrum, respectively. The localized electronic state has a single circular distribution around the defects with a radius comparable to the magnetic length. The localized LDOS is in good agreement with a spatial distribution of a calculated wave function for a single electron in 2D in a Coulomb potential in magnetic fields.Comment: 4 pages, 4 figure

Anlaytic mean-field Hall crystal solution at nu=1/3: composite fermion like sub-bands and correlation effects

An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully occupied and the other empty, as in the composite fermion model. The localized orbitals associated to the Bloch like single electron wavefunctions are nearly static, resembling the angular momentum eigenstates within a Landau level for non-interacting fermions. Strong correlations are expected owing to the large charge density overlap between neighboring plaquettes. A numerical evaluation brings the cohesive energy close to that of the best present day models. It is also found that correlations are long range, requiring over 50 particles spread over a finite sample to approach convergence. Since presently allowed exact calculations are far from this number, the question of how relevant the considered wave-function is for the description of the ground state of the 2DEG system remains open.Comment: 24 pages, 4 figures, content exposed in the: Symposium Quantum Hall Effect: "Past, Present and Future", Sttutgart, Germany, 2-5 July 2003 and in the Third Stig Lundquist Conference on Advancing Frontiers of Condensed Matter Physics 11-15 August 2003, ICTP, Trieste Ital

Localized Distributions of Quasi Two-Dimensional Electronic States near Defects Artificially Created at Graphite Surfaces in Magnetic Fields

We measured the local density of states of a quasi two-dimensional electron system (2DES) near defects, artificially created by Ar-ion sputtering, on surfaces of highly oriented pyrolytic graphite (HOPG) with scanning tunneling spectroscopy (STS) in high magnetic fields. At valley energies of the Landau level spectrum, we found two typical localized distributions of the 2DES depending on the defects. These are new types of distributions which are not observed in the previous STS work at the HOPG surface near a point defect [Y. Niimi \textit{et al}., Phys. Rev. Lett. {\bf 97}, 236804 (2006).]. With increasing energy, we observed gradual transformation from the localized distributions to the extended ones as expected for the integer quantum Hall state. We show that the defect potential depth is responsible for the two localized distributions from comparison with theoretical calculations.Comment: 4 pages, 3 figure

Magnetoelasticity theory of incompressible quantum Hall liquids

A simple and physically transparent magnetoelasticity theory is proposed to describe linear dynamics of incompressible fractional quantum Hall states. The theory manifestly satisfies the Kohn theorem and the $f$-sum rule, and predicts a gaped intra-Landau level collective mode with a roton minimum. In the limit of vanishing bare mass $m$ the correct form of the static structure factor, $s(q)\sim q^4$, is recovered. We establish a connection of the present approach to the fermionic Chern-Simons theory, and discuss further extensions and applications. We also make an interesting analogy of the present theory to the theory of visco-elastic fluids.Comment: RevTeX 4, 6 pages; expanded version to appear in PRB; more technical details, and discussions of the physics adde

Broadening effects due to alloy scattering in Quantum Cascade Lasers

We report on calculations of broadening effects in QCL due to alloy scattering. The output of numerical calculations of alloy broadened Landau levels compare favorably with calculations performed at the self-consistent Born approximation. Results for Landau level width and optical absorption are presented. A disorder activated forbidden transition becomes significant in the vicinity of crossings of Landau levels which belong to different subbands. A study of the time dependent survival probability in the lowest Landau level of the excited subband is performed. It is shown that at resonance the population relaxation occurs in a subpicosecond scale.Comment: 7 pages, 8 figure

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].Comment: 8 pages, 8 figure

On transport in quantum Hall systems with constrictions

Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the constriction is seen to arise from the matching of the properties of the edge-current excitations in the constriction ($\nu_{2}$) and bulk ($\nu_{1}$) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. In this way, we find satisfactory explanations for many recent puzzling experimental results.Comment: 4 pages, 4 figure

Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.Comment: 10 pages, 4 Fig