Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system

Far-Field and Non-Intrusive Optical Mapping of Nanoscale Structures

Far-field high-density optics storage and readout involve the interaction of a sub-100 nm beam profile laser to store and retrieve data with nanostructure media. Hence, understanding the light–matter interaction responding in the far-field in such a small scale is essential for effective optical information processing. We present a theoretical analysis and an experimental study for far-field and non-intrusive optical mapping of nanostructures. By a comprehensive analytical derivation for interaction between the modulated light and the target in a confocal laser scanning microscopy (CLSM) configuration, it is found that the CLSM probes the local density of states (LDOSs) in the far field rather than the sample geometric morphology. With a radially polarized (RP) light for illumination, the far-field mapping of LDOS at the optical resolution down to 74 nm is obtained. In addition, it is experimentally verified that the target morphology is mapped only when the far-field mapping of LDOS coincides with the geometric morphology, while light may be blocked from entering the nanostructures medium with weak or missing LDOS, hence invalidating high-density optical information storage and retrieval. In this scenario, nanosphere gaps as small as 33 nm are clearly observed. We further discuss the characterization for far-field and non-intrusive interaction with nanostructures of different geometric morphology and compare them with those obtainable with the projection of near-field LDOS and scanning electronic microscopic results.

Direct Observation of Global Elastic Intervalley Scattering Induced by Impurities on Graphene

The scattering process induced by impurities in graphene plays a key role in transport properties. Especially, the disorder impurities can drive the ordered state with a hexagonal superlattice on graphene by electron-mediated interaction at a transition temperature. Using angle-resolved photoemission spectroscopy (ARPES), we reveal that the epitaxial monolayer and bilayer graphene with various impurities display global elastic intervalley scattering and quantum interference below the critical temperature (34 K), which leads to a set of new folded Dirac cones at the Brillouin-zone center by mixing two inequivalent Dirac cones. The Dirac electrons generated from intervalley scattering without chirality can be due to the breaking of the sublattice symmetry. In addition, the temperature-dependent ARPES measurements indicate the thermal damping of quantum interference patterns from Dirac electron scattering on impurities. Our results demonstrate that the electron scattering and interference induced by impurities can completely modulate the Dirac bands of graphene.

On the origin of the electron accumulation layer at clean InAs(111) surfaces

In this paper, we provide a comprehensive theoretical analysis of the electronic structure of InAs(111) surfaces with special attention paid to the energy region close to the fundamental bandgap. Starting from the bulk electronic structure of InAs calculated using the PBE functional with the inclusion of Hubbard correction and spin-orbit coupling, we derive proper values for the bandgap, split-off energy, as well as effective electron, light-hole and heavy-hole masses in full consistent with the available experimental results. Besides that we address the projected density of states associated with p orbitals of bulk indium and arsenic atoms. On the basis of optimized atomic surfaces we recover scanning tunneling microscopy images and calculate the band structure and orbital distributions of surface atoms, which along with accessible experimental data make it possible to speculate on the formation of the electron accumulation layer for both As- and In-terminated InAs(111) surfaces. Moreover, these results are accompanied by charge density distribution simulations.

Dielectric Confinement and Excitonic Effects in Two-Dimensional Nanoplatelets

Quasi-two-dimensional (2D) semiconductor nanoplatelets manifest strong quantum confinement with exceptional optical characteristics of narrow photoluminescence peaks with energies tunable by thickness with monolayer precision. We employed scanning tunneling spectroscopy (STS) in conjunction with optical measurements to probe the thickness-dependent band gap and density of excited states in a series of CdSe nanoplatelets. The tunneling spectra, measured in the double-barrier tunnel junction configuration, reveal the effect of quantum confinement on the band gap taking place mainly through a blue-shift of the conduction band edge, along with a signature of 2D electronic structure intermixed with finite lateral-size and/or defects effects. The STS fundamental band gaps are larger than the optical gaps as expected from the contributions of exciton binding in the absorption, as confirmed by theoretical calculations. The calculations also point to strong valence band mixing between the light- and split-off hole levels. Strikingly, the energy difference between the heavy-hole and light-hole levels in the tunneling spectra are significantly larger than the corresponding values extracted from the absorption spectra. Possible explanations for this, including an interplay of nanoplatelet charging, dielectric confinement, and difference in exciton binding energy for light and heavy holes, are analyzed and discussed.

Circularly polarized near-field optical mapping of spin-resolved quantum Hall chiral edge states

We have successfully developed a circularly polarized near-field scanning optical microscope (NSOM) that enables us to irradiate circularly polarized light with spatial resolution below the diffraction limit. As a demonstration, we perform real-space mapping of the quantum Hall chiral edge states near the edge of a Hall-bar structure by injecting spin polarized electrons optically at low temperature. The obtained real-space mappings show that spin-polarized electrons are injected optically to the two-dimensional electron layer. Our general method to locally inject spins using a circularly polarized NSOM should be broadly applicable to characterize a variety of nanomaterials and nanostructures.

Near-field optical mapping of quantum Hall edge states

We report on the mapping of quantum-Hall edge states by quasiresonant photovoltage measurements using a near-field scanning optical microscope. We have observed fine structures near sample edges that shift inward with an increase in magnetic field in accordance with the shift of the positions of the quantum-Hall edge states. We have found a transition from the weak disorder regime where compressible-incompressble strips are visible to the strong disorder regime where fluctuations smear out incompressible strips.

Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy

Using low-temperature scanning tunneling spectroscopy applied to the Cs-induced two-dimensional electron system (2DES) on p-type InSb(110), we probe electron-electron interaction effects in the quantum Hall regime. The 2DES is decoupled from bulk states and exhibits spreading resistance within the insulating quantum Hall phases. In quantitative agreement with calculations we find an exchange enhancement of the spin splitting. Moreover, we observe that both the spatially averaged as well as the local density of states feature a characteristic Coulomb gap at the Fermi level. These results show that electron-electron interaction can be probed down to a resolution below all relevant length scales.

Scaling and localization lengths of a topologically disordered system

We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical evidence that this model displays the same universal behavior as the standard Anderson model. We use finite-size scaling to find the localization length as a function of energy and density, including localized states away from the delocalization transition. Results at many energies all fit onto the same universal scaling curve.

Critical parameters from a generalized multifractal analysis at the Anderson transition

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wave function amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wave function statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent ν=1.58±0.03.

Multifractal analysis with the probability density function at the three-dimensional anderson transition

The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.

Quantum Hall transition in real space: from localized to extended states

Using scanning tunneling spectroscopy in an ultrahigh vacuum at low temperature (T=0.3 K) and high magnetic fields (B<or=12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with theoretical predictions, we observe the evolution from localized drift states in the insulating phases to branched extended drift states at the quantum critical point. The observed microscopic behavior close to the extended state indicates points of localized quantum tunneling, which are considered to be decisive for a quantitative description of the transition.

Combined low-temperature scanning tunneling/atomic force microscope for atomic resolution imaging and site-specific force spectroscopy

We present the design and first results of a low-temperature, ultrahigh vacuum scanning probe microscope enabling atomic resolution imaging in both scanning tunneling microscopy (STM) and noncontact atomic force microscopy (NC-AFM) modes. A tuning-fork-based sensor provides flexibility in selecting probe tip materials, which can be either metallic or nonmetallic. When choosing a conducting tip and sample, simultaneous STM/NC-AFM data acquisition is possible. Noticeable characteristics that distinguish this setup from similar systems providing simultaneous STM/NC-AFM capabilities are its combination of relative compactness (on-top bath cryostat needs no pit), in situ exchange of tip and sample at low temperatures, short turnaround times, modest helium consumption, and unrestricted access from dedicated flanges. The latter permits not only the optical surveillance of the tip during approach but also the direct deposition of molecules or atoms on either tip or sample while they remain cold. Atomic corrugations as low as 1 pm could successfully be resolved. In addition, lateral drifts rates of below 15 pm/h allow long-term data acquisition series and the recording of site-specific spectroscopy maps. Results obtained on Cu(111) and graphite illustrate the microscope's performance.

Local electronic structure near Mn acceptors in InAs: surface-induced symmetry breaking and coupling to host states

We present low-temperature scanning tunneling spectroscopy measurements on Mn acceptors in InAs in comparison with tight-binding calculations. We find a strong (001)-mirror asymmetry of the bound hole wave function close to the (110) surface. In addition, multiple acceptor-related peaks are observed and are attributed to a spin-orbit splitting of the acceptor level. Because of the p-d exchange interaction the local density of states near the acceptors is enhanced in the valence band and suppressed in the conduction band. We also observe signs of anisotropic scattering of the conduction band states by neutral acceptors.

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 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.

The effect of adsorbed oxygen on the surface potential of n-GaAs(110)

Potential variations on semiconductor surfaces are often mapped using a combination of constant current topographic and local surface photo-voltage (SPV) imaging. SPV imaging provides a direct measurement of surface-potential variations at large lateral distances from a charged defect or adsorbate. However, directly above the defect, variations in the SPV signal need to be interpreted in terms of surface screening, traps, and band bending. We have examined these effects using isolated oxygen atoms on a GaAS(110) surface, which is free of surface states. We interpret variations in the SPV signal in terms of a simple electrostatic model which considers the oxygen-induced Coulomb potential and corresponding image potential, both of which affect the surface density of states.

Direct measurement of the local density of states of a disordered one-dimensional conductor

One-dimensional electron systems (1DESs) containing two and one occupied subbands are found below the different types of [11;2] steps of the InAs(110) surface. Using low-temperature scanning tunneling spectroscopy, we determined the subband energies, the disorder potential, and the local density of states of these 1DESs. The rather complete knowledge of the 1DES allowed us to compare the measured LDOS with a single-particle calculation. Surprisingly, we did not find significant deviations from the calculation albeit the electron-electron interaction in the 1DESs is stronger than the electron-disorder interaction.

Real-space observation of drift States in a two-dimensional electron system at high magnetic fields

The local density of states of the adsorbate-induced two-dimensional electron system is studied in magnetic fields up to B=6 T. Landau quantization is observed and drift states with a width of about the magnetic length are found in agreement with theoretical predictions. At the tails of the Landau levels the states form closed paths indicating localization. These states show the expected energy dependence. A multifractal analysis applied to the data results in a nice parabolic shape of the characteristic f(alpha) spectra, but we find only a slight displacement of the origin from alpha=2.0 for the states in the center of the Landau level.