In the integer quantum Hall (IQH) regime, an antidot provides a finite, controllable `edge' of quantum Hall fluid that is an ideal laboratory for investigating the collective dynamics of large numbers of interacting electrons. Transport measurements of single antidots probe the excitation spectra of the antidot edge, and gate-defined antidot devices offer the flexibility to vary both the antidot's dimensions and its couplings to extended IQH edge modes which serve as leads. We also use the spin-selectivity of the IQH edge modes to perform spin-resolved transport measurements, from which we can infer the antidot spin-structure. This thesis describes a combination of such transport experiments and related computational models designed to investigate the effects of electron-electron interactions in quantum antidots, with general implications for the physics of spin and charge in IQH systems.
In the present work we have investigated the transport properties in a number of Si/SiGe samples with square antidot lattices of different periods. In samples with lattice periods equal to 700 nm and 850 nm we have observed the conventional low-field commensurability magnetoresistance peaks consistent with the previous observations in GaAs/AlGaAs and Si/SiGe samples with antidot lattices. In samples with a 600 nm lattice period a new series of well-developed magnetoresistance oscillations has been found beyond the last commensurability peak which are supposed to originate from periodic skippin…
We report on several unusual properties of a graphene antidot created by a piecewise constant potential in a magnetic field. We find that the total probability of finding the electron in the barrier can be nearly one while it is almost zero outside the barrier. In addition, for each electron state of a graphene antidot there is a dot state with exactly the same wavefunction but with a different energy. This symmetry is a consequence of Klein tunneling of Dirac electrons. Moreover, in zigzag nanoribbons we find strong coupling between some antidot states and zigzag edge states. Experimental tes…
A quantum antidot, a submicron depletion region in a two-dimensional electron system, has been actively studied in the past two decades, providing a powerful tool for understanding quantum Hall systems. In a perpendicular magnetic field, electrons form bound states around the antidot. Aharonov-Bohm resonances through such bound states have been experimentally studied, showing interesting phenomena such as Coulomb charging, h/2e oscillations, spectator modes, signatures of electron interactions in the line shape, Kondo effect, etc. None of them can be explained by a simple noninteracting electr…
We present far-infrared (FIR) photo-conductivity measurements for a two-dimensional electron gas in an array of nano-structured antidots. We detect, resistively and spectrally resolved, both the magnetoplasmon and the edge-magnetoplasmon modes. Temperature-dependent measurements demonstrates that both modes contribute to the photo resistance by heating the electron gas via resonant absorption of the FIR radiation. Influences of spin effect and phonon bands on the collective excitations in the antidot lattice are observed.
Recently, a logarithmic decrease of conductivity has been observed in topological insulators at low temperatures, implying a tendency of localization of surface electrons. Here, we report quantum transport experiments on the topological insulator Bi2Te3 thin films with arrayed antidot nanostructures. With increasing density of the antidots, a systematic decrease is observed in the slope of the logarithmic temperature-dependent conductivity curves, indicating the electron-electron interaction can be tuned by the antidots. Meanwhile, the weak anti-localization effect revealed in magnetoconductiv…
Nanostructuring of graphene is in part motivated by the requirement to open a gap in the electronic band structure. In particular, a periodically perforated graphene sheet in the form of an antidot lattice may have such a gap. Such systems have been investigated with a view towards application in transistor or waveguiding devices. The desired properties have been predicted for atomically precise systems, but fabrication methods will introduce significant levels of disorder in the shape, position and edge configurations of individual antidots. We calculate the electronic transport properties of…
We study graphene antidot lattices -- superlattices of perforations (antidots) in a graphene sheet -- using a model that accounts for the phonon-modulation of the $π$-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semi-empirical methods. Based on the adopted model, we quantify the nature of charge carriers in the system by computing the quasiparticle weight due to the electron-phonon interaction for an excess electron in the conduction band. We find a very strong phonon-induced renormalization, with the effective electron masses exh…
The microwave (MW) photoresistance has been measured on a high-mobility two-dimensional electron gas patterned with a shallow triangular antidot lattice, where both the MW-induced resistance oscillations (MIRO) and magnetoplasmon (MP) resonance are observed superposing on sharp commensurate geometrical resonance (GR). Analysis shows that the MIRO, MP, and GR are decoupled from each other in these experiments.
We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in…
We explore the effect of antidot size on electronic and magnetic properties of graphene antidot lattices from first-principles calculations. The spin-polarized density of states, band gap, formation energy and the total magnetization of two different equilateral triangular and right triangular antidots with zigzag and mixed zigzag-armchair edges are studied. We find that although the values of band gap, formation energy and the total magnetization of both structures are different, these values may increase when the number of zigzag edges is increased. The armchair edges have no contribution in…
We report ballistic transport measurements in a two-dimensional electron system confined to an AlAs quantum well and patterned with square antidot lattices of period $a = $0.6, 0.8, 1.0 and 1.5 $μ$m. In this system two in-plane conduction-band valleys with elliptical Fermi contours are occupied. The low-field magneto-resistance traces exhibit peaks corresponding to the commensurability of the cyclotron orbits and the antidot lattice. From the dependence of the position of the peak associated with the smallest commensurate orbit on electron density and $a$, we deduce the ratio of the longitudin…
We investigate a quantum antidot in the integer quantum Hall regime (the filling factor is two) by using a Hartree-Fock approach and by transforming the electron antidot into a system which confines holes via an electron-hole transformation. We find that its ground state is the maximum density droplet of holes in certain parameter ranges. The competition between electron-electron interactions and the confinement potential governs the properties of the hole droplet such as its spin configuration. The ground-state transitions between the droplets with different spin configurations occur as magne…
Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero-energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasi-flat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out …
We have investigated the role of pseudospin polarization in electron wave packet dynamics in pristine graphene and in a graphene antidot lattice subject to an external magnetic field. Employing a Green's function formalism, we show that the electron dynamics can be controlled by tuning pseudospin polarization. We find that in Landau quantized pristine graphene both the propagation of an electron wave packet and Zitterbewegung oscillations strongly depend on pseudospin polarization. The electron wave packet is found to propagate in the direction of initial pseudospin polarization. We also show …
We suggest and study designed defects in an otherwise periodic potential modulation of a two-dimensional electron gas as an alternative approach to electron spin based quantum information processing in the solid-state using conventional gate-defined quantum dots. We calculate the band structure and density of states for a periodic potential modulation, referred to as an antidot lattice, and find that localized states appear, when designed defects are introduced in the lattice. Such defect states may form the building blocks for quantum computing in a large antidot lattice, allowing for coheren…
We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a large magnetic field B. The field confines electrons around the antidot in closed orbits, the areas of which are quantised through the Aharonov-Bohm effect. Increasing B reduces each state's area, pushing electrons closer to the centre, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. Addition and excitation spectra in DC bias confirm the Coulomb blockade of tunnelling.
Quantum antidot, a small potential hill introduced into a two-dimensional electron system, presents an attractive tool to study quantum mechanics of interacting electrons.Here, we report experiments on electron resonant tunneling via a quantum antidot on the integer i = 1, 2, 3, 4, 5, and 6 quantum Hall plateaus. Several new features are reported. First, as a function of magnetic field, we observe up to six quasiperiodic resonant tunneling peaks within the fundamental flux period: when flux h/e is added to the area of the antidot there are i peaks on the i-th integer plateau, when i spin-polar…
We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a perpendicular magnetic field B. The field confines electrons around the antidot in closed orbits, the areas of which are quantised through the Aharonov-Bohm effect. Increasing B reduces each state's area, pushing electrons closer to the centre, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. We have also studied h/2e oscillations and found evidence for coupling of oppos…
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken, by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a novel bilayer graphene heterostructure, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band structure engineering can be performed to obtain linearly dispersi…
We measure the high magnetic field ($B$) microwave conductivity, Re$σ_{xx}$, of a high mobility 2D electron system containing an antidot array. Re$σ_{xx}$ vs frequency ($f$) increases strongly in the regime of the fractional quantum Hall effect series, with Landau filling $1/3<ν<2/3$. At microwave $f$, Re$σ_{xx}$ vs $B$ exhibits a broad peak centered around $ν=1/2$. On the peak, the 10 GHz Re$σ_{xx}$ can exceed its dc-limit value by a factor of 5. This enhanced microwave conductivity is unobservable for temperature $T \gtrsim 0.5$ K, and grows more pronounced as $T$ is decreased. The effect ma…
In order to use graphene for semiconductor applications, such as transistors with high on/off ratios, a band gap must be introduced into this otherwise semimetallic material. A promising method of achieving a band gap is by introducing nanoscale perforations (antidots) in a periodic pattern, known as a graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this paper, we will use the Dirac equation (DE) with a spatially varying mass term to calculate the electronic transport through such structur…
The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values o…
A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics processing units, show that disorder that destroys the band gap can give rise to a transport gap caused by Anderson localization. The size of the defect induced transport gap is found to be proportiona…
Classical transport properties of an electron, moving in plain, in an array of magnetic antidot has been calculated. The homogeneous magnetic field in z-direction fills the whole space except of cylinders of radius r_0. The magnetoresistance shows additional peak and minimum according to pinned orbits at antidots and to propagating orbits in transport direction, respectively.
Non-Abelian Anyon Braiding with Quantum-Antidot Interferometry
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices（北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
We propose a new physical implementation of spin qubits for quantum information processing, namely defect states in antidot lattices defined in the two-dimensional electron gas at a semiconductor heterostructure. Calculations of the band structure of a periodic antidot lattice are presented. A point defect is created by removing a single antidot, and calculations show that localized states form within the defect, with an energy structure which is robust against thermal dephasing. The exchange coupling between two electrons residing in two tunnel-coupled defect states is calculated numerically.…
We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on a single orbital tight-binding model and the Brenner potential. We show that both electronic and thermal transport properties converge fast toward the bulk limit with increasing length of the lattice: only a few repetitions (~6) of the fundamental unit cell are required to recover the electronic band gap of the infinite lattice as a transport gap for the finite lattice. We investigate how different antidot shap…
Silicene systems, due to the buckled structure of the lattice, manifest remarkable intrinsic spin-orbit interaction triggering a topological phase transition in the low-energy regime. Thus, we found that protected edge states are present in silicene antidots and dots, being polarized in valley-spin pairs. We have also studied the effect of the lattice termination on the properties of the single electron energy levels and electron density distribution of silicene antidots and dots situated in a perpendicular magnetic field. Our calculations confirmed that the topological edge states are propaga…
The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an appro…
Tunable inter-edge interactions in a bilayer graphene quantum Hall antidot
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Research Center for Functional Materials, National Institute for Materials Science（国立材料研究所功能材料研究中心）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（国立材料研究所国际纳米材料架构中心）；Institute of Experimental and Applied Physics and Halle-Berlin-Regensburg Cluster of Excellence CCE, University of Regensburg（雷根斯堡大学实验与应用物理研究所及哈勒-柏林-雷根斯堡卓越集群CCE）；Center for Quantum Science and Engineering (QSE Center), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
Antidot lattices, defined on a two-dimensional electron gas at a semiconductor heterostructure, are a well-studied class of man-made structures with intriguing physical properties. We point out that a closely related system, graphene sheets with regularly spaced holes ("antidots"), should display similar phenomenology, but within a much more favorable energy scale, a consequence of the Dirac fermion nature of the states around the Fermi level. Further, by leaving out some of the holes one can create defect states, or pairs of coupled defect states, which can function as hosts for electron spin…
The effect of microwave radiation on low-temperature electron magnetotransport in a square antidot lattice with a period of d = 0.8 micrometer based on a GaAs quantum well with two occupied energy subbands E1 and E2 is investigated. It is shown that, owing to a significant difference between the electron densities in the subbands, commensurability oscillations of the resistance in the investigated antidot lattice are observed only for the first subband. It is found that microwave irradiation under the cyclotron resonance condition results in the formation of resistance oscillations periodic in…
We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectr…
Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance ($G$) maps for a clean QPC as well as for a system including an antidot within the constriction are evaluated. The step-like locally flat $G$ maps for clean QPCs turn into circular resonances that are reentrant in external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of t…
We derive a general capacitive interaction model for an antidot-based interferometer in the integer quantum Hall regime, and study Aharonov-Bohm resonances in a single antidot with multiple bound modes, as a function of the external magnetic field or the gate voltage applied to the antidot. The pattern of Aharonov-Bohm resonances is significantly different from the case of noninteracting electrons. The origin of the difference includes charging effects of excess charges, charge relaxation between the bound modes, the capacitive interaction between the bound modes and the extended edge channels…
Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the "Altshuler-Aronov correction" $δG_{AA}$. Here we study the counterpart of this correction for a ballistic conductor, in which the electron motion is governed by chaotic classical dynamics. In the ballistic conductance, the Ehrenfest time $τ_{E}$ enters as an additional time scale that determines the magnitude of quantum interference effects. The Ehrenfest time effectively poses a short-time threshold for the trajectories contributing to the interaction correction. As a consequence, $δG_…
We propose an efficient spin filter including an antidot fabricated on semiconductor heterostructures with strong spin-orbit interaction. The antidot creates a tunable potential on two-dimensional electron gas in the heterostructures, which may be attractive as well as repulsive. Our idea is based on the enhancement of extrinsic spin Hall effect by resonant scattering when the attractive potential is properly tuned. Numerical studies for three- and four-terminal devices indicate that the efficiency of the spin filter can be more than 50% by tuning the potential to the resonant condition.
We calculate the electronic and thermal transport properties of devices based on finite graphene antidot lattices (GALs) connected to perfect graphene leads. We use an atomistic approach based on the $π$-tight-binding model, the Brenner potential, and employing recursive Green's functions. We consider the effect of random disorder on the electronic and thermal transport properties, and examine the potential gain of thermoelectric merit by tailoring of the disorder. We propose several routes to optimize the transport properties of the GAL systems. Finally, we illustrate how quantum thermal tran…
It is shown that a polarized microwave radiation creates directed transport in an asymmetric antidot superlattice in a two dimensional electron gas. A numerical method is developed that allows to establish the dependence of this ratchet effect on several parameters relevant for real experimental studies. It is applied to the concrete case of a semidisk Galton board where the electron dynamics is chaotic in the absence of microwave driving. The obtained results show that high currents can be reached at a relatively low microwave power. This effect opens new possibilities for microwave control o…
We report Kondo-like behaviour in a quantum antidot (a submicron depleted region in a two-dimensional electron gas) in the quantum-Hall regime. When both spin branches of the lowest Landau level encircle the antidot in a magnetic field ($\sim 1$ T), extra resonances occur between extended edge states via antidot bound states when tunnelling is Coulomb blockaded. These resonances appear only in alternating Coulomb-blockaded regions, and become suppressed when the temperature or source-drain bias is raised. Although the exact mechanism is unknown, we believe that Kondo-like correlated tunnelling…
We study the influences of antidot-induced bound states on transport properties of two- dimensional quantum spin Hall insulators. The bound statesare found able to induce quantum percolation in the originally insulating bulk. At some critical antidot densities, the quantum spin Hall phase can be completely destroyed due to the maximum quantum percolation. For systems with periodic boundaries, the maximum quantum percolationbetween the bound states creates intermediate extended states in the bulk which is originally gapped and insulating. The antidot in- duced bound states plays the same role a…
Resistance fluctuation phenomenon in antidot lattices in the quantum Hall regime are studied. Magnetoresistance of finite antidot array systems in the quantum Hall plateau transition regime exhibits two types of oscillatory effect. One is the aperiodic resistance fluctuations (RFs) and the other is the Aharonov-Bohm (AB)-type oscillations. Their dependences on the magnetic field and the gate voltage are quite distinct. While the aperiodic RFs are attributed to the complex evolution of the conducting network of compressible channels, the AB-type oscillations are interpreted in terms of edge sta…
We explain the experimentally observed Aharonov-Bohm (AB) resonance patterns of an antidot cluster by means of quantum and classical simulations and Feynman path integral theory. We demonstrate that the observed behavior of the AB period signals the crossover from a low B regime which can be understood in terms of electrons following classical orbits to an inherently quantum high B regime where this classical picture and semiclassical theories based on it do not apply.
The edge states which were observed on a linear edge of graphene may also persist on a curved edge. We calculate the elastic transport scattering cross section on a graphene nanohole supporting the edge states. Resonant peaks in the gate voltage dependence of conductivity of graphene with such nanoholes are obtained. Position and height of the resonances are determined by the localization depth of the quasibound edge states, and width -- by their lifetime. The scattering amplitude near the resonant energies has a strong valley asymmetry. We evaluate the effect of moderate edge rippling, inhomo…
The studies of quantum states and optics in n- and p-type heterojunctions with lateral surface quantum dot (antidots) superlattice and in the presence of perpendicular magnetic field are performed. The Azbel' - Hofstadter problem is solved for electrons in conduction band and for holes in valence band described by 4x4 Luttinger Hamiltonian. Under the conditions of non-interactive Landau levels the set of magnetic subbands is obtained for separate electron and hole levels in wide interval of magnetic fields. The influence of spin-orbit interaction onto wavefunctions and energy spectrum in hole …
We consider single-electron tunnelling through antidot states using a Coulomb-blockade model, and give an explanation for h/2e Aharonov-Bohm oscillations, which are observed experimentally when the two spins of the lowest Landau level form bound states. We show that the edge channels may contain compressible regions, and using simple electrostatics, that the resonance through the outer spin states should occur twice per h/e period. An antidot may be a powerful tool for investigating quantum Hall edge states in general, and the interplay of spin and charging effects that occurs in quantum dots.
We have investigated spin-related effects on the electronic transport in a single antidot system in the vicinity of the $ν= 2$ quantum Hall state where two edge states with different spins of the lowest Landau level are formed around the antidot. The conductance exhibits the paired $h/2e$ Aharonov-Bohm (AB) oscillations. Using a tilted magnetic field technique, we have observed the evolution of the oscillations with the total magnetic field and a concomitant change in the source-drain bias dependence of the differential conductance. From the observation, we extract the effect of the Zeeman ene…
We provide a systematic quantitative description of the edge state structure around a quantum antidot in the integer quantum Hall regime. The calculations for spinless electrons within the Hartree approximation reveal that the widely used Chklovskii et al. electrostatic description greatly overestimates the widths of the compressible strips; the difference between these approaches diminishes as the size of the antidot increases. By including spin effects within density functional theory in the local spin-density approximation, we demonstrate that the exchange interaction can suppress the forma…
We have calculated the linear conductance associated with tunneling of individual quasiparticles of primary quantum Hall liquids with filling factors $ν=1/(2m+1)$ through a system of two antidots in series. On-site Coulomb interaction simulates the Fermi exclusion and makes the quasiparticle dynamics similar to that of tunneling electrons. The liquid edges serve as the quasiparticle reservoirs, and also create the dissipation mechanism for tunneling between the antidots. In the regime of strong dissipation, the conductance should exhibit resonant peaks of unusual form and a width proportional …
The magneto-resistance of antidot lattices shows pronounced peaks, which became a hallmark of ballistic electron transport. While most studies agree that they reflect the interplay of regular and chaotic motion in the quasi-classical dynamics, the exact mechanism has been surprisingly controversial. Inspired by recent experiments on graphene antidot lattices showing that the effect survives strong impurity scattering, we give a new explanation of the peaks linked to a fundamental relation between collision times and accessible phase space volumes, accounting for their robustness. Due to the fu…
In this study, we have obtained the exact solutions of the Schrödinger equation for a multi-layered quantum antidot (MLQAD) within the effective mass approximation and dielectric continuum model for the spherical symmetry. The MLQAD is nano-structured semiconductor system that consists of a spherical core (e.g. $Ga_{1-x}Al_{x}As $) and a coated spherical shell (e.g. $Ga_{1-y}Al_{y}As $) as the whole anti-dot is embedded inside a bulk material (e.g. $GaAs $). The dependence of the electron energy spectrum and its radial probability density on nano-system radius are studied. The numeric calculat…
Quantum Antidot (AD) structures have remarkable properties in the integer quantum Hall regime, exhibiting Coulomb-blockade charging and the Kondo effect despite their open geometry. In some regimes a simple single-particle (SP) model suffices to describe experimental observations while in others interaction effects are clearly important, although exactly how and why interactions emerge is unclear. We present a combination of experimental data and the results of new calculations concerning SP orbital states which show how the observed suppression of the energy spacing between states can be expl…
We study a crystallographic etching process of graphene nanostructures where zigzag edges can be prepared selectively. The process involves heating exfoliated single-layer graphene samples with a predefined pattern of antidot arrays in an argon atmosphere at 820 C, which selectively removes carbon atoms located on armchair sites. Atomic force microscopy and scanning electron microscopy cannot resolve the structure on the atomic scale. However, weak localization and Raman measurements - which both probe intervalley scattering at armchair edges - indicate that zigzag regions are enhanced compare…
We consider tunneling through two point contacts between two edges of Quantum Hall liquids of different filling factors $ν_{0,1}=1/ (2m_{0,1}+1)$ with $m_0-m_1\equiv m>0$. Properties of the antidot formed between the point contacts in the strong-tunneling limit are shown to be very different from the $ν_0 =ν_1$ case, and include vanishing average total current in the two contacts and quasiparticles of charge $e/m$. For $m>1$, quasiparticle tunneling leads to non-trivial $m$-state dynamics of effective flux through the antidot which restores the regular ``electron'' periodicity of the current i…
