Electron pinball and commensurate orbits in a periodic array of scatterers

Intrinsically Patterned Two-Dimensional Transition Metal Halides

Patterning and defect engineering are key methods for tuning the properties and enabling distinctive functionalities in two-dimensional (2D) materials. However, generating 2D periodic patterns of point defects in 2D materials, such as vacancy lattices that can serve as antidot lattices, has been elusive until now. Herein, we report on 2D transition metal dihalides epitaxially grown on metal surfaces featuring periodically assembled halogen vacancies that result in alternating coordination of the transition metal atom. Using low-temperature scanning probe microscopy and low-energy electron diffraction, we identified the structural properties of intrinsically patterned FeBr2 and CoBr2 monolayers grown epitaxially on Au(111). Density functional theory reveals that Br vacancies are facilitated by low formation energies, and the formation of a vacancy lattice results in a substantial decrease in the lattice mismatch with the underlying Au(111). We demonstrate that interfacial strain engineering presents a versatile strategy for controlled patterning in two dimensions with atomic precision over several hundred nanometers to solve a long-standing challenge of growing atomically precise antidot lattices. In particular, patterning of 2D materials containing transition metals provides a versatile method to achieve unconventional spin textures with noncollinear spin.

Atomic-scale interpretation of the quantum oscillations in cuprate superconductors

Cuprate superconductors display unusual features in bothkspace and real space as the superconductivity is suppressed-a broken Fermi surface, charge density wave, and pseudogap. Contrarily, recent transport measurements on cuprates under high magnetic fields report quantum oscillations (QOs), which imply rather a usual Fermi liquid behavior. To settle the disagreement, we investigated Bi₂Sr₂CaCu₂O_8+δunder a magnetic field in an atomic scale. A particle-hole (p-h) asymmetrically dispersing density of states (DOSs) modulation was found at the vortices on a slightly underdoped sample, while on a highly underdoped sample, no trace of the vortex was found even at 13 T. However, a similar p-h asymmetric DOS modulation persisted in almost an entire field of view. From this observation, we infer an alternative explanation of the QO results by providing a unifying picture where the aforementioned seemingly conflicting evidence from angle-resolved photoemission spectroscopy, spectroscopic imaging scanning tunneling microscopy, and magneto-transport measurements can be understood solely in terms of the DOS modulations.

Nanoscale View of Engineered Massive Dirac Quasiparticles in Lithographic Superstructures

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects, and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is reported, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of 0.64 ± 0.03 eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The methodology demonstrates band structure engineering guided by directly viewing structurally and electrically tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale.

Resonant Scattering in Proximity-Coupled Graphene/Superconducting Mo2 C Heterostructures

The realization of high-quality heterostructures or hybrids of graphene and superconductor is crucial for exploring various novel quantum phenomena and devices engineering. Here, the electronic transport on directly grown high-quality graphene/Mo₂ C vertical heterostructures with clean and sharp interface is comprehensively investigated. Owing to the strong interface coupling, the graphene layer feels an effective confinement potential well imposed by two-dimensional (2D) Mo₂ C crystal. Employing cross junction device geometry, a series of resonance-like magnetoresistance peaks are observed at low temperatures. The temperature and gate voltage dependences of the observed resonance peaks give evidence for geometric resonance of electron cyclotron orbits with the formed potential well. Moreover, it is found that both the amplitude of resonance peaks and conductance fluctuation exhibit different temperature-dependent behaviors below the superconducting transition temperature of 2D Mo₂ C, indicating the correlation of quantum fluctuations and superconductivity. This study offers a promising route toward integrating graphene with 2D superconducting materials, and establishes a new way to investigate the interplay of massless Dirac fermion and superconductivity based on graphene/2D superconductor vertical heterostructures.

Suspended semiconductor nanostructures: physics and technology

The current state of research on quantum and ballistic electron transport in semiconductor nanostructures with a two-dimensional electron gas separated from the substrate and nanoelectromechanical systems is reviewed. These nanostructures fabricated using the surface nanomachining technique have certain unexpected features in comparison to their non-suspended counterparts, such as additional mechanical degrees of freedom, enhanced electron-electron interaction and weak heat sink. Moreover, their mechanical functionality can be used as an additional tool for studying the electron transport, complementary to the ordinary electrical measurements. The article includes a comprehensive review of spin-dependent electron transport and multichannel effects in suspended quantum point contacts, ballistic and adiabatic transport in suspended nanostructures, as well as investigations on nanoelectromechanical systems. We aim to provide an overview of the state-of-the-art in suspended semiconductor nanostructures and their applications in nanoelectronics, spintronics and emerging quantum technologies.

Estimating Lyapunov exponents in billiards

Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here, the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software on its implementation.

New Generation of Moiré Superlattices in Doubly Aligned hBN/Graphene/hBN Heterostructures

The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superlattices can result in a third superlattice with a period larger than the maximum period (14 nm) in the graphene/hBN system, which we explain in a simple model. This new type of band structure engineering allows one to artificially create an even wider spectrum of electronic properties in two-dimensional materials.

Normal and Anomalous Diffusion in Soft Lorentz Gases

Motivated by electronic transport in graphenelike structures, we study the diffusion of a classical point particle in Fermi potentials situated on a triangular lattice. We call this system a soft Lorentz gas, as the hard disks in the conventional periodic Lorentz gas are replaced by soft repulsive scatterers. A thorough computational analysis yields both normal and anomalous (super)diffusion with an extreme sensitivity on model parameters. This is due to an intricate interplay between trapped and ballistic periodic orbits, whose existence is characterized by tonguelike structures in parameter space. These results hold even for small softness, showing that diffusion in the paradigmatic hard Lorentz gas is not robust for realistic potentials, where we find an entirely different type of diffusion.

Suppression of magnetoresistance in PtSe2 microflakes with antidot arrays

Suppression of magnetoresistance (MR) is meaningful for sensor applications to immure magnetic fields. Herein, we report the observation of suppressed MR in PtSe₂ microflakes by introducing the antidot arrays (AAs). We have compared the magnetotransport properties of PtSe₂ microflakes before and after milling of AAs. The enhanced resistivity and notable MR suppression were observed while the AAs are milled in the PtSe₂ microflakes. Their physical mechanism has been ascribed to the enhanced electron scattering rate due to the additional electron-antidot interactions. This work gave an example to suppress MR in materials by introducing AAs, which may be useful for sensor applications in magnetic fields.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Nonmonotonic Classical Magnetoconductivity of a Two-Dimensional Electron Gas in a Disordered Array of Obstacles

Magnetotransport measurements in combination with molecular dynamics simulations on two-dimensional disordered Lorentz gases in the classical regime are reported. In quantitative agreement between experiment and simulation, the magnetoconductivity displays a pronounced peak as a function of the perpendicular magnetic field B which cannot be explained by existing kinetic theories. This peak is linked to the onset of a directed motion of the electrons along the contour of the disordered obstacle matrix when the cyclotron radius becomes smaller than the size of the obstacles. This directed motion leads to transient superdiffusive motion and strong scaling corrections in the vicinity of the insulator-to-conductor transitions of the Lorentz gas.

Ballistic geometric resistance resonances in a single surface of a topological insulator

Transport in topological matter has shown a variety of novel phenomena over the past decade. Although numerous transport studies have been conducted on three-dimensional topological insulators (TIs), study of ballistic motion and thus exploration of potential landscapes on a hundred nanometer scale is for the prevalent TI materials almost impossible due to their low carrier mobility. Therefore, it is unknown whether helical Dirac electrons in TIs, bound to interfaces between topologically distinct materials, can be manipulated on the nanometer scale by local gates or locally etched regions. Here we impose a submicron periodic potential onto a single surface of Dirac electrons in high-mobility strained mercury telluride (HgTe), which is a strong TI. Pronounced geometric resistance resonances constitute the clear-cut observation of a ballistic effect in three-dimensional TIs.

Ballistic motion on nanometer scale of topological surface states has rarely been studied. Here, Maier et al. report pronounced geometric resistance resonances of high-mobility Dirac electrons in strained HgTe, suggesting a ballistic effect in three-dimensional topological insulators.

Recent progress in van der Waals heterojunctions

Following the development of many novel two-dimensional (2D) materials, investigations of van der Waals heterojunctions (vdWHs) have attracted significant attention due to their excellent properties such as smooth heterointerface, highly gate-tunable bandgap, and ultrafast carrier transport. Benefits from the atom-scale thickness, physical and chemical properties and ease of manipulation of the heterojunctions formulated by weak vdW forces were demonstrated to indicate their outstanding potential in electronic and optoelectronic applications, including photodetection and energy harvesting, and the possibility of integrating them with the existing semiconductor technology for the next-generation electronic and sensing devices. In this review, we summarized the recent developments of vdWHs and emphasized their applications. Basically, we introduced the physical properties and some newly discovered phenomena in vdWHs. Then, we emphatically presented four classical vdWHs and some novel heterostructures formed by vdW forces. Based on their unique physical properties and structures, we highlighted the applications of vdWHs including in photodiodes, phototransistors, tunneling devices, and memory devices. Finally, we provided a conclusion on the recent advances in vdWHs and outlined our perspectives. We aim for this review to serve as a solid foundation in this field and to pave the way for future research on vdW-based materials and their heterostructures.

Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal

When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings (ν≪1), its direct observation has been elusive. Here we present a new technique and experimental results directly probing the magnetic-field-induced WC. We measure the magnetoresistance of a bilayer electron system where one layer has a very low density and is in the WC regime (ν≪1), while the other ("probe") layer is near ν=1/2 and hosts a sea of composite fermions (CFs). The data exhibit commensurability oscillations in the magnetoresistance of the CF layer, induced by the periodic potential of WC electrons in the other layer, and provide a unique, direct glimpse at the symmetry of the WC, its lattice constant, and melting. They also demonstrate a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasiparticles of another many-body state.

High-mobility capacitively-induced two-dimensional electrons in a lateral superlattice potential

In the presence of a lateral periodic potential modulation, two-dimensional electrons may exhibit interesting phenomena, such as a graphene-like energy-momentum dispersion, Bloch oscillations, or the Hofstadter butterfly band structure. To create a sufficiently strong potential modulation using conventional semiconductor heterostructures, aggressive device processing is often required, unfortunately resulting in strong disorder that masks the sought-after effects. Here, we report a novel fabrication process flow for imposing a strong lateral potential modulation onto a capacitively induced two-dimensional electron system, while preserving the host material quality. Using this process flow, the electron density in a patterned Si/SiGe heterostructure can be tuned over a wide range, from 4.4 × 10(10) cm(-2) to 1.8 × 10(11) cm(-2), with a peak mobility of 6.4 × 10(5) cm(2)/V·s. The wide density tunability and high electron mobility allow us to observe sequential emergence of commensurability oscillations as the density, the mobility, and in turn the mean free path, increase. Magnetic-field-periodic quantum oscillations associated with various closed orbits also emerge sequentially with increasing density. We show that, from the density dependence of the quantum oscillations, one can directly extract the steepness of the imposed superlattice potential. This result is then compared to a conventional lateral superlattice model potential.

Ballistic Transport in Graphene Antidot Lattices

The bulk carrier mobility in graphene was shown to be enhanced in graphene-boron nitride heterostructures. However, nanopatterning graphene can add extra damage and drastically degrade the intrinsic properties by edge disorder. Here we show that graphene embedded into a heterostructure with hexagonal boron nitride (hBN) on both sides is protected during a nanopatterning step. In this way, we can prepare graphene-based antidot lattices where the high mobility is preserved. We report magnetotransport experiments in those antidot lattices with lattice periods down to 50 nm. We observe pronounced commensurability features stemming from ballistic orbits around one or several antidots. Due to the short lattice period in our samples, we can also explore the boundary between the classical and the quantum transport regime, as the Fermi wavelength of the electrons approaches the smallest length scale of the artificial potential.

Radiation-assisted magnetotransport in two-dimensional electron gas systems: appearance of zero resistance states

Zero-resistance states (ZRS) are normally associated with superconducting and quantum Hall phases. Experimental detection of ZRS in two-dimensional electron gas (2DEG) systems irridiated by microwave(MW) radiation in a magnetic field has been quite a surprise. We develop a semiclassical transport formalism to explain the phenomena. We find a sequence of Zero-Resistance States (ZRS) inherited from the suppression of Shubnikov-de Haas (SdH) oscillations under the influence of high-frequency and large amplitude microwave radiation. Furthermore, the ZRS are well pronounced and persist up to broad intervals of magnetic field as observed in experiments on microwave illuminated 2DEG systems.

Artificial Gauge Field and Topological Phase in a Conventional Two-dimensional Electron Gas with Antidot Lattices

Based on the Born-Oppemheimer approximation, we divide the total electron Hamiltonian in a spin-orbit coupled system into the slow orbital motion and the fast interband transition processes. We find that the fast motion induces a gauge field on the slow orbital motion, perpendicular to the electron momentum, inducing a topological phase. From this general designing principle, we present a theory for generating artificial gauge field and topological phase in a conventional two-dimensional electron gas embedded in parabolically graded GaAs/InxGa1-xAs/GaAs quantum wells with antidot lattices. By tuning the etching depth and period of the antidot lattices, the band folding caused by the antidot potential leads to the formation of minibands and band inversions between neighboring subbands. The intersubband spin-orbit interaction opens considerably large nontrivial minigaps and leads to many pairs of helical edge states in these gaps.

Magnetoresistance oscillations in topological insulator Bi2Te3 nanoscale antidot arrays

Nanoscale antidot arrays were fabricated on a single-crystal microflake of topological insulator Bi2Te3. The introduction of antidot arrays significantly increased the resistance of the microflake, yet the temperature dependence of the resistance remains metallic. We observed that small oscillations that are periodic in magnetic field B appeared on top of the weak anti-localization magnetoresistance. Since the electron coherence length at low temperature becomes comparable to the feature size in our device, we argued that the magnetoresistance oscillations are the manifestation of quantum interference induced by the nanostructure. Our work demonstrates that the transport of topological insulators could indeed be controlled by artificially created nanostructures, and paves the way for future technological applications of this class of materials.

Ratchet effect and amplitude dependence of phase locking in a two-dimensional Frenkel-Kontorova model

We demonstrate the ratchet and phase locking effects in a two-dimensional overdamped Frenkel-Kontorova model with a square symmetric periodic substrate when both a longitudinal dc drive and a circular ac drive are applied. Besides the harmonic steps, the large half integer steps can also clearly be seen in the longitudinal (x) direction. These half integer steps are directly correlated to the appearance of positive and negative ratchet effects in the transverse (y) direction due to the symmetry breaking in the combination of the dc and ac drives. The angle between the net displacement and the longitudinal direction is analytically obtained in a single period of the ac drive. In the examination of the amplitude dependence of the ac drive, the maxima decrease monotonically with the amplitude, while the anomalies occur for the critical depinning force and the harmonic steps due to the spatial symmetry breaking of orbits in the presence of the ac drive.

Cloning of Dirac fermions in graphene superlattices

Superlattices have attracted great interest because their use may make it possible to modify the spectra of two-dimensional electron systems and, ultimately, create materials with tailored electronic properties. In previous studies (see, for example, refs 1-8), it proved difficult to realize superlattices with short periodicities and weak disorder, and most of their observed features could be explained in terms of cyclotron orbits commensurate with the superlattice. Evidence for the formation of superlattice minibands (forming a fractal spectrum known as Hofstadter's butterfly) has been limited to the observation of new low-field oscillations and an internal structure within Landau levels. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential acts as a superlattice and leads to profound changes in the graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity, accompanied by reversal of the Hall effect. The latter indicates that the effective sign of the charge carriers changes within graphene's conduction and valence bands. Strong magnetic fields lead to Zak-type cloning of the third generation of Dirac points, which are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices such as this one provide a way of studying the rich physics expected in incommensurable quantum systems and illustrate the possibility of controllably modifying the electronic spectra of two-dimensional atomic crystals by varying their crystallographic alignment within van der Waals heterostuctures.

Symmetry breaking for ratchet transport in the presence of interactions and a magnetic field

We study the microwave induced ratchet transport of two-dimensional electrons on an oriented semidisk Galton board. The magnetic field symmetries of ratchet transport are analyzed in the presence of electron-electron interactions. Our results show that a magnetic field asymmetric ratchet current can appear due to two contributions, a Hall drift of the rectified current that depends only weakly on electron-electron interactions and a breaking of the time reversal symmetry due to the combined effects of interactions and magnetic field. In the latter case, the asymmetry between positive and negative magnetic fields vanishes in the weak interaction limit. We also discuss the recent experimental results on ratchet transport in asymmetric nanostructures.

Magnetic modulation of the tunnelling between defect states in antidot superlattices

We show theoretically that the tunnelling between properly designed defects in periodic antidot lattices can be strongly modulated by applied magnetic fields. Further, transport channels made up of linear arrangements of tunnel-coupled defects can accommodate Aharonov-Bohm cages, suggesting a magnetic control of the transport through the system. Evidence supporting an unusual robustness of the caging effect against electron-electron interactions is also provided.

The role of dissipation in time-dependent non-integrable focusing billiards

In this study, we compare the dynamical properties of chaotic and nearly integrable time-dependent focusing billiards with elastic and dissipative boundaries. We show that in the system without dissipation the average velocity of particles scales with the number of collisions as ̅V∝n(α). In the fully chaotic case, this scaling corresponds to a diffusion process with α≈1/2, whereas in the nearly integrable case, this dependence has a crossover; slow particles accelerate in a slow subdiffusive manner with α<1/2, while acceleration of fast particles is much stronger and their average velocity grows super-diffusively, i.e., α>1/2. Assuming ̅V∝n(α) for a non-dissipative system, we obtain that in its dissipative counterpart the average velocity approaches to ̅V(fin)∝1/δ(α), where δ is the damping coefficient. So that ̅V(fin)∝√1/δ in the fully chaotic billiards, and the characteristics exponents α changes with δ from α(1)>1/2 to α(2)<1/2 in the nearly integrable systems. We conjecture that in the limit of moderate dissipation the chaotic time-depended billiards can accelerate the particles more efficiently. By contrast, in the limit of small dissipations, the nearly integrable billiards can become the most efficient accelerator. Furthermore, due to the presence of attractors in this system, the particles trajectories will be focused in narrow beams with a discrete velocity spectrum.

Biomineralization as an inspiration for materials chemistry

Living organisms are well known for building a wide range of specially designed organic-inorganic hybrid materials such as bone, teeth, and shells, which are highly sophisticated in terms of their adaptation to function. This has inspired physicists, chemists, and materials scientists to mimic such structures and their properties. In this Review we describe how strategies used by nature to build and tune the properties of biominerals have been applied to the synthesis of materials for biomedical, industrial, and technological purposes. Bio-inspired approaches such as molecular templating, supramolecular templating, organized surfaces, and phage display as well as methods to replicate the structure and function of biominerals are discussed. We also show that the application of in situ techniques to study and visualize the bio-inspired materials is of paramount importance to understand, control, and optimize their preparation. Biominerals are synthesized in aqueous media under ambient conditions, and these approaches can lead to materials with a reduced ecological footprint than can traditional methods.

Confinement and deconfinement in the potential of antidot arrays of a massless Dirac electron in magnetic fields

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length [Formula: see text], probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/ℓ < 1 inter-Landau level mixing is strong and probability densities with energy less than the potential height are non-chiral and localized inside antidot potentials. However, in the strong magnetic field limit R/ℓ ≫ 1, where inter-Landau level mixing is small, they are delocalized outside antidot potentials, and are chiral for N = 0 Landau level (LL) states while non-chiral for N = 1. In the non-trivial crossover regime R/ℓ ∼ 1 localized and delocalized probability densities coexist. States that are delocalized outside antidots when R/ℓ > 1 form a nearly degenerate band and their probability densities are independent of k, in contrast to the case of R/ℓ < 1.

Quantum Hall ferromagnetism in the presence of tunable disorder

In this Letter, we report our recent experimental results on the energy gap of the ν=1 quantum Hall state (Δ(ν=1)) in a quantum antidot array sample, where the effective disorder potential can be tuned continuously. Δ(ν=1) is nearly constant at small effective disorders, and collapses at a critical disorder. Moreover, in the weak disorder regime, Δ(ν=1) shows a B(total)(1/2) dependence in tilted magnetic field measurements, while in the strong disorder regime, Δ(ν=1) is linear in B(total), where B(total) is the total magnetic field at ν=1. We discuss our results within several models involving the quantum Hall ferromagnetic ground state and its interplay with sample disorder.

Collapse of Landau levels in gated graphene structures

We describe a new regime of magnetotransport in two-dimensional electron systems in the presence of a narrow potential barrier. In such systems, the Landau level states, which are confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. Transport measurements on a top-gated graphene device are presented. Shubnikov-de Haas (SdH) oscillations, observed in the unipolar regime, are found to abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories.

Investigation of Diblock Copolymer thin film Morphology for Nanolithography

The microphase separated morphology of diblock copolymers can be used to generate well-ordered nanometer scale patterns over a large area. To achieve this goal, it is important to understand and control the behavior of diblock copolymer thin films on substrates, which can differ from the bulk behavior. We have investigated the morphologies and ordering in thin polystyrene-polybutadiene (PS-PB) diblock copolymer films on bare silicon and silicon nitride substrates, and also on polymethylmethacrylate (PMMA) coated substrates. The PS-PB copolymers are synthesized to form, in bulk, PB cylinders or spheres in a PS matrix. In thin films (10–60 nm thick), prepared by spin-coating, we observe that the morphology and ordering of the microdomains are affected by strong wetting constraints and a reduced chain mobility on the substrate. The thinnest self-assembled layer of the copolymer films shows no in-plane microphase separation on both types of substrates. The PS blocks wet the PMMA substrates whereas the PB blocks wet the bare substrates as well as the air interface. Hence, different film thicknesses are necessary on the two types of substrates to obtain a uniform film of the first self-assembled cylindrical or spherical microdomain layer. The first layer of the cylindrical copolymer can vary from cylindrical to spherical morphology with a few nanometer decrease in film thickness. In the case of spherical PS-PB diblock copolymer films, we observe that the ordering of the microdomains is improved in the films on the PMMA substrates, compared to those on the bare substrates. We also demonstrate a successful transfer of the microdomain patterns to silicon nitride substrates by a reactive ion etching technique.

Phase-space composition of driven elliptical billiards and its impact on Fermi acceleration

We demonstrated very recently [Lenz, New J. Phys. 11, 083035 (2009)] that an ensemble of particles in the driven elliptical billiard shows a surprising crossover from subdiffusion to normal diffusion in momentum space. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. In this work, we consider three different driving modes of the elliptical billiard and perform a comprehensive analysis of the corresponding four-dimensional phase space. The composition of this phase space is different in the high-velocity regime compared to the low-velocity regime. We will show, among others, by investigating periodic orbits and probability distributions of laminar phases that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change in the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion.

Band structures and transport properties of zigzag graphene nanoribbons with antidot arrays

We study the band and transport features of zigzag graphene nanoribbon with an antidot lattice. It is found that an antidot lattice could turn semi-metal graphene into a semiconductor. The size of the band gap can be tuned by the position of the antidots and the distance D between the two nearest antidots. For a finite superlattice with N antidots and a large D, a group of (N - 1) splitting resonant peaks and transmission-blockade regions appear alternately in the conductance spectrum. This indicates the formation of minibands and minigaps. In addition, Fano resonances can be observed when the antidots are localized near one edge of the nanoribbon. These features provide potential applications for graphene-based electronic and optoelectronic devices.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.

Graphene antidot lattices: designed defects and spin qubits

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 qubits. We present a detailed study of the energetics of periodic graphene antidot lattices, analyze the level structure of a single defect, calculate the exchange coupling between a pair of spin qubits, and identify possible avenues for further developments.

Strain-induced fermi contour anisotropy of GaAs 2D holes

We report measurements of magnetoresistance commensurability peaks, induced by a square array of antidots, in GaAs (311)A two-dimensional holes as a function of applied in-plane strain. The data directly probe the shapes of the Fermi contours of the two spin subbands that are split thanks to the spin-orbit interaction and strain. The experimental results are in quantitative agreement with the predictions of accurate energy band calculations, and reveal that the majority spin subband has a severely distorted Fermi contour whose anisotropy can be tuned with strain.

Anomalous giant piezoresistance in AlAs 2D electron systems with antidot lattices

An AlAs two-dimensional electron system patterned with an antidot lattice exhibits a giant piezoresistance effect at low temperatures, with a sign opposite to the piezoresistance observed in the unpatterned region. We suggest that the origin of this anomalous giant piezoresistance is the nonuniform strain in the antidot lattice and the exclusion of electrons occupying the two conduction-band valleys from different regions of the sample. This is analogous to the well-known giant magnetoresistance effect, with valley playing the role of spin and strain the role of magnetic field.

Photoconductivity in AC-driven modulated two-dimensional electron gas in a perpendicular magnetic field

In this work we study the microwave photoconductivity of a two-dimensional electron system (2DES) in the presence of a magnetic field and a two-dimensional modulation (2D). The model includes the microwave and Landau contributions in a non-perturbative exact way; the periodic potential is treated perturbatively. The Landau-Floquet states provide a convenient base with respect to which the lattice potential becomes time dependent, inducing transitions between the Landau-Floquet levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. The total longitudinal conductivity and resistivity exhibit strong oscillations, determined by ϵ = ω/ω(c), with ω the radiation frequency and ω(c) the cyclotron frequency. The oscillations follow a pattern with minima centred at [Formula: see text], and maxima centred at [Formula: see text], where j = 1,2,3..., δ∼1/5 is a constant shift and l is the dominant multipole contribution. Negative resistance states (NRSs) develop as the electron mobility and the intensity of the microwave power are increased. These NRSs appear in a narrow window region of values of the lattice parameter (a), around a∼l(B), where l(B) is the magnetic length. It is proposed that these phenomena may be observed in artificially fabricated arrays of periodic scatterers at the interface of ultraclean GaAs /Al(x)Ga(1-x)As heterostructures.

Signature of directed chaos in the conductance of a nanowire

We study the conductance of chaotic or disordered wires in a situation where equilibrium transport decomposes into biased diffusion and a countermoving regular current. A possible realization is a semiconductor nanostructure with a transversal magnetic field and suitably patterned surfaces. We find a nontrivial dependence of the conductance on the wire length. It differs qualitatively from Ohm's law by the existence of a characteristic length scale and a finite saturation value.

Role of chaos in one-dimensional heat conductivity

We investigate the heat conduction in a quasi-one-dimensional gas model with various degrees of chaos. Our calculations indicate that the heat conductivity kappa is independent of system size when the chaos of the channel is strong enough. The different diffusion behaviors for the cases of chaotic and nonchaotic channels are also studied. The numerical results of divergent exponent alpha of heat conduction and diffusion exponent beta are consistent with the formula alpha = 2 - 2/beta. We explore the temperature profiles numerically and analytically, which show that the temperature jump is primarily attributed to superdiffusion for both nonchaotic and chaotic cases, and for the latter case of superdiffusion the finite size affects the value of beta remarkably.

Reentrant onset of chaos in tubular image states

We investigate the reentrant onset of chaos in "tubular image states," which are loosely bound states of electrons formed in the vicinity (20-40 nm) of conducting nanotubes. Chaos is shown to arise when an electron is placed in the vicinity of two metallic nanotubess with a magnetic field applied along the tubes. At stronger magnetic fields B approximately 10 T, we observe the formation of Landau-like states encircling the two-tube system, which wipe out the chaos. We can reinstall the chaos by charging oppositely the nanotubes, thus breaking the symmetry of the system and correspondingly the shape of the Landau-like states. Detailed analysis of the onset of chaos is done by studying the statistical properties of the eigenvalues spectrum and by investigating the spatial autocorrelation functions of individual eigenstates.

Nonequilibrium stationary states with ratchet effect

An ensemble of particles in thermal equilibrium at temperature T, modeled by Nosè-Hoover dynamics, moves on a triangular lattice of oriented semidisk elastic scatterers. Despite the scatterer asymmetry, a directed transport is clearly ruled out by the second law of thermodynamics. Introduction of a polarized zero mean monochromatic field creates a directed stationary flow with nontrivial dependence on temperature and field parameters. We give a theoretical estimate of directed current induced by a microwave field in an antidot superlattice in semiconductor heterostructures.

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of a omega/(2 pi), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a nonzero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.

Potential landscapes and induced charges near metallic islands in three dimensions

We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D) uses an efficient grid relaxation technique. The well-known relaxation algorithm for solving the Poisson equation in two dimensions is generalized to 3D. In addition, all charges on the system, free as well as induced charges, are determined accurately and self-consistently to satisfy the desired boundary conditions. This allows the straightforward calculation of the potential on the outer boundary using the free space electrostatic Green's function, as well as the calculation of the entire capacitance matrix of the system. Physically interesting examples of nanoscale systems are presented and analyzed.

Absolute transverse mobility and ratchet effect on periodic two-dimensional symmetric substrates

We present a simple model of an overdamped particle moving on a two-dimensional symmetric periodic substrate with a dc drive in the longitudinal direction and additional ac drives in both the longitudinal and transverse directions. For certain regimes we find that a finite longitudinal dc force produces a net dc response only in the transverse direction, which we term absolute transverse mobility. Additionally, we find regimes exhibiting a ratchet effect in the absence of an applied dc drive.

Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two-dimensional inverse magnetic domain, where the magnetic field is zero inside the domain and constant outside. As an example, we present detailed analysis for stadium-shaped domain. In the case of infinite magnetic field, the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields, the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (based on the technique of Jacobi fields) and the regular-to-chaotic phase space volume ratio show that both quantities can smoothly be tuned by varying the external magnetic field. A possible experimental realization of the inverse magnetic billiard is also discussed.

Tunneling spectroscopy of a two-dimensionally periodic electron system

The tunneling current between an electron gas with a periodic potential in two dimensions and a plain two-dimensional electron system (2DES) has been studied. The strength of the periodic potential, the subband energy of the plain 2DES, and an applied in-plane magnetic field were varied, mapping the Fourier transform of the periodic wave function. Periodic peaks were observed and explained by translations in the reciprocal lattice. When the potential was strongly modulated to form an array of antidots, commensurability peaks were seen in lateral transport, but, as expected, not in tunneling.

Rectification and phase locking for particles on symmetric two-dimensional periodic substrates

We demonstrate a rectification phenomenon for overdamped particles interacting with a 2D symmetric periodic substrate when driven with a dc and a circular ac drive. As a function of longitudinal dc amplitude, the longitudinal velocity increases in a series of quantized steps distinct from Shapiro steps with transverse rectification occurring near these transitions. The rectification phenomenon is explained using symmetry arguments and a simple model.