Effective quantities and effective rules in two-dimensional ferromagnetic antidot lattices

In this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested.     

三维拓扑绝缘体antidot阵列结构中的磁致输运研究

利用聚焦离子束刻蚀技术在拓扑绝缘体Bi_2Se_3薄膜中刻蚀了纳米尺度的反点(antidot)阵列,并对制作的三个器件进行了系统的电学输运测量研究.低温下,所有器件中都观察到明显的弱反局域化效应.通过对弱反局域化效应的分析,发现器件一(Dev-1,不含有antidot阵列)和器件二(Dev-2,含有周期较大的antidot阵列)是始终由一个导电通道主导的量子输运系统,但在器件三(Dev-3,含有周期较小的antidot阵列)中能明确观察到较低温度下存在两个独立的导电通道,而在较高温度下Dev-3表现为由一个导电通道主导的量子输运系统.     

Quantum interference and decoherence in hexagonal antidot lattices

The Altshuler–Aronov–Spivak (AAS) oscillations and the Aharonov–Bohm (AB) type oscillations both at low and high magnetic fields were observed in hexagonal antidot lattices fabricated from a GaAs/AlGaAs two-dimensional electron gas sample. The periodicities in the magnetic field and in the gate bias voltage, of the high field AB oscillation furnish information on the edge states localized around the antidots. The temperature dependences of these quantum oscillations are studied.     

Semiclassical theory of transport in antidot lattices

Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal time/T . The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constant and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.This paper is dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Localization and antilocalization in InSb and InAs antidot lattices

We report on the observation of localization, antilocalization and Altshuler–Aronov–Spivak (AAS) oscillations in antidot lattices patterned on high-mobility InSb/InAlSb and InAs/AlGaSb heterostructures. In addition, the antidot lattices display ballistic commensurability features. The strength of the localization peak in InSb antidot lattices decreases exponentially with temperature, with a high characteristic temperature of 25 K between 0.4 and 50 K. Analysis of the AAS oscillations enables the extraction of phase and spin coherence lengths in InAs.     

Ensemble expectations for structures on two-dimensional lattices

Expressions are obtained for the limiting behavior of ensemble expectations, as functions of coverage, of the number of simultaneous occurrences of various structures when indistinguishable single particles are arranged on a two-dimensional lattice. For the general expressions obtained no restrictions are placed on the geometrical nature of the lattice. Averages for specific geometrical arrays, such as rectangular and hexagonal arrays, may be calculated directly from the general results.     

Blue-Sisyphus cooling in cesium gray molasses and antidot lattices

We present an experimental study of the kinetic temperature of cesium atoms interacting with laser beams tuned on the blue side of the transition. In the case of a three-dimensional four-beam molasses, temperatures as low as 800 nK were found. These low temperatures are compatible with a good capture efficiency. The influence of other hyperfine transitions on the temperature is significant. In the presence of a static magnetic field (antidot lattices), the temperatures are slightly higher but show a much weaker dependence on the other hyperfine transitions. Received: 14 May 1998 / Received in final form: 16 October 1998 / Accepted: 2 November 1998     

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.     

Magnetotransport in a modulated two-dimensional electron gas

We propose a semiclassical theory of dc magnetotransport in a two-dimensional electron gas modulated along one direction with weak electrostatic modulations. We show that oscillations of the magnetoresistivity ρ_∥ corresponding to the current driven along the modulation lines observed at moderately low magnetic fields can be explained as commensurability oscillations.     

Spatial confinement of ferromagnetic resonances in honeycomb antidot lattices

We report on a theoretical investigation of the magnetic static and dynamic properties of a thin ferromagnetic film with honeycomb lattice of circular antidots using micromagnetic simulations and analytical calculations. The theoretical model is based on the Landau–Lifshitz equations and directly accounts for the effects of the magnetic state nonuniformity. A direct calculation of local dynamic susceptibility tensor yields that the resonance spectra consist of four different quasi-uniform modes of the magnetization precession related to the confinement of magnetic domains by the hole mesh. Three of four resonant modes follow a two-fold variation with respect to the in-plane orientation of the applied magnetic field. The easy axes of these modes are mutually rotated by 60° and combine to yield the apparent six-fold configurational anisotropy. Additionally, a mode with intrinsic six-fold symmetry behavior exists, as well. Micromagnetic calculations of the local dynamic susceptibility tensor allow identifying the magnetic unit cell areas/domains responsible for each resonance mode.     

From antidot to dot superlattices: Magnetoresistance anomalies

For low Fermi energies and large antidot diameters an antidot superlattice changes into a dot superlattice. A negative magnetoresistance (NMR) for low magnetic fields coexisting with a commensurability peak is observed in this transition regime. We reproduce these features for both classical and quantum-mechanical calculations in a model, which traces the NMR back to saddle points with varying heights between the antidots. 1997 Elsevier Science B.V. All rights reserved.     

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.     

First-principles studies of graphene antidot lattices on monolayer h-BN substrate

The structures and electronic structures of hetero bilayers composed of graphene antidot lattice (GAL) on monolayer h-BN substrate are studied in first-principles method. Bond lengths, interlayer distances, flatness, biaxial strain effects, and effects of translating the GAL layer are studied and analyzed in detail. Results show that introducing a monolayer BN substrate makes the zero-bandgap $5\times 5$ GAL open a bandgap up to 28 meV, while it makes the semiconducting $6\times 6$ GAL keep its low-energy electronic structure almost intact except a small bandgap change by tens of meV at most. Our studies demonstrate that h-BN is a promising substrate for GAL.     

Fabrication of two-dimensional photonic lattices in GaAs: the regular graphite structures

Two-dimensional photonic lattices have been fabricated in GaAs by using standard electron beam lithography and reactive ion etching techniques. In order to obtain absolute photonic band gaps at near-infrared frequencies, graphite structures which consist of parallel cylindrical rods of GaAs at the vertices of regular hexagons have been studied. Typically, for quarter micron diameter rods and half micron nearest spacing, an etching depth of more than one micron was obtained. Preliminary results from optical characterization are also presented.     

Microwave control of directed transport in asymmetric antidot structures

It is shown that a polarized microwave radiation creates directed transport in an asymmetric antidot superlattice in 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 strong currents can be reached at a relatively low microwave power. This effect opens new possibilities for microwave control of transport in asymmetric superlattices.     

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.     

Spontaneous magnetism of quantum dot lattices

The magnetism of square lattices of quantum dots with up to 12 electrons per dot is studied using the spin-density functional formalism. At small values of the lattice constant, all lattices are nonmagnetic and gapless. When the lattice constant is increased, the shell structure of the single dots governs the magnetism of the lattice. At closed shells, the lattices are nonmagnetic and have a gap at the Fermi level. At the beginning and at the end of a shell, they become ferromagnetic and stay gapless up to large values of the lattice constant. Antiferromagnetism was observed only at midshell after a band gap was opened.