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Rashidi A, Ahadi S, Munyan S, Mitchell WJ, Stemmer S. Tuning Displacement Fields in a Two-Dimensional Topological Insulator Using Nanopatterned Gates. NANO LETTERS 2024; 24:7366-7372. [PMID: 38842923 PMCID: PMC11194848 DOI: 10.1021/acs.nanolett.4c01518] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Revised: 05/03/2024] [Accepted: 05/29/2024] [Indexed: 06/07/2024]
Abstract
Epitaxial heterostructures with topological insulators enable novel quantum phases and practical device applications. Their topological electronic states are sensitive to the microscopic parameters, including structural inversion asymmetry (SIA), which is an inherent feature of many real heterostructures. Controlling SIA is challenging, because it requires the ability to tune the displacement field across the topological film. Here, using nanopatterned gates, we demonstrate a tunable displacement field in a heterostructure of the two-dimensional topological insulator cadmium arsenide. Transport studies in magnetic fields reveal an extreme sensitivity of the band inversion to SIA. We show that a relatively small displacement field (∼50 mV/nm) converts the crossing of the two zeroth Landau levels in magnetic field to an avoided crossing, signaling a change to trivial band order. This work demonstrates a universal methodology for tuning electronic states in topological thin films.
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Affiliation(s)
- Arman Rashidi
- Materials
Department, University of California, Santa Barbara, California 93106-5050, United
States
| | - Sina Ahadi
- Materials
Department, University of California, Santa Barbara, California 93106-5050, United
States
| | - Simon Munyan
- Materials
Department, University of California, Santa Barbara, California 93106-5050, United
States
| | - William J. Mitchell
- Department
of Electrical and Computer Engineering, University of California, Santa
Barbara, California 93106-5050, United States
| | - Susanne Stemmer
- Materials
Department, University of California, Santa Barbara, California 93106-5050, United
States
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2
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Pogosov AG, Shevyrin AA, Pokhabov DA, Zhdanov EY, Kumar S. Suspended semiconductor nanostructures: physics and technology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:263001. [PMID: 35477698 DOI: 10.1088/1361-648x/ac6308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 03/31/2022] [Indexed: 06/14/2023]
Abstract
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.
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Affiliation(s)
- A G Pogosov
- Rzhanov Institute of Semiconductor Physics SB RAS, 13 Lavrentiev Ave., Novosibirsk 630090, Russia
- Department of Physics, Novosibirsk State University, 2 Pirogov Str., Novosibirsk 630090, Russia
| | - A A Shevyrin
- Rzhanov Institute of Semiconductor Physics SB RAS, 13 Lavrentiev Ave., Novosibirsk 630090, Russia
| | - D A Pokhabov
- Rzhanov Institute of Semiconductor Physics SB RAS, 13 Lavrentiev Ave., Novosibirsk 630090, Russia
- Department of Physics, Novosibirsk State University, 2 Pirogov Str., Novosibirsk 630090, Russia
| | - E Yu Zhdanov
- Rzhanov Institute of Semiconductor Physics SB RAS, 13 Lavrentiev Ave., Novosibirsk 630090, Russia
- Department of Physics, Novosibirsk State University, 2 Pirogov Str., Novosibirsk 630090, Russia
| | - S Kumar
- Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
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3
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Datseris G, Hupe L, Fleischmann R. Estimating Lyapunov exponents in billiards. CHAOS (WOODBURY, N.Y.) 2019; 29:093115. [PMID: 31575126 DOI: 10.1063/1.5099446] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 08/23/2019] [Indexed: 06/10/2023]
Abstract
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.
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Affiliation(s)
- George Datseris
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Faculty of Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
| | - Lukas Hupe
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Faculty of Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
| | - Ragnar Fleischmann
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Faculty of Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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4
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Klages R, Gallegos SSG, Solanpää J, Sarvilahti M, Räsänen E. Normal and Anomalous Diffusion in Soft Lorentz Gases. PHYSICAL REVIEW LETTERS 2019; 122:064102. [PMID: 30822076 DOI: 10.1103/physrevlett.122.064102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Revised: 11/02/2018] [Indexed: 06/09/2023]
Abstract
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.
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Affiliation(s)
- Rainer Klages
- Queen Mary University of London, School of Mathematical Sciences, Mile End Road, London E1 4NS, United Kingdom
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
| | - Sol Selene Gil Gallegos
- Queen Mary University of London, School of Mathematical Sciences, Mile End Road, London E1 4NS, United Kingdom
| | - Janne Solanpää
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Mika Sarvilahti
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Esa Räsänen
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
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5
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Siboni NH, Schluck J, Pierz K, Schumacher HW, Kazazis D, Horbach J, Heinzel T. Nonmonotonic Classical Magnetoconductivity of a Two-Dimensional Electron Gas in a Disordered Array of Obstacles. PHYSICAL REVIEW LETTERS 2018; 120:056601. [PMID: 29481203 DOI: 10.1103/physrevlett.120.056601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2017] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- N H Siboni
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - J Schluck
- Institut für Experimentelle Physik der kondensierten Materie, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - K Pierz
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - H W Schumacher
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - D Kazazis
- CNRS, Université Paris-Sud, Université Paris-Saclay, C2N Marcoussis, 91460 Marcoussis, France
| | - J Horbach
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - T Heinzel
- Institut für Experimentelle Physik der kondensierten Materie, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
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6
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Ballistic geometric resistance resonances in a single surface of a topological insulator. Nat Commun 2017; 8:2023. [PMID: 29222407 PMCID: PMC5722899 DOI: 10.1038/s41467-017-01684-0] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Accepted: 10/09/2017] [Indexed: 12/03/2022] Open
Abstract
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.
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7
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Lu TM, Laroche D, Huang SH, Chuang Y, Li JY, Liu CW. High-mobility capacitively-induced two-dimensional electrons in a lateral superlattice potential. Sci Rep 2016; 6:20967. [PMID: 26865160 PMCID: PMC4750089 DOI: 10.1038/srep20967] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Accepted: 01/13/2016] [Indexed: 12/02/2022] Open
Abstract
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.
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Affiliation(s)
- T. M. Lu
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - D. Laroche
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - S.-H. Huang
- Department of Electrical Engineering and Graduate Institute of Electronic Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C
- National Nano Device Laboratories, Hsinchu 30077, Taiwan, R.O.C
| | - Y. Chuang
- Department of Electrical Engineering and Graduate Institute of Electronic Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C
- National Nano Device Laboratories, Hsinchu 30077, Taiwan, R.O.C
| | - J.-Y. Li
- Department of Electrical Engineering and Graduate Institute of Electronic Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C
- National Nano Device Laboratories, Hsinchu 30077, Taiwan, R.O.C
| | - C. W. Liu
- Department of Electrical Engineering and Graduate Institute of Electronic Engineering, National Taiwan University, Taipei 10617, Taiwan, R.O.C
- National Nano Device Laboratories, Hsinchu 30077, Taiwan, R.O.C
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8
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Sandner A, Preis T, Schell C, Giudici P, Watanabe K, Taniguchi T, Weiss D, Eroms J. Ballistic Transport in Graphene Antidot Lattices. NANO LETTERS 2015; 15:8402-8406. [PMID: 26598218 DOI: 10.1021/acs.nanolett.5b04414] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
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.
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Affiliation(s)
- Andreas Sandner
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
| | - Tobias Preis
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
| | - Christian Schell
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
| | - Paula Giudici
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Dieter Weiss
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
| | - Jonathan Eroms
- Institute of Experimental and Applied Physics, University of Regensburg , D-93040 Regensburg, Germany
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9
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Wang CL, Tekić J, Duan WS, Shao ZG, Yang L. Ratchet effect and amplitude dependence of phase locking in a two-dimensional Frenkel-Kontorova model. J Chem Phys 2013; 138:034307. [PMID: 23343276 DOI: 10.1063/1.4776226] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
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Affiliation(s)
- Cang-Long Wang
- Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
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10
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Nudelman F, Sommerdijk NAJM. Biomineralisation als Inspirationsquelle für die Materialchemie. Angew Chem Int Ed Engl 2012. [DOI: 10.1002/ange.201106715] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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11
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Nudelman F, Sommerdijk NAJM. Biomineralization as an inspiration for materials chemistry. Angew Chem Int Ed Engl 2012; 51:6582-96. [PMID: 22639420 DOI: 10.1002/anie.201106715] [Citation(s) in RCA: 301] [Impact Index Per Article: 25.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Revised: 01/19/2012] [Indexed: 11/06/2022]
Abstract
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.
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Affiliation(s)
- Fabio Nudelman
- Laboratory of Materials and Interface Chemistry and Soft Matter CryoTEM Unit, Eindhoven University of Technology, P. O. Box 513, 5600 MB, Eindhoven, The Netherlands
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12
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Kolovsky AR, Mantica G. Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041123. [PMID: 21599131 DOI: 10.1103/physreve.83.041123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2010] [Indexed: 05/30/2023]
Abstract
This paper studies the quantum dynamics of a charged particle in a two-dimensional square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions ensuring directed transport with the drift velocity. We also describe the effect of disorder in the system.
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13
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14
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Nogaret A. Electron dynamics in inhomogeneous magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:253201. [PMID: 21393794 DOI: 10.1088/0953-8984/22/25/253201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This review explores the dynamics of two-dimensional electrons in magnetic potentials that vary on scales smaller than the mean free path. The physics of microscopically inhomogeneous magnetic fields relates to important fundamental problems in the fractional quantum Hall effect, superconductivity, spintronics and graphene physics and spins out promising applications which will be described here. After introducing the initial work done on electron localization in random magnetic fields, the experimental methods for fabricating magnetic potentials are presented. Drift-diffusion phenomena are then described, which include commensurability oscillations, magnetic channelling, resistance resonance effects and magnetic dots. We then review quantum phenomena in magnetic potentials including magnetic quantum wires, magnetic minibands in superlattices, rectification by snake states, quantum tunnelling and Klein tunnelling. The third part is devoted to spintronics in inhomogeneous magnetic fields. This covers spin filtering by magnetic field gradients and circular magnetic fields, electrically induced spin resonance, spin resonance fluorescence and coherent spin manipulation.
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Affiliation(s)
- Alain Nogaret
- Department of Physics, University of Bath, Bath, UK.
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15
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Soba A, Tierno P, Fischer TM, Saguès F. Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:060401. [PMID: 18643203 DOI: 10.1103/physreve.77.060401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/26/2023]
Abstract
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.
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Affiliation(s)
- Alejandro Soba
- Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, Barcelona, Spain
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16
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Shabani J, Shayegan M, Winkler R. Strain-induced fermi contour anisotropy of GaAs 2D holes. PHYSICAL REVIEW LETTERS 2008; 100:096803. [PMID: 18352742 DOI: 10.1103/physrevlett.100.096803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2007] [Indexed: 05/26/2023]
Abstract
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.
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Affiliation(s)
- J Shabani
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
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17
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Chernov N, Dolgopyat D. Diffusive motion and recurrence on an idealized Galton board. PHYSICAL REVIEW LETTERS 2007; 99:030601. [PMID: 17678275 DOI: 10.1103/physrevlett.99.030601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2007] [Indexed: 05/16/2023]
Abstract
We study a mechanical model known as a Galton board--a particle rolling on a tilted plane under gravitation and bouncing off a periodic array of rigid pegs. Incidentally, this model is identical to a periodic Lorentz gas where an electron is driven by a uniform electric field. Previous heuristic and experimental studies have suggested that the particle's speed v(t) should grow as t(1/3) and its coordinate x(t) as t(2/3). We find exact limit distributions for the rescaled velocity t(-1/3)v(t) and position t(-2/3)x(t). In addition, we determine that the particle's motion is recurrent; i.e., the particle comes back to the top of the board with a probability of one.
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Affiliation(s)
- N Chernov
- Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA
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18
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19
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Rapoport A, Rom-Kedar V. Nonergodicity of the motion in three-dimensional steep repelling dispersing potentials. CHAOS (WOODBURY, N.Y.) 2006; 16:043108. [PMID: 17199386 DOI: 10.1063/1.2357331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
It is demonstrated numerically that smooth three degrees of freedom Hamiltonian systems that are arbitrarily close to three-dimensional strictly dispersing billiards (Sinai billiards) have islands of effective stability, and hence are nonergodic. The mechanism for creating the islands is corners of the billiards domain.
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20
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Reichhardt C, Olson Reichhardt CJ, Hastings MB. Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056115. [PMID: 15244891 DOI: 10.1103/physreve.69.056115] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2003] [Indexed: 05/24/2023]
Abstract
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.
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Affiliation(s)
- C Reichhardt
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Vörös Z, Tasnádi T, Cserti J, Pollner P. Tunable Lyapunov exponent in inverse magnetic billiards. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:065202. [PMID: 16241292 DOI: 10.1103/physreve.67.065202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2002] [Indexed: 05/04/2023]
Abstract
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.
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Affiliation(s)
- Zoltán Vörös
- Department of Physics of Complex Systems, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
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22
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Guantes R, Miret-Artés S. Chaotic transport of particles in two-dimensional periodic potentials driven by ac forces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046212. [PMID: 12786465 DOI: 10.1103/physreve.67.046212] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2002] [Revised: 01/23/2003] [Indexed: 05/24/2023]
Abstract
The diffusive and directed transport of particles in a two-dimensional periodic potential subjected to frictional and time-periodic forces is analyzed in detail. The model represents diffusion of atoms adsorbed on metal surfaces under an applied ac electric field (surface electromigration) in the low-temperature limit. The second dimension and the potential energy coupling are shown to play an important role on both diffusion and net currents, depending on the direction of the drive. A properly chosen biharmonic field is able to control the directed ratchetlike dynamics of atoms on symmetric surfaces, since current reversals take place by different stabilization of attractors. Reversals identified with hysteresis loops between periodic running attractors are robust against an increase of the second harmonic amplitude, and against temperature effects inside the experimental range for measurements of surface diffusion.
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Affiliation(s)
- R Guantes
- Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano, 123, 28006 Madrid, Spain.
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23
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Weiss M, Hufnagel L, Ketzmerick R. Can simple renormalization theories describe the trapping of chaotic trajectories in mixed systems? PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046209. [PMID: 12786462 DOI: 10.1103/physreve.67.046209] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2002] [Indexed: 05/24/2023]
Abstract
We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of the standard map as an example for generic Hamiltonian systems with a mixed phase space. We demonstrate that even in ideal situations when the phase-space structure is dominated by a single scaling, the long-time dynamics is not dominated by this scaling. This has consequences for the power-law decay of correlations and Poincaré recurrences.
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Affiliation(s)
- M Weiss
- Max-Planck-Institut für Strömungsforschung and Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstrasse 10, 37073 Göttingen, Germany
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24
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Zolleis KR, Ford CJB, Kardynal B, Ritchie DA, Linfield EH, Rose PD, Jones GAC. Tunneling spectroscopy of a two-dimensionally periodic electron system. PHYSICAL REVIEW LETTERS 2002; 89:146803. [PMID: 12366065 DOI: 10.1103/physrevlett.89.146803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2001] [Indexed: 05/23/2023]
Abstract
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.
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Affiliation(s)
- K R Zolleis
- Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
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25
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Reichhardt C, Olson CJ, Hastings MB. Rectification and phase locking for particles on symmetric two-dimensional periodic substrates. PHYSICAL REVIEW LETTERS 2002; 89:024101. [PMID: 12096996 DOI: 10.1103/physrevlett.89.024101] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2001] [Indexed: 05/23/2023]
Abstract
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.
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Affiliation(s)
- C Reichhardt
- CNLS, Theoretical, and Applied Physics Divisions, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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26
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Chepelianskii AD, Shepelyansky DL. Dynamical turbulent flow on the Galton board with friction. PHYSICAL REVIEW LETTERS 2001; 87:034101. [PMID: 11461559 DOI: 10.1103/physrevlett.87.034101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2001] [Indexed: 05/23/2023]
Abstract
We study numerically and analytically the dynamics of charged particles on the Galton board, a regular lattice of disk scatters, in the presence of constant external force, magnetic field, and friction. It is shown that under certain conditions friction leads to the appearance of a strange chaotic attractor. In this regime the average velocity and direction of particle flow can be effectively affected by electric and magnetic fields. We discuss the applications of these results to the charge transport in antidot superlattices and the stream of suspended particles in a viscous flow through scatters.
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Affiliation(s)
- A D Chepelianskii
- Lycée Pierre de Fermat, Parvis des Jacobins, 31068 Toulouse Cedex 7, France
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27
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Rakhlin DA. Enhanced diffusion in smoothly modulated superlattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:011112. [PMID: 11304239 DOI: 10.1103/physreve.63.011112] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2000] [Indexed: 05/23/2023]
Abstract
We investigate a superdiffusive behavior found in a quasiclassical model of a square-planar superlattice subjected to a perpendicular magnetic field. It is shown that certain accelerated domains are responsible for long trapping of tracers and setting them into near-ballistic motion. The mechanism of entrapment appears to be two-staged and multifractal. Relatively short trapping occurs in the vicinity of homoclinic tangles, created by intersections of stable and unstable manifolds of a hyperbolic fixed point, connected to itself. A structure of the quasitrap reveals families of multipulse solutions, doubly asymptotic to slow manifolds. The existence of orbits of this type was proved [G. Haller and S. Wiggins, Arch. Rational Mech. Anal. 130, 25 (1995)] for integrable two-degree-of-freedom Hamiltonian systems with perturbation. We describe mixing dynamics in this region and examine characteristic escape time scales. More prolonged quasitrapping is due to sticking to resonant multilayered island chains that are found to accelerate ballistic transport. Phase-space dynamics is analyzed. We successfully employ a renewal process formalism to relate Poincare recurrences and coordinate variance asymptotics for both quasitraps and also justify the use of this formalism for the specific case of gradually increasing average velocity.
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Affiliation(s)
- D A Rakhlin
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
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28
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Iomin A. Quantum response for chaotic resonances. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:442-9. [PMID: 11088479 DOI: 10.1103/physreve.62.442] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/1999] [Indexed: 11/07/2022]
Abstract
Chaotic dynamics of conducting electrons in the presence of a high-frequency electromagnetic field and a constant homogeneous magnetic field is considered. It is shown that quantum fluctuations become important in this case on a time scale shorter than mean free time. Nonperturbative approach for calculation of a kinetic coefficient (conductivity) is developed. An analytical expression for the kinetic coefficient as a function of the magnetic field and a localization length is obtained. Dependence of the conductivity on the quantum localization length is studied.
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Affiliation(s)
- A Iomin
- Physics Department, Technion, Haifa 32000, Israel
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29
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Panoiu NC. Anomalous diffusion in two-dimensional potentials with hexagonal symmetry. CHAOS (WOODBURY, N.Y.) 2000; 10:166-179. [PMID: 12779372 DOI: 10.1063/1.166484] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.
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Affiliation(s)
- N.-C. Panoiu
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003Institute of Atomic Physics, Department of Theoretical Physics, P.O. Box MG-6, Bucharest, Romania
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Abstract
Organic molecules can alter inorganic microstructures, offering a very powerful tool for the design of novel materials. In biological systems, this tool is often used to create microstructures in which the organic manipulators are a minority component. Three groups of materials-biomaterials, ceramics, and semiconductors-have been selected to illustrate this concept as used by nature and by synthetic laboratories exploring its potential in materials technology. In some of nature's biomaterials, macromolecules such as proteins, glycoproteins, and polysaccharides are used to control nucleation and growth of mineral phases and thus manipulate microstructure and physical properties. This concept has been used synthetically to generate apatite-based materials that can function as artificial bone in humans. Synthetic polymers and surfactants can also drastically change the morphology of ceramic particles, impart new functional properties, and provide new processing methods for the formation of useful objects. Interesting opportunities also exist in creating semiconducting materials in which molecular manipulators connect quantum dots or template cavities, which change their electronic properties and functionality.
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Affiliation(s)
- S I Stupp
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
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32
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Kleber X, Gusev GM, Gennser U, Maude DK, Portal JC, Lubyshev DI, Basmaji P, Rossi JC, Nastaushev YV. Chaotic electron dynamics around a single elliptically shaped antidot. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13859-13867. [PMID: 9985302 DOI: 10.1103/physrevb.54.13859] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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33
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Ketzmerick R. Fractal conductance fluctuations in generic chaotic cavities. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10841-10844. [PMID: 9984881 DOI: 10.1103/physrevb.54.10841] [Citation(s) in RCA: 130] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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34
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Lu W. Theoretical study on commensurability oscillation in anisotropic antidot lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8049-8056. [PMID: 9984483 DOI: 10.1103/physrevb.54.8049] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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35
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Nakanishi T, Ando T. Quantum interference effects in antidot lattices in magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8021-8027. [PMID: 9984479 DOI: 10.1103/physrevb.54.8021] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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36
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Rotter P, Suhrke M, Rössler U. Observability of the magnetic band structure of lateral superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:4452-4455. [PMID: 9986394 DOI: 10.1103/physrevb.54.4452] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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Heremans J, Fuller BK, Thrush CM, Bayot V. Temperature dependence of the magnetoresistance of InxGa1-xAs antidot lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:2685-2690. [PMID: 9986118 DOI: 10.1103/physrevb.54.2685] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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38
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Uryu S, Ando T. Electronic states in antidot lattices: Scattering-matrix formalism. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:13613-13623. [PMID: 9983107 DOI: 10.1103/physrevb.53.13613] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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39
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Zozoulenko IV, Maao FA, Hauge EH. Coherent magnetotransport in confined arrays of antidots. I. Dispersion relations and current densities. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7975-7986. [PMID: 9982253 DOI: 10.1103/physrevb.53.7975] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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40
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Chakraborty T, Pietiläinen P. Electron correlations in antidot arrays in a magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:4664-4667. [PMID: 9984024 DOI: 10.1103/physrevb.53.4664] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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41
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Lei M, Zhu N, Guo H. Quantum Hall effect in the presence of an antidot potential. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:16784-16792. [PMID: 9981084 DOI: 10.1103/physrevb.52.16784] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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42
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Eckhardt B, Fishman S, Keating J, Agam O, Main J, Müller K. Approach to ergodicity in quantum wave functions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:5893-5903. [PMID: 9964105 DOI: 10.1103/physreve.52.5893] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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43
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Neto MA, Schulz PA. Hofstadter spectra in two-dimensional superlattice potentials with arbitrary modulation strength. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14093-14097. [PMID: 9980627 DOI: 10.1103/physrevb.52.14093] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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44
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Schuster R, Ensslin K, Dolgopolov V, Kotthaus JP, Böhm G, Klein W. Edge-state transport in finite antidot lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14699-14703. [PMID: 9980806 DOI: 10.1103/physrevb.52.14699] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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45
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Vasiliadou E, Fleischmann R, Weiss D, Heitmann D, Klitzing KV, Geisel T, Bergmann R, Schweizer H, Foxon CT. Cyclotron-resonance anomalies in an antidot array measured by microwave photoconductivity. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:R8658-R8661. [PMID: 9979919 DOI: 10.1103/physrevb.52.r8658] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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46
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Tsukagoshi K, Wakayama S, Oto K, Takaoka S, Murase K, Gamo K. Magnetotransport through disordered and anisotropic antidot lattices in GaAs/AlxGa1-xAs heterostructures. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:8344-8347. [PMID: 9979836 DOI: 10.1103/physrevb.52.8344] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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47
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Bollweg K, Kurth T, Heitmann D, Vasiliadou E, Eberl K, Brugger H. Circular polarization of far-infrared modes in antidot arrays. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:8379-8383. [PMID: 9979841 DOI: 10.1103/physrevb.52.8379] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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48
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Fromhold TM, Wilkinson PB, Sheard FW, Eaves L, Miao J, Edwards G. Manifestations of classical chaos in the energy level spectrum of a quantum well. PHYSICAL REVIEW LETTERS 1995; 75:1142-1145. [PMID: 10060216 DOI: 10.1103/physrevlett.75.1142] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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49
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Ishizaka S, Nihey F, Nakamura K, Sone J, Ando T. Quantum transport in antidot arrays in magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:9881-9890. [PMID: 9977661 DOI: 10.1103/physrevb.51.9881] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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50
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Zozulenko IV, Maao FA, Hauge EH. Quantum magnetotransport in a mesoscopic antidot lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:7058-7063. [PMID: 9977264 DOI: 10.1103/physrevb.51.7058] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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