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Yesilyurt C, Siu ZB, Tan SG, Liang G, Yang SA, Jalil MBA. Electrically tunable valley polarization in Weyl semimetals with tilted energy dispersion. Sci Rep 2019; 9:4480. [PMID: 30872691 PMCID: PMC6418200 DOI: 10.1038/s41598-019-40947-2] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Accepted: 02/18/2019] [Indexed: 11/16/2022] Open
Abstract
Tunneling transport across electrical potential barriers in Weyl semimetals with tilted energy dispersion is investigated. We report that the electrons around different valleys experience opposite direction refractions at the barrier interface when the energy dispersion is tilted along one of the transverse directions. Chirality dependent refractions at the barrier interface polarize the Weyl fermions in angle-space according to their valley index. A real magnetic barrier configuration is used to select allowed transmission angles, which results in electrically controllable and switchable valley polarization. Our findings may pave the way for experimental investigation of valley polarization, as well as valleytronic and electron optic applications in Weyl semimetals.
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Affiliation(s)
- Can Yesilyurt
- Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Republic of Singapore.
| | - Zhuo Bin Siu
- Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Republic of Singapore
| | - Seng Ghee Tan
- Department of Optoelectric Physics, Chinese Culture University, Taipei, 11114, Taiwan
| | - Gengchiau Liang
- Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Republic of Singapore
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, 487372, Singapore
| | - Mansoor B A Jalil
- Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Republic of Singapore.
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2
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Liu Y, Rodrigues JNB, Luo YZ, Li L, Carvalho A, Yang M, Laksono E, Lu J, Bao Y, Xu H, Tan SJR, Qiu Z, Sow CH, Feng YP, Neto AHC, Adam S, Lu J, Loh KP. Tailoring sample-wide pseudo-magnetic fields on a graphene-black phosphorus heterostructure. NATURE NANOTECHNOLOGY 2018; 13:828-834. [PMID: 29941889 DOI: 10.1038/s41565-018-0178-z] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Accepted: 05/23/2018] [Indexed: 05/22/2023]
Abstract
Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of developing a valley filter.
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Affiliation(s)
- Yanpeng Liu
- Department of Chemistry, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
| | - J N B Rodrigues
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Yong Zheng Luo
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Linjun Li
- Department of Chemistry, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
| | - Alexandra Carvalho
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Ming Yang
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
- Institute of Materials Research and Engineering, Agency for Science, Technology and Research, Singapore, Singapore
| | - Evan Laksono
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Junpeng Lu
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Yang Bao
- Department of Chemistry, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
| | - Hai Xu
- Department of Chemistry, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
| | - Sherman J R Tan
- NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore, Singapore
| | - Zhizhan Qiu
- NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore, Singapore
| | - Chorng Haur Sow
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Yuan Ping Feng
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - A H Castro Neto
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Shaffique Adam
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore.
- Department of Physics, National University of Singapore, Singapore, Singapore.
- Yale-NUS College, Singapore, Singapore.
| | - Jiong Lu
- Department of Chemistry, National University of Singapore, Singapore, Singapore.
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore.
| | - Kian Ping Loh
- Department of Chemistry, National University of Singapore, Singapore, Singapore.
- Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore.
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3
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Yesilyurt C, Tan SG, Liang G, Jalil MBA. Klein tunneling in Weyl semimetals under the influence of magnetic field. Sci Rep 2016; 6:38862. [PMID: 27941894 PMCID: PMC5150982 DOI: 10.1038/srep38862] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Accepted: 11/15/2016] [Indexed: 11/09/2022] Open
Abstract
Klein tunneling refers to the absence of normal backscattering of electrons even under the case of high potential barriers. At the barrier interface, the perfect matching of electron and hole wavefunctions enables a unit transmission probability for normally incident electrons. It is theoretically and experimentally well understood in two-dimensional relativistic materials such as graphene. Here we investigate the Klein tunneling effect in Weyl semimetals under the influence of magnetic field induced by ferromagnetic stripes placed at barrier boundaries. Our results show that the resonance of Fermi wave vector at specific barrier lengths gives rise to perfect transmission rings, i.e., three-dimensional analogue of the so-called magic transmission angles in two-dimensional Dirac semimetals. Besides, the transmission profile can be shifted by application of magnetic field in the central region, a property which may be utilized in electro-optic applications. When the applied potential is close to the Fermi level, a particular incident vector can be selected by tuning the magnetic field, thus enabling highly selective transmission of electrons in the bulk of Weyl semimetals. Our analytical and numerical calculations obtained by considering Dirac electrons in three regions and using experimentally feasible parameters can pave the way for relativistic tunneling applications in Weyl semimetals.
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Affiliation(s)
- Can Yesilyurt
- Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
| | - Seng Ghee Tan
- Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
- Data Storage Institute, Agency of Science, Technology and Research (A* Star), Singapore 138634, Republic of Singapore
| | - Gengchiau Liang
- Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
| | - Mansoor B. A. Jalil
- Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Republic of Singapore
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Lee M, Wallbank JR, Gallagher P, Watanabe K, Taniguchi T, Fal’ko VI, Goldhaber-Gordon D. Ballistic miniband conduction in a graphene superlattice. Science 2016; 353:1526-1529. [DOI: 10.1126/science.aaf1095] [Citation(s) in RCA: 94] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Accepted: 08/26/2016] [Indexed: 01/23/2023]
Affiliation(s)
- Menyoung Lee
- Department of Physics and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - John R. Wallbank
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
| | - Patrick Gallagher
- Department of Physics and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
| | - 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
| | - Vladimir I. Fal’ko
- National Graphene Institute, University of Manchester, Manchester M13 9PL, UK
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
| | - David Goldhaber-Gordon
- Department of Physics and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
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6
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Lin YP, Lin CY, Ho YH, Do TN, Lin MF. Magneto-optical properties of ABC-stacked trilayer graphene. Phys Chem Chem Phys 2015; 17:15921-7. [PMID: 26020611 DOI: 10.1039/c5cp02496j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene.
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Affiliation(s)
- Yi-Ping Lin
- Department of Physics
- National Cheng Kung University
- 701 Tainan
- Taiwan
| | - Chiun-Yan Lin
- Department of Physics
- National Cheng Kung University
- 701 Tainan
- Taiwan
| | - Yen-Hung Ho
- National Tsing Hua University
- 300 Hsinchu
- Taiwan
| | - Thi-Nga Do
- Department of Physics
- National Cheng Kung University
- 701 Tainan
- Taiwan
| | - Ming-Fa Lin
- Department of Physics
- National Cheng Kung University
- 701 Tainan
- Taiwan
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7
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Lu MW, Wang ZY, Chen SY, Zhang GL. Voltage-controllable spin beam splitter based on realistic magnetic-barrier nanostructure. Micron 2012. [PMID: 23182680 DOI: 10.1016/j.micron.2012.10.007] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
We report a theoretical investigation on the Goos-Hänchen (GH) effect of spin electron beams in realistic magnetic-barrier (MB) nanostructures under an applied voltage, which can be experimentally created by lithographic patterning of ferromagnetic (FM) or superconducting films. GH shifts of spin electron beams are calculated numerically for the InAs material system, with the help of the stationary phase method. It is shown that a significant spin polarization effect can be induced by such MB nanostructures with symmetric magnetic field profiles. It also is shown that both magnitude and sign of the spin polarization is closely relative to the electric barrier (EB) produced by a constant voltage applied to the metallic FM stripe of system. These interesting properties may provide an alternative way to spin injection into the semiconductor, and such nanostructures can serve as voltage-tunable spin beam splitters.
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Affiliation(s)
- Mao-Wang Lu
- College of Science, Guilin University of Technology, Guilin 541004, People's Republic of China.
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Firoz Islam SK, Ghosh TK. Magnetotransport properties of a magnetically modulated two-dimensional electron gas with the spin-orbit interaction. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:185303. [PMID: 22481295 DOI: 10.1088/0953-8984/24/18/185303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study the electrical transport properties of a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction in the presence of a constant perpendicular magnetic field (B(0)( ̂z) which is weakly modulated by B1 = B1 cos(qx) ̂z, where B(1) ≪ B(0) and q = 2π/a with a the modulation period. We obtain the analytical expressions of the diffusive conductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and produce beating patterns in the amplitude of the Weiss and Shubnikov-de Haas oscillations. We show that the Rashba strength can be determined by analyzing the beating pattern in the Weiss oscillation. We find a simple equation which determines the Rashba spin-orbit interaction strength if the number of Weiss oscillations between any two successive nodes is known from the experiment. We compare our results with the electrically modulated 2DEG with the Rashba interaction. For completeness, we also study the beating pattern formation in the collisional and the Hall conductivities.
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Affiliation(s)
- S K Firoz Islam
- Department of Physics, Indian Institute of Technology-Kanpur, Kanpur-208 016, India.
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9
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Firoz Islam SK, Singh NK, Ghosh TK. Thermodynamic properties of a magnetically modulated graphene monolayer. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:445502. [PMID: 22004991 DOI: 10.1088/0953-8984/23/44/445502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in the presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their bandwidth oscillates with magnetic field, leading to Weiss-type oscillations in the thermodynamic properties. The effect of magnetic modulation on the thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen oscillations at low and high magnetic fields, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene compared to electrically modulated graphene. On the other hand, the phase remains the same and the amplitude of the oscillation is large when compared with the magnetically modulated two-dimensional electron gas (2DEG). Explicit asymptotic expressions of the density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.
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Affiliation(s)
- S K Firoz Islam
- Department of Physics, Indian Institute of Technology-Kanpur, Kanpur 208 016, India
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10
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Milpas E, Torres M, Murguía G. Magnetic field barriers in graphene: an analytically solvable model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:245304. [PMID: 21628785 DOI: 10.1088/0953-8984/23/24/245304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with a hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum mechanics, and leads to an exactly solvable model. We study in detail the bound-state spectrum. For a narrow barrier the spectrum is characterized by a few bands, except for the zero energy level that remains degenerated. As the width of the barrier increases we can track the band's evolution into the degenerated Landau levels. In the scattering regime a simple analytical formula is obtained for the transmission coefficient, this result allows us to identify the resonant conditions at which the barrier becomes transparent.
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Affiliation(s)
- Enrique Milpas
- Instituto de Física, Universidad Nacional Autónoma de México, México Distrito Federal, Mexico
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11
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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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12
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Tarasov A, Hugger S, Xu H, Cerchez M, Heinzel T, Zozoulenko IV, Gasser-Szerer U, Reuter D, Wieck AD. Quantized magnetic confinement in quantum wires. PHYSICAL REVIEW LETTERS 2010; 104:186801. [PMID: 20482195 DOI: 10.1103/physrevlett.104.186801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2009] [Indexed: 05/29/2023]
Abstract
Ballistic quantum wires are exposed to longitudinal profiles of perpendicular magnetic fields composed of a spike and a homogeneous part. An asymmetric magnetoconductance peak as a function of the homogeneous magnetic field is found, comprising quantized conductance steps in the interval where the homogeneous magnetic field and the magnetic barrier have identical polarities, and a characteristic shoulder with several resonances in the interval of opposite polarities. The observations are interpreted in terms of inhomogeneous diamagnetic shifts of the quantum wire modes leading to magnetic confinement.
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Affiliation(s)
- A Tarasov
- Condensed Matter Physics Laboratory, Heinrich-Heine-Universität, Universitätsstrasse 1, 40225 Düsseldorf, Germany
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13
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Tahir M, Sabeeh K, MacKinnon A. The magnetoplasmon spectrum of a weakly modulated two-dimensional electron gas system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:015801. [PMID: 21386234 DOI: 10.1088/0953-8984/22/1/015801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The magnetoplasmon spectrum of a magnetically modulated two-dimensional electron gas (2DEG) is investigated. We derive the inter- and intra-Landau-band magnetoplasmon spectrum within the self-consistent field approach. The derivation is performed at zero temperature as well as at finite temperature. Results are presented for the inter- and intra-Landau-band magnetoplasmon spectrum as a function of the inverse magnetic field. Magnetic Weiss oscillations are found to occur in the magnetoplasmon spectrum as a result of magnetic modulation. Furthermore, our finite temperature theory facilitates the analysis of effects of temperature on the magnetoplasmon spectrum. The results are compared with those obtained for an electrically modulated 2DEG system. In addition, we derive and discuss the effects of simultaneous electric and magnetic modulations on the magnetoplasmon spectrum of the 2DEG when the modulations are in phase as well as when they are out of phase. Magnetic oscillations are affected by the relative phase of the two modulations and the position of the oscillations depends on the relative strength of the two modulations in the former case while we find complete suppression of Weiss oscillations for a particular relative strength of the modulations in the latter case.
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Affiliation(s)
- M Tahir
- Department of Physics, Blackett Laboratory, Imperial College London, South Kensington Campus, London, UK.
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14
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Nogaret A, Portal JC, Beere HE, Ritchie DA, Phillips C. Quantum interference of magnetic edge channels activated by intersubband optical transitions in magnetically confined quantum wires. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:025303. [PMID: 21813973 DOI: 10.1088/0953-8984/21/2/025303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We investigate the photoresistance of a magnetically confined quantum wire in which microwave-coupled edge channels interfere at two pinning sites in the fashion of a Mach-Zehnder interferometer. The conductance is strongly enhanced by microwave power at B = 0 and develops a complex series of oscillations when the magnetic confinement increases. Both results are quantitatively explained by the activation of forward scattering in a multimode magnetically confined quantum wire. By varying the strength of the magnetic confinement we are able to tune the phase of electrons in the arms of the interferometer. Quantum interferences which develop between pinning sites explain the oscillations of the conductance as a function of the magnetic field. A fit of the data gives the distance between pinning sites as 11 µm. This result suggests that quantum coherence is conserved over a distance three times longer than the electron mean free path.
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Affiliation(s)
- A Nogaret
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
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15
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Soskin SM, Mannella R, Yevtushenko OM. Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036221. [PMID: 18517499 DOI: 10.1103/physreve.77.036221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2006] [Revised: 10/10/2007] [Indexed: 05/26/2023]
Abstract
We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.
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Affiliation(s)
- S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
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16
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Ho JH, Lai YH, Chiu YH, Lin MF. Modulation effects on Landau levels in a monolayer graphene. NANOTECHNOLOGY 2008; 19:035712. [PMID: 21817597 DOI: 10.1088/0957-4484/19/03/035712] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Magnetoelectronic properties of a single-layer graphene are studied by the Peierls tight-binding model. A new numerical technique is developed to obtain a band-like Hamiltonian matrix. A spatially modulated magnetic field B' could drastically alter the Landau levels due to a uniform magnetic field B. The modulation effects include enhancement in dimensionality, change of energy dispersions, destruction of state degeneracy and creation of band-edge states. The dispersionless Landau levels, those at the Fermi levels excepted, become the 1D parabolic bands. The density of states thus exhibits many pairs of asymmetric prominent peaks. The height, frequency and number of pronounced peaks strongly depend on the modulation strength. These characteristics are hardly affected by the period and direction when B' is much weaker than B. The predicted results could be verified by experimental measurements on magneto-optical absorption spectra.
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Affiliation(s)
- J H Ho
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
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17
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De Martino A, Dell'Anna L, Egger R. Magnetic confinement of massless Dirac fermions in graphene. PHYSICAL REVIEW LETTERS 2007; 98:066802. [PMID: 17358966 DOI: 10.1103/physrevlett.98.066802] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2006] [Indexed: 05/14/2023]
Abstract
Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.
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Affiliation(s)
- A De Martino
- Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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18
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Soskin SM, Yevtushenko OM, Mannella R. Drastic facilitation of the onset of global chaos. PHYSICAL REVIEW LETTERS 2003; 90:174101. [PMID: 12786071 DOI: 10.1103/physrevlett.90.174101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2002] [Indexed: 05/24/2023]
Abstract
We show that the onset of global chaos in a time periodically perturbed Hamiltonian system may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. We develop the asymptotic theory and verify it in simulations.
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Affiliation(s)
- S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev
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Sim HS, Ihm G, Kim N, Chang KJ. Magnetic quantum dot: a magnetic transmission barrier and resonator. PHYSICAL REVIEW LETTERS 2001; 87:146601. [PMID: 11580664 DOI: 10.1103/physrevlett.87.146601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2001] [Indexed: 05/23/2023]
Abstract
We study the ballistic edge-channel transport in quantum wires with a magnetic quantum dot, which is formed by two different magnetic fields B(*) and B0 inside and outside the dot, respectively. We find that the electron states located near the dot and the scattering of edge channels by the dot strongly depend on whether B(*) is parallel or antiparallel to B0. For parallel fields, two-terminal conductance as a function of channel energy is quantized except for resonances, while, for antiparallel fields, it is not quantized and all channels can be completely reflected in some energy ranges. All these features are attributed to the characteristic magnetic confinements caused by nonuniform fields.
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Affiliation(s)
- H S Sim
- Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
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Nogaret A, Bending SJ, Henini M. Resistance resonance effects through magnetic edge states. PHYSICAL REVIEW LETTERS 2000; 84:2231-2234. [PMID: 11017251 DOI: 10.1103/physrevlett.84.2231] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/1999] [Indexed: 05/23/2023]
Abstract
We report on the magnetoresistance of a two-dimensional electron gas subjected to an abrupt magnetic field gradient arising from a ferromagnetic stripe fabricated at its surface. A sharp resistance resonance effect is observed at B(p) due to the formation of two types of magnetic edge states that drift in opposite directions perpendicular to the magnetic field gradient for B<B(p) and B>B(p). A semiclassical drift-diffusion model gives a good description of the effects of the magnetic confinement on both the diagonal and off-diagonal components of the resistivity tensor.
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Affiliation(s)
- A Nogaret
- Department of Physics, University of Bath, Bath BA2 7AY, UK
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Majumdar A. Effects of intrinsic spin on electronic transport through magnetic barriers. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:11911-11913. [PMID: 9985028 DOI: 10.1103/physrevb.54.11911] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ji ZL, Sprung DW. Electronic transport in quantum wires in nonuniform magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8044-8048. [PMID: 9984482 DOI: 10.1103/physrevb.54.8044] [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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Kim CS, Olendski O. Landau levels and persistent currents in nonuniform magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:12917-12928. [PMID: 9982966 DOI: 10.1103/physrevb.53.12917] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gusev GM, Gennser U, Kleber X, Maude DK, Portal JC, Lubyshev DI, Basmaji P, Silva M, Rossi JC, Nastaushev YV. Quantum interference effects in a strongly fluctuating magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:13641-13644. [PMID: 9983110 DOI: 10.1103/physrevb.53.13641] [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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Gerhardts RR. Quasiclassical calculation of magnetoresistance oscillations of a two-dimensional electron gas in spatially periodic magnetic and electrostatic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:11064-11075. [PMID: 9982679 DOI: 10.1103/physrevb.53.11064] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gerhardts RR, Pfannkuche D, Gudmundsson V. Hofstadter-type energy spectra in lateral superlattices defined by periodic magnetic and electrostatic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:9591-9594. [PMID: 9982508 DOI: 10.1103/physrevb.53.9591] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Krakovsky A. Electronic band structure in a periodic magnetic field. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:8469-8472. [PMID: 9982350 DOI: 10.1103/physrevb.53.8469] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Brown D, Band YB, Avishai Y. Magnetoresistance of two-dimensional mesoscopic structures: A variational approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:4855-4869. [PMID: 9984048 DOI: 10.1103/physrevb.53.4855] [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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Ibrahim IS, Peeters FM. Two-dimensional electrons in lateral magnetic superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:17321-17334. [PMID: 9981162 DOI: 10.1103/physrevb.52.17321] [Citation(s) in RCA: 53] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Foden CL, Leadbeater ML, Pepper M. Quantum magnetic confinement and transport in spherical two-dimensional electron gases. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:R8646-R8649. [PMID: 9979916 DOI: 10.1103/physrevb.52.r8646] [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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Leadbeater ML, Foden CL, Burroughes JH, Pepper M, Burke TM, Wang LL, Grimshaw MP, Ritchie DA. Magnetotransport in a nonplanar two-dimensional electron gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:R8629-R8632. [PMID: 9979911 DOI: 10.1103/physrevb.52.r8629] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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