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Lin CY, Weng DW, Chiu CW, Gumbs G. Unique electronic and optical properties of stacking-modulated bilayer graphene under external magnetic fields. Phys Chem Chem Phys 2024; 26:19316-19331. [PMID: 38963725 DOI: 10.1039/d4cp01576b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/06/2024]
Abstract
This study delves into the magneto-electronic and magneto-optical properties of stacking-modulated bilayer graphene. By manipulating domain walls (DWs) across AB-BA domains periodically, we unveil oscillatory Landau subbands and the associated optical excitations. The DWs act as periodic potentials, yielding fascinating 1D spectral features. Our exploration reveals 1D phenomena localized to Bernal stacking, DW regions, and stacking boundaries, highlighting the intriguing formation of Landau state quantization influenced by the commensuration between the magnetic length and the system. The stable quantized localization within different regions leads to the emergence of unconventional quantized subbands. This study provides valuable insights into the essential properties of stacking-modulated bilayer graphene.
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Affiliation(s)
- Chiun-Yan Lin
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Da-We Weng
- Department of Physics, National Kaohsiung Normal University, Kaohsiung 82446, Taiwan
| | - Chih-Wei Chiu
- Department of Physics, National Kaohsiung Normal University, Kaohsiung 82446, Taiwan
| | - Godfrey Gumbs
- Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, NY 10065, USA.
- The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York, NY 10016, USA
- Donostia International Physics Center (DIPC), P de Manuel Lardizabal, 4, 20018 San Sebastian, Basque Country, Spain
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2
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Liu HY, Lin SY, Wu JY. Stacking-configuration-enriched essential properties of bilayer graphenes and silicenes. J Chem Phys 2020; 153:154707. [PMID: 33092355 DOI: 10.1063/5.0024421] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
First-principles calculations show that the geometric and electronic properties of silicene-related systems have diversified phenomena. Critical factors of group-IV monoelements, like buckled/planar structures, stacking configurations, layer numbers, and van der Waals interactions of bilayer composites, are considered simultaneously. The theoretical framework developed provides a concise physical and chemical picture. Delicate evaluations and analyses have been made on the optimal lattices, energy bands, and orbital-projected van Hove singularities. They provide decisive mechanisms, such as buckled/planar honeycomb lattices, multi-/single-orbital hybridizations, and significant/negligible spin-orbital couplings. We investigate the stacking-configuration-induced dramatic transformations of essential properties by relative shift in bilayer graphenes and silicenes. The lattice constant, interlayer distance, buckling height, and total energy essentially depend on the magnitude and direction of the relative shift: AA → AB → AA' → AA. Apparently, sliding bilayer systems are quite different between silicene and graphene in terms of geometric structures, electronic properties, orbital hybridizations, interlayer hopping integrals, and spin interactions.
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Affiliation(s)
- Hsin-Yi Liu
- Department of Physics/QTC/Hi-GEM, National Cheng Kung University, Tainan, Taiwan
| | - Shih-Yang Lin
- Department of Physics, National Chung Cheng University, Chiayi, Taiwan
| | - Jhao-Ying Wu
- Center of General Studies, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan
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3
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Wu JY, Chen SC, Do TN, Su WP, Gumbs G, Lin MF. The diverse magneto-optical selection rules in bilayer black phosphorus. Sci Rep 2018; 8:13303. [PMID: 30185872 PMCID: PMC6125359 DOI: 10.1038/s41598-018-31358-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Accepted: 08/13/2018] [Indexed: 11/30/2022] Open
Abstract
The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A uniform perpendicular electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and unique magnetoabsorption spectra arise from the very close relations among the geometric structures, multiple intralayer and interlayer hopping integrals and composite external fields.
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Affiliation(s)
- Jhao-Ying Wu
- Center of General Studies, National Kaohsiung Marine University, Kaohsiung, 811, Taiwan.
| | - Szu-Chao Chen
- Department of Physics, National Cheng Kung University, Tainan, 701, Taiwan
| | - Thi-Nga Do
- Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan
| | - Wu-Pei Su
- Department of Physics, University of Houston, Houston, Texas, USA
| | - Godfrey Gumbs
- Department of Physics and Astronomy, Hunter College at the City University of New York, New York, 10065, USA.
- Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal 4, 20018, San Sebastían Donostia, Spain.
| | - Ming-Fa Lin
- Hierarchical Green-Energy Materials/quantum topology centers, Tainan, 701, Taiwan
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Do TN, Chang CP, Shih PH, Wu JY, Lin MF. Stacking-enriched magneto-transport properties of few-layer graphenes. Phys Chem Chem Phys 2017; 19:29525-29533. [DOI: 10.1039/c7cp05614a] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The quantum Hall effects in sliding bilayer graphene and a AAB-stacked trilayer system are investigated using the Kubo formula and the generalized tight-binding model.
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Affiliation(s)
- Thi-Nga Do
- Department of Physics, National Cheng Kung University
- Tainan
- Taiwan
| | - Cheng-Peng Chang
- Center for General Education, Tainan University of Technology, Tainan
- Taiwan
| | - Po-Hsin Shih
- Department of Physics, National Cheng Kung University
- Tainan
- Taiwan
| | - Jhao-Ying Wu
- Center of General Studies, National Kaohsiung Marine University, Kaohsiung
- Taiwan
| | - Ming-Fa Lin
- Department of Physics, National Cheng Kung University
- Tainan
- Taiwan
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5
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Chung HC, Chang CP, Lin CY, Lin MF. Electronic and optical properties of graphene nanoribbons in external fields. Phys Chem Chem Phys 2016; 18:7573-616. [PMID: 26744847 DOI: 10.1039/c5cp06533j] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.
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Affiliation(s)
- Hsien-Ching Chung
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan. and Center for Micro/Nano Science and Technology (CMNST), National Cheng Kung University, Tainan 70101, Taiwan
| | - Cheng-Peng Chang
- Center for General Education, Tainan University of Technology, Tainan 701, Taiwan
| | - Chiun-Yan Lin
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan.
| | - Ming-Fa Lin
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan.
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Do TN, Shih PH, Chang CP, Lin CY, Lin MF. Rich magneto-absorption spectra of AAB-stacked trilayer graphene. Phys Chem Chem Phys 2016; 18:17597-605. [PMID: 27305856 DOI: 10.1039/c6cp02275h] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.
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Affiliation(s)
- Thi-Nga Do
- Department of Physics, National Cheng Kung University, Tainan, Taiwan.
| | - Po-Hsin Shih
- Department of Physics, National Cheng Kung University, Tainan, Taiwan.
| | - Cheng-Peng Chang
- Center for General Education, Tainan University of Technology, Tainan, Taiwan
| | - Chiun-Yan Lin
- Department of Physics, National Cheng Kung University, Tainan, Taiwan.
| | - Ming-Fa Lin
- Department of Physics, National Cheng Kung University, Tainan, Taiwan.
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Lin CY, Wu JY, Ou YJ, Chiu YH, Lin MF. Magneto-electronic properties of multilayer graphenes. Phys Chem Chem Phys 2015; 17:26008-35. [PMID: 26388455 DOI: 10.1039/c5cp05013h] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.
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Affiliation(s)
- Chiun-Yan Lin
- Department of Physics, National Cheng Kung University, Taiwan.
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Wu JY, Lin CY, Gumbs G, Lin MF. The effect of perpendicular electric field on temperature-induced plasmon excitations for intrinsic silicene. RSC Adv 2015. [DOI: 10.1039/c5ra07721d] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
We use the tight-binding model and the random-phase approximation to investigate the intrinsic plasmon in silicene.
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Affiliation(s)
- Jhao-Ying Wu
- Department of Physics
- National Cheng Kung University
- Tainan
- Taiwan 701
| | - Chiun-Yan Lin
- Department of Physics
- National Cheng Kung University
- Tainan
- Taiwan 701
| | - Godfrey Gumbs
- Department of Physics and Astronomy
- Hunter College at the City University of New York
- New York 10065
- USA
| | - Ming-Fa Lin
- Department of Physics
- National Cheng Kung University
- Tainan
- Taiwan 701
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9
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Abstract
Hofstadter butterfly of molybdenum disulfide monolayer resulting from multiple hoppings between 4d orbitals and intrinsic spin–orbit coupling.
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Affiliation(s)
- Yen-Hung Ho
- Department of Physics
- National Tsing Hua University
- Hsinchu 300
- Taiwan
- Department of Physics and Texas Center for Superconductivity
| | - Wu-Pei Su
- Department of Physics and Texas Center for Superconductivity
- University of Houston
- Houston
- USA
| | - Ming-Fa Lin
- Department of Physics
- National Cheng Kung University
- Tainan 701
- Taiwan
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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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Huang YK, Chen SC, Ho YH, Lin CY, Lin MF. Feature-rich magnetic quantization in sliding bilayer graphenes. Sci Rep 2014; 4:7509. [PMID: 25515085 PMCID: PMC4268647 DOI: 10.1038/srep07509] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2014] [Accepted: 11/14/2014] [Indexed: 01/09/2023] Open
Abstract
The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.
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Affiliation(s)
- Yao-Kung Huang
- Department of Physics, National Cheng Kung University, Taiwan
| | - Szu-Chao Chen
- Department of Physics, National Cheng Kung University, Taiwan
| | - Yen-Hung Ho
- Department of Physics and Texas Center for Superconductivity, University of Houston, Texas, U.S.A
| | - Chiun-Yan Lin
- Department of Physics, National Cheng Kung University, Taiwan
| | - Ming-Fa Lin
- 1] Department of Physics, National Cheng Kung University, Taiwan [2] National Center for Theoretical Sciences (south), Taiwan
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Liu Y, Yang H, Liao N, Yang P. Investigation on thermal conductivity of bilayer graphene nanoribbons. RSC Adv 2014. [DOI: 10.1039/c4ra07339h] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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13
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Ou YC, Chiu YH, Yang PH, Lin MF. The selection rule of graphene in a composite magnetic field. OPTICS EXPRESS 2014; 22:7473-7491. [PMID: 24718122 DOI: 10.1364/oe.22.007473] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the modulated one accounts for a strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules that are subsequently induced can be explained. When the modulated field increases, each symmetric peak, under a uniform magnetic field, splits into a pair of asymmetric peaks with lower intensities. The threshold absorption frequency exhibits an obvious evolution in terms of a redshift. These absorption peaks obey the same selection rule that is followed by Landau level transitions. Moreover, at a sufficiently strong modulation strength, the extra peaks in the absorption spectrum might arise from different selection rules.
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Chang CP. An analytical approach for the energy spectrum and optical properties of gated bilayer graphene. RSC Adv 2014. [DOI: 10.1039/c4ra03430a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
An analytical approach is developed to access the exact energy spectrum, wave functions, dipole matrix element (Mfi) and absorption spectra (A(ω)) of gated Bernal bilayer graphene.
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Affiliation(s)
- Cheng-Peng Chang
- Center for General Education
- Tainan University of Technology
- 710 Tainan, Taiwan
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Li TS, Lin MF, Chang SC, Chung HC. Optical excitations in carbon nanoscrolls. Phys Chem Chem Phys 2011; 13:6138-44. [PMID: 21350758 DOI: 10.1039/c0cp02097d] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
The optical properties of carbon nanoscrolls in the presence of uniform electric fields are investigated by using gradient approximation. Absorption spectra exhibit rich prominent peaks structures, which is caused by one-dimensional sub-bands. The numbers, spectral intensities, and energies of the absorption peaks are strongly dependent on the geometry and the electric field strength. There exists an optical selection rule originating from the two equivalent sublattices in graphene. The two-fold degeneracy of the absorption peaks can be lifted by the inter-wall interactions or the electric field. The variations of the absorption peak energies with the geometry and field strength are also explored. These theoretical predictions can be validated by optical absorption measurements.
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Affiliation(s)
- To Sing Li
- Department of Electrical Engineering, Kun Shan University, Tainan, Taiwan, Republic of China.
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Wu JY, Chen SC, Roslyak O, Gumbs G, Lin MF. Plasma excitations in graphene: their spectral intensity and temperature dependence in magnetic field. ACS NANO 2011; 5:1026-1032. [PMID: 21204567 DOI: 10.1021/nn1024847] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this paper, we calculated the dielectric function, the loss function, the magnetoplasmon dispersion relation and the temperature-induced transitions for graphene in a uniform perpendicular magnetic field B. The calculations were performed using the Peierls tight-binding model to obtain the energy band structure and the random-phase approximation to determine the collective plasma excitation spectrum. The single-particle and collective excitations have been precisely identified based on the resonant peaks in the loss function. The critical wave vector at which plasmon damping takes place is clearly established. This critical wave vector depends on the magnetic field strength as well as the levels between which the transition takes place. The temperature effects were also investigated. At finite temperature, there are plasma resonances induced by the Fermi distribution function. Whether such plasmons exist is mainly determined by the field strength, temperature, and momentum. The inelastic light scattering spectroscopies could be used to verify the magnetic field and temperature induced plasmons.
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Affiliation(s)
- Jhao-Ying Wu
- Department of Physics, National Cheng Kung University, Tainan, Taiwan 701
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Chiu CW, Huang YC, Chen SC, Lin MF, Shyu FL. Low-frequency electronic and optical properties of rhombohedral graphite. Phys Chem Chem Phys 2011; 13:6036-42. [PMID: 21336387 DOI: 10.1039/c0cp01830a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Affiliation(s)
- Chih-Wei Chiu
- Department of Physics, National Cheng Kung University, Tainan, Taiwan
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