Theory of coherent phonons in carbon nanotubes and graphene nanoribbons

Journal of Physics Condensed Matter

Volumn 25, Issue 14, 2013, Pages

  Sanders, G D ^a   Nugraha, A R T ^b   Sato, K ^b   Kim, J H ^c,d   Kono, J ^c,d,e   Saito, R ^b   Stanton, C J ^a  

^a University of Florida   (United States)

^b TOHOKU UNIVERSITY   (Japan)

^c Rice University   (United States)

^d RICE UNIVERSITY   (United States)

^e RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EFFECTIVE-MASS THEORY; EXPERIMENTAL OBSERVATION; EXTENDED TIGHT BINDINGS; OPTICAL MATRIX ELEMENT; OSCILLATOR EQUATIONS; PHOTOEXCITED CARRIERS; RADIAL BREATHING MODE; VALENCE FORCE FIELDS;

CHIRALITY; ELECTRON-PHONON INTERACTIONS; ELECTRONIC STRUCTURE; GRAPHENE; NANORIBBONS; SINGLE-WALLED CARBON NANOTUBES (SWCN);

NANOSTRUCTURES;

EID: 84875173172     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/25/14/144201     Document Type: Review

References (131)

1. Aldersey-Williams H 1995 The Most Beautiful Molecule: The Discovery of the Buckyball (New York: Wiley)
2. Prato M 1997 [60] Fullerene chemistry for materials science applications J. Mater. Chem. 7 1097-109 (Pubitemid 127731260)
3. Fowler P W and Manolopoulos D E 1995 An Atlas of Fullerenes (Oxford: Oxford University Press)
4. Neto A H C, Guinea F, Peres N, Novoselov K and Geim A 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109-62
5. Novoselov K 2011 Nobel lecture: graphene: materials in the flatland Rev. Mod. Phys. 83 837
6. Geim A K 2011 Nobel lecture: random walk to graphene Rev. Mod. Phys. 83 851
7. Charlier J C, Blase X and Roche S 2007 Electronic and transport properties on nanotubes Rev. Mod. Phys. 79 677-732 (Pubitemid 47139984)
8. Harris P J F 2009 Carbon Nanotube Science: Synthesis Properties and Applications (Cambridge: Cambridge University Press)
9. Anantram M P and Leonard F 2006 Physics of carbon nanotube electronic devices Rep. Prog. Phys. 69 507 (Pubitemid 43306354)
10. Wong H S P and Akinwande D 2010 Carbon Nanotube and Graphene Device Physics (Cambridge: Cambridge University Press)
11. Choi W and Lee J W 2011 Graphene: Synthesis and Applications vol 3 (Boca Raton, FL: CRC Press)
12. Thomsen C, Strait J, Vardeny Z, Maris H J, Tauc J and Hauser J J 1984 Coherent phonon generation and detection by picosecond light pulses Phys. Rev. Lett. 53 989-92
13. Cho G C, Kütt W and Kurz H 1990 Subpicosecond time-resolved coherent-phonon oscillations in GaAs Phys. Rev. Lett. 65 764-6
14. Sun C K, Liang J C, Stanton C J, Abare A, Coldren L and DenBaars S P 1999 Large coherent acoustic-phonon oscillation observed in InGaN/GaN multiple-quantum wells Appl. Phys. Lett. 75 1249-51 (Pubitemid 129308564)
15. Sun C K, Liang J C and Yu X Y 2000 Coherent acoustic phonon oscillations in semiconductor multiple quantum wells with piezoelectric fields Phys. Rev. Lett. 84 179-82
16. Yee K J, Lee K G, Oh E, Kim D S and Lim Y S 2002 Coherent optical phonon oscillations in bulk GaN excited by far below the band gap photons Phys. Rev. Lett. 88 105501
17. Stanton C J et al 2003 Coherent phonons, nanoseismology and THz radiation in InGaN/GaN heterostructures Superlatt. Microstruct. 34 525
18. Chern G W, Sun C K, Sanders G D and Stanton C J 2004 Generation of coherent acoustic phonons in nitride-based semiconductor nanostructures Topics in Applied Physics vol 92 ed KT Tsen (New York: Springer) pp 339-94
19. 1-x As/GaSb Phys. Rev. B 72 153311 (Pubitemid 43024157)
20. 1-x N/GaN heterostructures Phys. Rev. B 72 195335 (Pubitemid 43029462)
21. Sanders G D and Stanton C J 2006 Carrier dynamics and coherent acoustic phonons in nitride heterostructures Phys. Rev. B 74 205303 (Pubitemid 44684408)
22. Noe G, Haugan H, Brown G, Sanders G, Stanton C and Kono J 2012 Coherent phonon dynamics in short-period InAs/GaSb superlattices Superlatt. Microstruct. 52 1071-7
23. Ishioka K and Misochko O V 2010 Coherent Lattice Oscillations in Solids and Their Optical Control (Springer Series in Chemical Physics) vol 98 (Berlin: Springer) pp 23-46
24. Hase M and Kitajima M 2010 Interaction of coherent phonons with defects and elementary excitations J. Phys.: Condens. Matter 22 073201
25. Dresselhaus M S, Dresselhaus G, Saito R and Jorio A 2005 Raman spectroscopy of carbon nanotubes Phys. Rep. 409 47-99 (Pubitemid 40317386)
26. Malard L, Pimenta M, Dresselhaus G and Dresselhaus M 2009 Raman spectroscopy in graphene Phys. Rep. 473 51-87
27. Dresselhaus M S, Jorio A, Hofmann M, Dresselhaus G and Saito R 2010 Perspectives on carbon nanotubes and graphene Raman spectroscopy Nano Lett. 10 751-8
28. Dresselhaus M, Jorio A and Saito R 2010 Characterizing graphene, graphite, and carbon nanotubes by Raman spectroscopy Annu. Rev. Condens. Matter Phys. 1 89-108
29. Jorio A, Dresselhaus M S, Saito R and Dresselhaus G 2011 Raman Spectroscopy in Graphene Related Systems (Weinheim: Wiley-VCH)
30. Iijima S 1991 Helical microtubules of graphitic carbon Nature 354 56-8 (Pubitemid 21896780)
31. Bethune D S et al 1993 Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls Nature 363 605-7
32. Iijima S and Ichihashi T 1993 Single-shell carbon nanotubes of 1-nm diameter Nature 363 603-5
33. Joselevich E, Dai H, Liu J, Hata K and Windle A H 2008 Carbon nanotube synthesis and organization Carbon Nanotubes, Topics in Applied Physics (Berlin: Springer)
34. Saito R, Dresselhaus G and Dresselhaus M S 1998 Physical Properties of Carbon Nanotubes (London: Imperial College Press)
35. 60 Phys. Rev. B 46 1804-11
36. Saito R, Dresselhaus G and Dresselhaus M S 2000 Trigonal warping effect of carbon nanotubes Phys. Rev. B 61 2981-90
37. Jiang J et al 2007 Chirality dependence of exciton effects in single-wall carbon nanotubes: tight-binding model Phys. Rev. B 75 035407
38. Saito R, Takeya T, Kimura T, Dresselhaus G and Dresselhaus M S 1998 Raman intensity of single-wall carbon nanotubes Phys. Rev. B 57 4145-53 (Pubitemid 128489294)
39. Saito R, Hofmann M, Dresselhaus G, Jorio A and Dresselhaus M S 2011 Raman spectroscopy of graphene and carbon nanotubes Adv. Phys. 60 413-550
40. Zhang B, Shimazaki K, Shiokawa T, Suzuki M, Ishibashi K and Saito R 2006 Stimulated Raman scattering from individual single-wall carbon nanotubes Appl. Phys. Lett. 88 241101
41. Kosynkin D V et al 2009 Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons Nature. 458 872-6
42. Han M Y, Özyilmaz B, Zhang Y and Kim P 2007 Energy band-gap engineering of graphene nanoribbons Phys. Rev. Lett. 98 206805 (Pubitemid 47139572)
43. Masubuchi S, Ono M, Yoshida K, Hirakawa K and Machida T 2009 Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope Appl. Phys. Lett. 94 082107
44. Tapaszto L, Dobrik G, Lambin P and Biro L P 2008 Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography Nature Nanotechnol. 3 397-401
45. Campos-Delgado J et al 2008 Bulk production of a new form of sp2 carbon: crystalline graphene nanoribbons Nano Lett. 8 2773-8
46. Jia X, Campos-Delgado J, Terrones M, Meunier V and Dresselhaus M S 2011 Graphene edges: a review of their fabrication and characterization Nanoscale 3 86-95
47. Sanders G D, Nugraha A R T, Saito R and Stanton C J 2012 Coherent radial-breathing-like phonons in graphene nanoribbons Phys. Rev. B 85 205401
48. Nanot S, Hároz E H, Kim J H, Hauge R H and Kono J 2012 Optoelectronic properties of single-wall carbon nanotubes Adv. Mater. 24 4977-94
49. Makino K, Hirano A, Shiraki K, Maeda Y and Hase M 2009 Ultrafast vibrational motion of carbon nanotubes in different pH environments Phys. Rev. B 80 245428
50. Kim J H et al 2009 Chirality-selective excitation of coherent phonons in carbon nanotubes by femtosecond optical pulses Phys. Rev. Lett. 102 037402
51. Manzoni C, Gambetta A, Menna E, Meneghetti M, Lanzani G and Cerullo G 2005 Intersubband exciton relaxation dynamics in single-walled carbon nanotubes Phys. Rev. Lett. 94 207401 (Pubitemid 41481111)
52. Lim Y S et al 2006 Coherent lattice vibrations in single-walled carbon nanotubes Nano Lett. 6 2696-700 (Pubitemid 46131337)
53. Lim Y S et al 2007 Chirality assignment of micelle-suspended single-walled carbon nanotubes using coherent phonon oscillations J. Korean Phys. Soc. 51 306-11
54. Sanders G D et al 2009 Resonant coherent phonon spectroscopy of single-walled carbon nanotubes Phys. Rev. B 79 205434
55. Lim Y S et al 2010 Resonant coherent phonon generation in single-walled carbon nanotubes through near-band-edge Excitation ACS Nano. 4 3222
56. Booshehri L G et al 2011 Polarization dependence of coherent phonon generation and detection in highly-aligned single-walled carbon nanotubes Phys. Rev. B 83 195411
57. Gambetta A et al 2006 Real-time observation of nonlinear coherent phonon dynamics in single-walled carbon nanotubes Nature Phys. 2 515-20 (Pubitemid 44167274)
58. Lüer L, Gadermaier C, Crochet J, Hertel T, Brida D and Lanzani G 2009 Coherent phonon dynamics in semiconducting carbon nanotubes: a quantitative study of electron-phonon coupling Phys. Rev. Lett. 102 127401
59. Sasaki K and Saito R 2008 Pseudospin and deformation-induced gauge field in graphene Prog. Theor. Phys. Suppl. 176 253-78
60. Bosma W B, Mukamel S, Greene B I and Schmitt-Rink S 1992 Femtosecond pump-probe spectroscopy of conjugated polymers: coherent and sequential contributions Phys. Rev. Lett. 68 2456-9
61. 1-y As strained-layer single-quantum-well diode lasers: comparison of theory and experiment Phys. Rev. B 50 8539-58
62. Alexandrou A, Berger V and Hulin D 1995 Direct observation of electron relaxation in intrinsic GaAs using femtosecond pump-probe spectroscopy Phys. Rev. B 52 4654
63. 1-x N/GaN double heterostructure Phys. Rev. B 63 195302
64. Peng P, Milliron D J, Hughes S M, Johnson J C, Alivisatos A P and Saykally R J 2005 Femtosecond spectroscopy of carrier relaxation dynamics in type II CdSe/CdTe tetrapod heteronanostructures Nano Lett. 5 1809-13 (Pubitemid 41396169)
65. Tribuzy C V B et al 2006 Femtosecond pump-probe spectroscopy of intersubband relaxation dynamics in narrow InGaAs/AlAsSb quantum well structures Appl. Phys. Lett. 89 171104 (Pubitemid 44656616)
66. Gambetta A et al 2008 Sub-100 fs pump-probe spectroscopy of single wall carbon nanotubes with a 100 MHz Er-fiber laser system Opt. Express 16 11727-34
67. French P 1999 The generation of ultrashort laser pulses Rep. Prog. Phys. 58 169
68. Krausz F and Ivanov M 2009 Attosecond physics Rev. Mod. Phys. 81 163
69. Henriksen N E and Engel V 2001 Femtosecond pump-probe spectroscopy: a theoretical analysis of transient signals and their relation to nuclear wave-packet motion Int. Rev. Phys. Chem. 20 93-126 (Pubitemid 32899774)
70. Kuznetsov A V and Stanton C J 1994 Theory of Coherent Phonon Oscillations in Semiconductors Phys. Rev. Lett. 73 3243-6 (Pubitemid 24976201)
71. Dumitricǎ T, Garcia M E, Jeschke H O and Yakobson B I 2004 Selective cap opening in carbon nanotubes driven by laser-induced coherent phonons Phys. Rev. Lett. 92 117401
72. Dumitricǎ T, Garcia M E, Jeschke H O and Yakobson B I 2006 Breathing coherent phonons and caps fragmentation in carbon nanotubes following ultrafast laser pulses Phys. Rev. B 74 193406 (Pubitemid 44722412)
73. Ge Y, Yang F, Liang Q and Dong J 2011 Coherent phonons in excited-state carbon nanotubes: a simulation by tight-binding molecular dynamics Physica E 43 1585-91
74. Nugraha A R T, Sanders G D, Sato K, Stanton C J, Dresselhaus M S and Saito R 2011 Chirality dependence of coherent phonon amplitudes in single-wall carbon nanotubes Phys. Rev. B 84 174302
75. Dresselhaus M, Dresselhaus G and Jorio A 2004 Unusual properties and structure of carbon nanotubes Annu. Rev. Mater. Res. 34 247-78
76. Dresselhaus M S, Dresselhaus G and Ph A 2001 Carbon Nanotubes: Synthesis, Structure, Properties, and Applications (Berlin: Springer)
77. Harris P J F 1999 Carbon Nanotubes and Related Structures: New Materials for the Twenty-First Century (Cambridge: Cambridge University Press)
78. Terrones M 2003 Synthesis, properties, and applications of carbon nanotubes Annu. Rev. Mater. Sci. 33 419-501
79. Saito R et al 2005 Cutting lines near the Fermi energy of single-wall carbon nanotubes Phys. Rev. B 72 153413 (Pubitemid 43022209)
80. Blase X, Benedict L X, Shirley E L and Louie S G 1994 Hybridization effects and metallicity in small radius carbon nanotubes Phys. Rev. Lett. 72 1878-81 (Pubitemid 24975052)
81. Samsonidze G G et al 2004 Family behavior of the optical transition energies in single-wall carbon nanotubes of smaller diameters Appl. Phys. Lett. 85 5703-5 (Pubitemid 40162569)
82. Porezag D, Frauenheim T, Köhler T, Seifert G and Kaschner R 1995 Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon Phys. Rev. B 51 12947
83. Popov V N 2004 Curvature effects on the structural, electronic and optical properties of isolated single-walled carbon nanotubes within a symmetry-adapted non-orthogonal tight-binding model New J. Phys. 6 17 (Pubitemid 38825984)
84. Chuang S L 1995 Physics of Optoelectronic Devices (New York: Wiley)
85. Bassani F and Parravicini G P 1975 Electronic States and Optical Transitions in Solids (New York: Pergamon)
86. Pedersen T G 2003 Analytic calculation of the optical properties of graphite Phys. Rev. B 67 113106
87. Taft E A and Philipp H R 1965 Optical properties of graphite Phys. Rev. 138 A197-202
88. Ehrenreich H and Cohen M H 1959 Self-consistent field approach to the many-electron problem Phys. Rev. 115 786-90
89. Yang L, Deslippe J, Park C H, Cohen M L and Louie S G 2009 Excitonic effects on the optical response of graphene and bilayer graphene Phys. Rev. Lett. 103 186802
90. Spataru C D, Ismail-Beigi S, Benedict L X and Louie S G 2004 Excitonic effects and optical spectra of single-walled carbon nanotubes Phys. Rev. Lett. 92 077402
91. Ando T 1997 Excitons in carbon nanotubes J. Phys. Soc. Japan 66 1066-73
92. Dresselhaus M S, Dresselhaus G, Saito R and Jorio A 2007 Exciton photophysics of carbon nanotubes Annu. Rev. Phys. Chem. 58 719-47 (Pubitemid 46877606)
93. Kahn D, Kim K W and Stroscio M A 2001 Quantized vibrational modes of nanospheres and nanotubes in the elastic continuum model J. Appl. Phys. 89 5107-11
94. Mahan G 2002 Oscillations of a thin hollow cylinder: carbon nanotubes Phys. Rev. B 65 235402
95. Raichura A, Dutta M and Stroscio M A 2003 Quantized acoustic vibrations of single-wall carbon nanotube J. Appl. Phys. 94 4060-5
96. Raichura A, Dutta M and Stroscio M A 2004 Quantized optical vibrational modes of finite-length multi wall nanotubes: optical deformation potential Superlatt. Microstruct. 35 147-53
97. Raichura A, Dutta M and Stroscio M A 2004 Continuum model for acoustic phonons in nanotubes: phonon bottleneck Phys. Status Solidi b 241 3448-53
98. Chico L, Pérez-Álvarez R and Cabrillo C 2006 Low-frequency phonons in carbon nanotubes: a continuum approach Phys. Rev. B 73 075425 (Pubitemid 43270754)
99. Qian J, Allen M J, Yang Y, Dutta M and Stroscio M A 2009 Quantized long-wavelength optical phonon modes in graphene nanoribbon in the elastic continuum model Superlatt. Microstruct. 46 881-8
100. Jishi R A, Venkataraman L, Dresselhaus M S and Dresselhaus G 1993 Phonon modes in carbon nanotubules Chem. Phys. Lett. 209 77
101. Lobo C and Martins J L 1997 Valence force field model for graphene and fullerenes Z. Phys. D. 39 159-64 (Pubitemid 127789699)
102. Mahan G D and Jeon G S 2004 Flexure modes in carbon nanotubes Phys. Rev. B 70 075405
103. Mazzamuto F, Saint-Martin J, Valentin A, Chassat C and Dollfus P 2011 Edge shape effect on vibrational modes in graphene nanoribbons: a numerical study J. Appl. Phys. 109 064516
104. Jeon G S and Mahan G 2005 Theory of infrared-active phonons in carbon nanotubes Phys. Rev. B 72 155415 (Pubitemid 43022284)
105. Kürti J, Kresse G and Kuzmany H 1998 First-principles calculations of the radial breathing mode of single-wall carbon nanotubes Phys. Rev. B 58 8869-72
106. Sánchez-Portal D, Artacho E, Soler J M, Rubio A and Ordejón P 1999 Ab initio structural, elastic, and vibrational properties of carbon nanotubes Phys. Rev. B 59 12678
107. Kürti J, Zólyomi V, Kertesz M and Sun G 2003 The geometry and the radial breathing mode of carbon nanotubes: beyond the ideal behaviour New J. Phys. 5 125
108. Dubay O and Kresse G 2003 Accurate density functional calculations for the phonon dispersion relations of graphite layer and carbon nanotubes Phys. Rev. B 67 035401
109. Ye L H, Liu B G, Wang D S and Han R 2004 Ab initio phonon dispersions of single-wall carbon nanotubes Phys. Rev. B 69 235409
110. Gillen R, Mohr M, Thomsen C and Maultzsch J 2009 Vibrational properties of graphene nanoribbons by first-principles calculations Phys. Rev. B 80 155418
111. Madelung O 1978 Introduction to Solid-State Theory (Berlin: Springer)
112. Jiang J W, Tang H, Wang B S and Su Z B 2006 Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes Phys. Rev. B 73 235434 (Pubitemid 43967809)
113. Jiang J et al 2005 Electron-phonon matrix elements in single-wall carbon nanotubes Phys. Rev. B 72 235408 (Pubitemid 43029152)
114. Grüneis A 2004 Resonance Raman Spectroscopy of Single Wall Carbon Nanotubes (Sendai: Tohoku University)
115. Sasaki K, Saito R, Dresselhaus G, Dresselhaus M S, Farhat H and Kong J 2008 Chirality-dependent frequency shift of radial breathing mode in metallic carbon nanotubes Phys. Rev. B 78 235405
116. Sanders G D et al 2011 Coherent phonons in carbon nanotubes and graphene AIP Conf. Proc. 1416 31
117. Machón M, Reich S, Telg H, Maultzsch J, Ordejón P and Thomsen C 2005 Strength of radial breathing mode in single-walled carbon nanotubes Phys. Rev. B 71 035416 (Pubitemid 40396468)
118. Kato K, Ishioka K, Kitajima M, Tang J, Saito R and Petek H 2008 Coherent phonon anisotropy in aligned single-walled carbon nanotubes Nano Lett. 8 3102-8
119. Ando T 2005 Theory of electronic states and transport in carbon nanotubes J. Phys. Soc. Japan 74 777-817 (Pubitemid 41282624)
120. Capaz R B, Spataru C D, Ismail-Beigi S and Louie S G 2006 Diameter and chirality dependence of exciton properties in carbon nanotubes Phys. Rev. B 74 121401 (Pubitemid 44396740)
121. Dukovic G, Wang F, Song D, Sfeir M Y, Heinz T F and Brus L E 2005 Structural dependence of excitonic optical transitions and band-gap energies in carbon nanotubes Nano Lett. 5 2314-8 (Pubitemid 41698960)
122. Miyauchi Y et al 2007 Dependence of exciton transition energy of single-walled carbon nanotubes on surrounding dielectric materials Chem. Phys. Lett. 442 394-9 (Pubitemid 47016426)
123. Kim J H et al 2009 Polarization anisotropy of transient carrier and phonon dynamics in carbon nanotubes J. Appl. Phys. 105 103506
124. Pint C L et al 2010 Dry contact transfer printing of aligned carbon nanotube patterns and characterization of their optical properties for diameter distribution and alignment ACS Nano 4 1131-45
125. Son Y W, Cohen M L and Louie S G 2006 Energy gaps in graphene nanoribbons Phys. Rev. Lett. 97 216803 (Pubitemid 44808139)
126. Raza H and Kan E C 2008 Armchair graphene nanoribbons: electronic structure and electric-field modulation Phys. Rev. B 77 245434
127. Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 Peculiar localized state at zigzag graphite edge J. Phys. Soc. Japan 65 1920-3
128. Nakada K, Fujita M, Dresselhaus G and Dresselhaus M S 1996 Edge state in graphene ribbons: nanometer size effect and edge shape dependence Phys. Rev. B 54 17954-61
129. Pisani L, Chan J A, Montanari B and Harrison N M 2007 Electronic structure and magnetic properties of graphitic ribbons Phys. Rev. B 75 064418
130. Sasaki K, Murakami S and Saito R 2006 Gauge field for edge state in graphene J. Phys. Soc. Japan 75 074713
131. Jiang J et al 2007 Exciton-photon, exciton-phonon matrix elements, and resonant Raman intensity of single-wall carbon nanotubes Phys. Rev. B 75 035405