Thermoelectricity and Heat Transport in Graphene and Other 2D Nanomaterials describes thermoelectric phenomena and thermal transport in graphene and other 2-dimentional nanomaterials and devices. Graphene, which is an example of an atomic monolayered material, has become the most important growth area in materials science research, stimulating an interest in other atomic monolayeric materials.
The book analyses flow management, measurement of the local temperature at the nanoscale level and thermoelectric transducers, with reference to both graphene and other 2D nanomaterials. The book covers in detail the mechanisms of thermoelectricity, thermal transport, interface phenomena, quantum dots, non-equilibrium states, scattering and dissipation, as well as coherent transport in low-dimensional junctions in graphene and its allotropes, transition metal dichalcogenides and boron nitride.
This book aims to show readers how to improve thermoelectric transducer efficiency in graphene and other nanomaterials. The book describes basic ingredients of such activity, allowing readers to gain a greater understanding of fundamental issues related to the heat transport and the thermoelectric phenomena of nanomaterials. It contains a thorough analysis and comparison between theory and experiments, complemented with a variety of practical examples.
1. Introduction - p. xiv 2. Chapter 1: Thermal transport in graphene and its allotropes - p. xxvi 3. Abstract - p. xxvi 4. 1.1. Thermoelectric transducer - p. 1 5. 1.2. Components of the heat transport - p. 7 6. 1.3. The phonon and electron fractions of the heat flow in graphene - p. 31 7. 1.4. Low-energy electron excitations in graphene - p. 33 8. 1.5. Relativistic dirac equation describing chiral fermions - p. 38 9. 1.6. Berry phase and topological singularity in graphene - p. 43 10. 1.7. Klein paradox and chiral tunneling - p. 47 11. 1.8. Electron and hole excitations in graphene - p. 51 12. 1.9. Topologically protected heavy chiral fermion state in graphene stripe - p. 55 13. Problems - p. 64 14. Chapter 2: Lattice dynamics and thermal flux - p. 68 15. Abstract - p. 68 16. 2.1. Lattice oscillations in graphene - p. 69 17. 2.2. Phonon Boltzmann equation - p. 81 18. 2.3. Lattice thermal conductivity - p. 83 19. 2.4. Phonon relaxation rates - p. 85 20. 2.5. Phonon group velocity - p. 86 21. 2.6. A model of lattice oscillations in 2D materials - p. 88 22. 2.7. Long-wavelength phonons in carbon nanotubes - p. 89 23. 2.8. Microscopic description of phonons in graphene - p. 94 24. 2.9. Effective mass equations - p. 97 25. 2.10. Electron–phonon interaction - p. 100 26. 2.11. Electron–phonon scattering and resistivity - p. 103 27. 2.12. Propagation of phonons in two-dimensional crystals - p. 109 28. 2.13. Phonon thermal conductivity of graphene nanoribbons - p. 114 29. 2.14. Phonon transport momentum diagram in graphene - p. 117 30. Problems - p. 119 31. Chapter 3: Graphene thermoelectric transducers - p. 123 32. Abstract - p. 123 33. 3.1. Thermoelectricity on the nanoscale - p. 125 34. 3.2. Efficiency of the thermoelectric device - p. 128 35. 3.3. Quantum model of electronic thermal transport - p. 130 36. 3.4. Elastic collisions and electron transport - p. 132 37. 3.5. Peltier cooling in carbon nanotube junctions - p. 134 38. 3.6. Fourier law - p. 136 39. 3.7. Phonon part of the thermal conductivity - p. 143 40. 3.8. Microscopic model of the thermoelectric phenomena - p. 146 41. 3.9. The graphene thermoelectric transducer based on nanoribbon with nanopores - p. 151 42. 3.10. Transduction by a graphene ribbon with heavy chiral fermions - p. 165 43. 3.11. Blocking of the phonon flow with multilayered electrodes - p. 170 44. 3.12. Molecular dynamics simulations - p. 174 45. 3.13. Nonequilibrium thermal injection - p. 175 46. 3.14. Prospects thermoelectricity of graphene - p. 180 47. Problems - p. 180 48. Chapter 4: Experimental study of thermoelectricity in carbon nanotubes and graphene - p. 185 49. Abstract - p. 185 50. 4.1. Measuring the thermal conductivity of graphene - p. 187 51. 4.2. Thermometry and thermal management of carbon nanotube circuits - p. 189 52. 4.3. Transduction between electrical energy and the heat in a carbon nanotube using a voltage-controlled doping - p. 194 53. 4.4. Conclusions - p. 202 54. 4.5. Modeling parameters of the CNT transducer - p. 202 55. 4.6. Raman scattering - p. 214 56. 4.7. The degrees of freedom - p. 215 57. 4.8. Infrared radiation and molecular vibrations - p. 216 58. 4.9. Light scattering processes - p. 217 59. 4.10. Stokes and anti-Stokes scattering - p. 218 60. 4.11. Fluorescence - p. 218 61. 4.12. Selection rules - p. 219 62. 4.13. Stimulated Raman scattering and Raman amplification - p. 219 63. 4.14. Requirement of the coherence - p. 220 64. 4.15. Practical implementations - p. 220 65. 4.16. Raman spectra of higher-orders - p. 221 66. 4.17. Raman spectroscopy of graphene - p. 221 67. 4.18. Kohn anomalies, double resonance, and D and G peaks - p. 222 68. 4.19. Deducing of electron–phonon coupling from the Raman line width - p. 226 69. 4.20. G and D peaks in graphene - p. 229 70. 4.21. Failure of adiabatic Born–Oppenheimer approximation in graphene - p. 233 71. 4.22. The role of atomic and structural disorder - p. 237 72. 4.23. Edges of the graphene ribbons - p. 239 73. Problems - p. 240 74. Chapter 5: Role of structural defects and imperfections - p. 247 75. Abstract - p. 247 76. 5.1. Phonon scattering in a few-layer graphene - p. 249 77. 5.2. Scattering of chiral fermions on impurities - p. 251 78. 5.3. Time of scattering of a heavy fermion on the impurities in graphene - p. 255 79. 5.4. Scattering in two dimensions - p. 258 80. 5.5. Phonon drag effect - p. 278 81. 5.6. Screening by the interacting electrons - p. 281 82. 5.7. Plasma oscillations - p. 286 83. 5.8. Plasma excitations in graphene - p. 289 84. 5.9. Effect of electron scattering on heavy adatoms and nanopores - p. 297 85. 5.10. Bimodal phonon scattering in graphene grain boundaries - p. 307 86. Problems - p. 334 87. Chapter 6: Contribution of many-body effects into thermoelectricity and heat transport in graphene - p. 339 88. Abstract - p. 339 89. 6.1. Electron–electron interaction - p. 341 90. 6.2. Electron self-energy - p. 342 91. 6.3. Quasiparticle excitation energy - p. 343 92. 6.4. Computational results - p. 344 93. 6.5. Phonon–phonon scattering rates in carbon nanotubes and graphene - p. 345 94. 6.6. Excitons - p. 355 95. 6.7. Wannier–Mott excitons - p. 360 96. 6.8. Excitonic states - p. 361 97. 6.9. Experimental study of excitons in graphene - p. 365 98. 6.10. Scattering of electrons on indirect excitons - p. 366 99. 6.11. Polariton excitations in layered 2D materials - p. 369 100. 6.12. Tomonaga–Luttinger liquid - p. 387 101. 6.13. Basic equations - p. 388 102. 6.14. Probing of the one-dimensional quantum wells by using the photon-assisted tunneling - p. 394 103. 6.15. Photon-assisted tunneling into the TLL state - p. 397 104. 6.16. The Tunneling Density of States of a long quantum well - p. 399 105. 6.17. Identifying the charge and the spin boson energy levels - p. 403 106. Problems - p. 407 107. Chapter 7: Principles of thermoelectric transport on nanoscale - p. 418 108. Abstract - p. 418 109. 7.1. Thermal and electric transport on nanoscale - p. 419 110. 7.2. Phonon–electron scattering in 2D atomic monolayers - p. 425 111. 7.3. Energy sensitivity of carrier transport and scattering - p. 437 112. 7.4. Quantized magnetothermoelectric transport in low-dimensional junctions - p. 445 113. Problems - p. 461 114. Chapter 8: THz-induced thermoelectric and thermal transport in atomic monolayers - p. 471 115. Index - p. 509
Thermoelectricity and Heat Transport in Graphene and Other 2D Nanomaterials describes thermoelectric phenomena and thermal transport in graphene and other 2-dimentional nanomaterials and devices. Graphene, which is an example of an atomic monolayered material, has become the most important growth area in materials science research, stimulating an interest in other atomic monolayeric materials.
The book analyses flow management, measurement of the local temperature at the nanoscale level and thermoelectric transducers, with reference to both graphene and other 2D nanomaterials. The book covers in detail the mechanisms of thermoelectricity, thermal transport, interface phenomena, quantum dots, non-equilibrium states, scattering and dissipation, as well as coherent transport in low-dimensional junctions in graphene and its allotropes, transition metal dichalcogenides and boron nitride.
This book aims to show readers how to improve thermoelectric transducer efficiency in graphene and other nanomaterials. The book describes basic ingredients of such activity, allowing readers to gain a greater understanding of fundamental issues related to the heat transport and the thermoelectric phenomena of nanomaterials. It contains a thorough analysis and comparison between theory and experiments, complemented with a variety of practical examples.
1. Introduction - p. xiv 2. Chapter 1: Thermal transport in graphene and its allotropes - p. xxvi 3. Abstract - p. xxvi 4. 1.1. Thermoelectric transducer - p. 1 5. 1.2. Components of the heat transport - p. 7 6. 1.3. The phonon and electron fractions of the heat flow in graphene - p. 31 7. 1.4. Low-energy electron excitations in graphene - p. 33 8. 1.5. Relativistic dirac equation describing chiral fermions - p. 38 9. 1.6. Berry phase and topological singularity in graphene - p. 43 10. 1.7. Klein paradox and chiral tunneling - p. 47 11. 1.8. Electron and hole excitations in graphene - p. 51 12. 1.9. Topologically protected heavy chiral fermion state in graphene stripe - p. 55 13. Problems - p. 64 14. Chapter 2: Lattice dynamics and thermal flux - p. 68 15. Abstract - p. 68 16. 2.1. Lattice oscillations in graphene - p. 69 17. 2.2. Phonon Boltzmann equation - p. 81 18. 2.3. Lattice thermal conductivity - p. 83 19. 2.4. Phonon relaxation rates - p. 85 20. 2.5. Phonon group velocity - p. 86 21. 2.6. A model of lattice oscillations in 2D materials - p. 88 22. 2.7. Long-wavelength phonons in carbon nanotubes - p. 89 23. 2.8. Microscopic description of phonons in graphene - p. 94 24. 2.9. Effective mass equations - p. 97 25. 2.10. Electron–phonon interaction - p. 100 26. 2.11. Electron–phonon scattering and resistivity - p. 103 27. 2.12. Propagation of phonons in two-dimensional crystals - p. 109 28. 2.13. Phonon thermal conductivity of graphene nanoribbons - p. 114 29. 2.14. Phonon transport momentum diagram in graphene - p. 117 30. Problems - p. 119 31. Chapter 3: Graphene thermoelectric transducers - p. 123 32. Abstract - p. 123 33. 3.1. Thermoelectricity on the nanoscale - p. 125 34. 3.2. Efficiency of the thermoelectric device - p. 128 35. 3.3. Quantum model of electronic thermal transport - p. 130 36. 3.4. Elastic collisions and electron transport - p. 132 37. 3.5. Peltier cooling in carbon nanotube junctions - p. 134 38. 3.6. Fourier law - p. 136 39. 3.7. Phonon part of the thermal conductivity - p. 143 40. 3.8. Microscopic model of the thermoelectric phenomena - p. 146 41. 3.9. The graphene thermoelectric transducer based on nanoribbon with nanopores - p. 151 42. 3.10. Transduction by a graphene ribbon with heavy chiral fermions - p. 165 43. 3.11. Blocking of the phonon flow with multilayered electrodes - p. 170 44. 3.12. Molecular dynamics simulations - p. 174 45. 3.13. Nonequilibrium thermal injection - p. 175 46. 3.14. Prospects thermoelectricity of graphene - p. 180 47. Problems - p. 180 48. Chapter 4: Experimental study of thermoelectricity in carbon nanotubes and graphene - p. 185 49. Abstract - p. 185 50. 4.1. Measuring the thermal conductivity of graphene - p. 187 51. 4.2. Thermometry and thermal management of carbon nanotube circuits - p. 189 52. 4.3. Transduction between electrical energy and the heat in a carbon nanotube using a voltage-controlled doping - p. 194 53. 4.4. Conclusions - p. 202 54. 4.5. Modeling parameters of the CNT transducer - p. 202 55. 4.6. Raman scattering - p. 214 56. 4.7. The degrees of freedom - p. 215 57. 4.8. Infrared radiation and molecular vibrations - p. 216 58. 4.9. Light scattering processes - p. 217 59. 4.10. Stokes and anti-Stokes scattering - p. 218 60. 4.11. Fluorescence - p. 218 61. 4.12. Selection rules - p. 219 62. 4.13. Stimulated Raman scattering and Raman amplification - p. 219 63. 4.14. Requirement of the coherence - p. 220 64. 4.15. Practical implementations - p. 220 65. 4.16. Raman spectra of higher-orders - p. 221 66. 4.17. Raman spectroscopy of graphene - p. 221 67. 4.18. Kohn anomalies, double resonance, and D and G peaks - p. 222 68. 4.19. Deducing of electron–phonon coupling from the Raman line width - p. 226 69. 4.20. G and D peaks in graphene - p. 229 70. 4.21. Failure of adiabatic Born–Oppenheimer approximation in graphene - p. 233 71. 4.22. The role of atomic and structural disorder - p. 237 72. 4.23. Edges of the graphene ribbons - p. 239 73. Problems - p. 240 74. Chapter 5: Role of structural defects and imperfections - p. 247 75. Abstract - p. 247 76. 5.1. Phonon scattering in a few-layer graphene - p. 249 77. 5.2. Scattering of chiral fermions on impurities - p. 251 78. 5.3. Time of scattering of a heavy fermion on the impurities in graphene - p. 255 79. 5.4. Scattering in two dimensions - p. 258 80. 5.5. Phonon drag effect - p. 278 81. 5.6. Screening by the interacting electrons - p. 281 82. 5.7. Plasma oscillations - p. 286 83. 5.8. Plasma excitations in graphene - p. 289 84. 5.9. Effect of electron scattering on heavy adatoms and nanopores - p. 297 85. 5.10. Bimodal phonon scattering in graphene grain boundaries - p. 307 86. Problems - p. 334 87. Chapter 6: Contribution of many-body effects into thermoelectricity and heat transport in graphene - p. 339 88. Abstract - p. 339 89. 6.1. Electron–electron interaction - p. 341 90. 6.2. Electron self-energy - p. 342 91. 6.3. Quasiparticle excitation energy - p. 343 92. 6.4. Computational results - p. 344 93. 6.5. Phonon–phonon scattering rates in carbon nanotubes and graphene - p. 345 94. 6.6. Excitons - p. 355 95. 6.7. Wannier–Mott excitons - p. 360 96. 6.8. Excitonic states - p. 361 97. 6.9. Experimental study of excitons in graphene - p. 365 98. 6.10. Scattering of electrons on indirect excitons - p. 366 99. 6.11. Polariton excitations in layered 2D materials - p. 369 100. 6.12. Tomonaga–Luttinger liquid - p. 387 101. 6.13. Basic equations - p. 388 102. 6.14. Probing of the one-dimensional quantum wells by using the photon-assisted tunneling - p. 394 103. 6.15. Photon-assisted tunneling into the TLL state - p. 397 104. 6.16. The Tunneling Density of States of a long quantum well - p. 399 105. 6.17. Identifying the charge and the spin boson energy levels - p. 403 106. Problems - p. 407 107. Chapter 7: Principles of thermoelectric transport on nanoscale - p. 418 108. Abstract - p. 418 109. 7.1. Thermal and electric transport on nanoscale - p. 419 110. 7.2. Phonon–electron scattering in 2D atomic monolayers - p. 425 111. 7.3. Energy sensitivity of carrier transport and scattering - p. 437 112. 7.4. Quantized magnetothermoelectric transport in low-dimensional junctions - p. 445 113. Problems - p. 461 114. Chapter 8: THz-induced thermoelectric and thermal transport in atomic monolayers - p. 471 115. Index - p. 509
