Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Colloquium: Phononic thermal properties of two-dimensional materials

Xiaokun Gu, Yujie Wei*, Xiaobo Yin, Baowen Li, and Ronggui Yang

Xiaokun Gu

  • Institute of Engineering Thermophysics, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China 200240 and Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA

Yujie Wei*

  • LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China, 100190

Xiaobo Yin

  • Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA

Baowen Li

  • Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA

Ronggui Yang

  • Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA

  • *yujie_wei@lnm.imech.ac.cn
  • Baowen.Li@Colorado.Edu
  • Ronggui.Yang@Colorado.Edu

Rev. Mod. Phys. 90, 041002 – Published 13 November, 2018

DOI: https://doi.org/10.1103/RevModPhys.90.041002

Abstract

Following the emergence of many novel two-dimensional (2D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications ranging from electronics, photonics, and phononics to thermal management and energy storage. In this Colloquium, a summary and comparison are given of the phonon properties, such as phonon dispersion and relaxation time, of pristine 2D materials with single-layer graphene to understand the role of crystal structure and dimension on thermal conductivity. A comparison is made of the phonon properties, contrasting idealized 2D crystals, realistic 2D crystals, and 3D crystals, and synthesizing this to develop a physical picture of how the sample size of 2D materials affects their thermal conductivity. The effects of geometry such as the number of layers and the nanoribbon width, together with the presence of defects, mechanical strain, and substrate interactions on the thermal properties of 2D materials are discussed. Intercalation affects both the group velocities and phonon relaxation times of layered crystals and thus tunes the thermal conductivity along both the through-plane and basal-plane directions. This Colloquium concludes with a discussion of the challenges in theoretical and experimental studies of thermal transport in 2D materials. The rich and special phonon physics in 2D materials make them promising candidates for exploring novel phenomena such as topological phonon effects and applications such as phononic quantum devices.

Physics Subject Headings (PhySH)

Article Text

References (290)

  1. Ackerman, C. C., B. Bertman, H. A. Fairbank, and R. Guyer, 1966, “Second sound in solid helium,” Phys. Rev. Lett. 16, 789.
  2. Aksamija, Z., and I. Knezevic, 2011, “Lattice thermal conductivity of graphene nanoribbons: Anisotropy and edge roughness scattering,” Appl. Phys. Lett. 98, 141919.
  3. Alam, M., R. Pulavarthy, C. Muratore, and M. A. Haque, 2015, “Mechanical strain dependence of thermal transport in amorphous silicon thin films,” Nanoscale Micro. Thermophys. Eng. 19, 1.
  4. Ashcroft, N. W., and N. D. Mermin, 1978, Solids State Physics (Holt, Rinehart and Winston, New York).
  5. Aspelmeyer, M., T. J. Kippenberg, and F. Marquardt, 2014, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391.
  6. Bae, M. H., Z. Li, Z. Aksamija, P. N. Martin, F. Xiong, Z. Y. Ong, I. Knezevic, and E. Pop, 2013, “Ballistic to diffusive crossover of heat flow in graphene ribbons,” Nat. Commun. 4, 1734.
  7. Balandin, A. A., 2011, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater. 10, 569.
  8. Balandin, A. A., S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, 2008, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902.
  9. Barbarino, G., C. Melis, and L. Colombo, 2015, “Intrinsic thermal conductivity in monolayer graphene is ultimately upper limited: A direct estimation by atomistic simulations,” Phys. Rev. B 91, 035416.
  10. Berciaud, S., S. Ryu, L. E. Brus, and T. F. Heinz, 2009, “Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers,” Nano Lett. 9, 346.
  11. Bhowmick, S., and V. B. Shenoy, 2006, “Effect of strain on the thermal conductivity of solids,” J. Chem. Phys. 125, 164513.
  12. Bonini, N., J. Garg, and N. Marzari, 2012, “Acoustic phonon lifetimes and thermal transport in free-standing and strained graphene,” Nano Lett. 12, 2673.
  13. Broido, D., M. Malorny, G. Birner, N. Mingo, and D. Stewart, 2007, “Intrinsic lattice thermal conductivity of semiconductors from first principles,” Appl. Phys. Lett. 91, 231922.
  14. Broido, D., A. Ward, and N. Mingo, 2005, “Lattice thermal conductivity of silicon from empirical interatomic potentials,” Phys. Rev. B 72, 014308.
  15. Cahill, D. G., S. K. Watson, and R. O. Pohl, 1992, “Lower limit to the thermal conductivity of disordered crystals,” Phys. Rev. B 46, 6131.
  16. Cai, W., A. L. Moore, Y. Zhu, X. Li, S. Chen, L. Shi, and R. S. Ruoff, 2010, “Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition,” Nano Lett. 10, 1645.
  17. Cao, H.-Y., Z.-X. Guo, H. Xiang, and X.-G. Gong, 2012, “Layer and size dependence of thermal conductivity in multilayer graphene nanoribbons,” Phys. Lett. A 376, 525.
  18. Carrete, J., W. Li, L. Lindsay, D. A. Broido, L. J. Gallego, and N. Mingo, 2016, “Physically founded phonon dispersions of few-layer materials and the case of borophene,” Mater. Res. Lett. 4, 204.
  19. Castellanos-Gomez, A., L. Vicarelli, E. Prada, J. O. Island, K. Narasimha-Acharya, S. I. Blanter, D. J. Groenendijk, M. Buscema, G. A. Steele, and J. Alvarez, 2014, “Isolation and characterization of few-layer black phosphorus,” 2D Mater. 1, 025001.
  20. Cepellotti, A., G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, and N. Marzari, 2015, “Phonon hydrodynamics in two-dimensional materials,” Nat. Commun. 6, 6400.
  21. Chang, C.-W., 2016, in Experimental Probing of Non-Fourier Thermal Conductors, edited by S. Lepri (Springer International Publishing, New York), p. 305.
  22. Chen, C.-C., Z. Li, L. Shi, and S. B. Cronin, 2014, “Thermal interface conductance across a graphene/hexagonal boron nitride heterojunction,” Appl. Phys. Lett. 104, 081908.
  23. Chen, G., 2001, “Ballistic-diffusive heat-conduction equations,” Phys. Rev. Lett. 86, 2297.
  24. Chen, G., 2005, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Oxford University Press, New York).
  25. Chen, J., S. Chen, and Y. Gao, 2016, “Anisotropy Enhancement of Thermal Energy Transport in Supported Black Phosphorene,” J. Phys. Chem. Lett. 7, 2518.
  26. Chen, J., G. Zhang, and B. Li, 2013, “Substrate coupling suppresses size dependence of thermal conductivity in supported graphene,” Nanoscale 5, 532.
  27. Chen, L., and S. Kumar, 2012, “Thermal transport in graphene supported on copper,” J. Appl. Phys. 112, 043502.
  28. Chen, S., et al., 2011, “Raman measurements of thermal transport in suspended monolayer graphene of variable sizes in vacuum and gaseous environments,” ACS Nano 5, 321.
  29. Chen, S., Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, A. A. Balandin, and R. S. Ruoff, 2012, “Thermal conductivity of isotopically modified graphene,” Nat. Mater. 11, 203.
  30. Chen, S., Y. Zhang, J. Wang, and H. Zhao, 2016, “Key role of asymmetric interactions in low-dimensional heat transport,” J. Stat. Mech. 03, 033205.
  31. Chen, Y., et al., 2009, “Experimental realization of a three-dimensional topological insulator, Bi2Te3,” Science 325, 178.
  32. Chen, Z., W. Jang, W. Bao, C. N. Lau, and C. Dames, 2009, “Thermal contact resistance between graphene and silicon dioxide,” Appl. Phys. Lett., 95, 161910.
  33. Cho, J., M. D. Losego, H. G. Zhang, H. Kim, J. Zuo, I. Petrov, D. G. Cahill, and P. V. Braun, 2014, “Electrochemically tunable thermal conductivity of lithium cobalt oxide,” Nat. Commun. 5, 4035.
  34. Clarke, R., and C. Uher, 1984, “High pressure properties of graphite and its intercalation compounds,” Adv. Phys. 33, 469.
  35. Cocemasov, A. I., D. L. Nika, and A. A. Balandin, 2015, “Engineering of the thermodynamic properties of bilayer graphene by atomic plane rotations: the role of the out-of-plane phonons,” Nanoscale 7, 12851.
  36. Conley, H. J., B. Wang, J. I. Ziegler, R. F. Haglund, Jr., S. T. Pantelides, and K. I. Bolotin, 2013, “Bandgap Engineering of Strained Monolayer and Bilayer MoS2,” Nano Lett. 13, 3626.
  37. Das, S. G., A. Dhar, and O. Narayan, 2014, “Heat Conduction in the αβ Fermi–Pasta–Ulam Chain,” J. Stat. Phys. 154, 204.
  38. Dhar, A., 2008, “Heat transport in low-dimensional systems,” Adv. Phys. 57, 457.
  39. Ding, Z., Q.-X. Pei, J.-W. Jiang, and Y.-W. Zhang, 2015, “Manipulating the thermal conductivity of monolayer MoS2 via lattice defect and strain engineering,” J. Phys. Chem. C 119, 16358.
  40. Donnelly, R. J., 2009, “The two-fluid theory and second sound in liquid helium,” Phys. Today 62, 34.
  41. Dresselhaus, M. S., and G. Dresselhaus, 1981, “Intercalation compounds of graphite,” Adv. Phys. 30, 139.
  42. Duan, X., et al., 2014, “Lateral epitaxial growth of two-dimensional layered semiconductor heterojunctions,” Nat. Nanotechnol. 9, 1024.
  43. Ecsedy, D. J., and P. G. Klemens, 1977, “Thermal resistivity of dielectric crystals due to four-phonon processes and optical modes,” Phys. Rev. B 15, 5957.
  44. Elzinga, M., D. Morelli, and C. Uher, 1982, “Thermal transport properties of SbCl5 graphite,” Phys. Rev. B 26, 3312.
  45. Ernst, M., E. Hauge, and J. Van Leeuwen, 1971, “Asymptotic time behavior of correlation functions. I. Kinetic terms,” Phys. Rev. A 4, 2055.
  46. Ernst, M., E. Hauge, and J. Van Leeuwen, 1976a, “Asymptotic time behavior of correlation functions. II. Kinetic and potential terms,” J. Stat. Phys. 15, 7.
  47. Ernst, M., E. Hauge, and J. Van Leeuwen, 1976b, “Asymptotic time behavior of correlation functions. III. Local equilibrium and mode-coupling theory,” J. Stat. Phys. 15, 23.
  48. Esfarjani, K., G. Chen, and H. T. Stokes, 2011, “Heat transport in silicon from first-principles calculations,” Phys. Rev. B 84, 085204.
  49. Evans, W. J., L. Hu, and P. Keblinski, 2010, “Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination,” Appl. Phys. Lett. 96, 203112.
  50. Fan, Z., L. F. C. Pereira, P. Hirvonen, M. M. Ervasti, K. R. Elder, D. Donadio, T. Ala-Nissila, and A. Harju, 2017, “Thermal conductivity decomposition in two-dimensional materials: Application to graphene,” Phys. Rev. B 95, 144309.
  51. Fasolino, A., J. H. Los, and M. I. Katsnelson, 2007, “Intrinsic ripples in grapheme,” Nat. Mater. 6, 858.
  52. Faugeras, C., B. Faugeras, M. Orlita, M. Potemski, R. R. Nair, and A. Geim, 2010, “Thermal conductivity of graphene in corbino membrane geometry,” ACS Nano 4, 1889.
  53. Feng, T., L. Lindsay, and X. L. Ruan 2017, “Four-phonon scattering significantly reduces intrinsic thermal conductivity of solids,” Phys. Rev. B 96, 161201(R).
  54. Ferrari, A., et al., 2006, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401.
  55. Fiore, V., Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, 2011, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601.
  56. Fleurial, J. P., L. Gailliard, R. Triboulet, H. Scherrer, and S. Scherrer, 1988, “Thermal properties of high quality single crystals of bismuth telluride—Part I: Experimental characterization,” J. Phys. Chem. Solids 49, 1237.
  57. Fu, Q., J. Yang, Y. Chen, D. Li, and D. Xu, 2015, “Experimental evidence of very long intrinsic phonon mean free path along the c-axis of graphite,” Appl. Phys. Lett. 106, 031905.
  58. Fugallo, G., A. Cepellotti, L. Paulatto, M. Lazzeri, N. Marzari, and F. Mauri, 2014, “Thermal conductivity of graphene and graphite: collective excitations and mean free paths,” Nano Lett. 14, 6109.
  59. Fugallo, G., M. Lazzeri, L. Paulatto, and F. Mauri, 2013, “Ab initio variational approach for evaluating lattice thermal conductivity,” Phys. Rev. B 88, 045430.
  60. Gao, Y., Q.-C. Liu, and B.-X. Xu, 2016, “Lattice Mismatch Dominant Yet Mechanically Tunable Thermal Conductivity in Bilayer Heterostructures,” ACS Nano, 10, 5431.
  61. Gao, Y., W. Z. Yang, and B.-X. Xu, 2017, “Tailoring Auxetic and Contractile Graphene to Achieve Interface Structures with Fully Mechanically Controllable Thermal Transports,” Adv.Mater. Interfaces 4, 1700278.
  62. Garg, J., N. Bonini, B. Kozinsky, and N. Marzari, 2011, “Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: A first-principles study,” Phys. Rev. Lett. 106, 045901.
  63. Gendelman, O. V., and A. V. Savin, 2000, “Normal Heat Conductivity of the One-Dimensional Lattice with Periodic Potential of Nearest-Neighbor Interaction,” Phys. Rev. Lett. 84, 2381.
  64. Gendelman, O. V., and A. V. Savin, 2014, “Normal heat conductivity in chains capable of dissociation,” Europhys. Lett. 106, 34004.
  65. Ghosh, S., W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, 2010, “Dimensional crossover of thermal transport in few-layer graphene,” Nat. Mater. 9, 555.
  66. Giardina, C., R. Livi, A. Politi, and M. Vassalli, 2000, “Finite Thermal Conductivity in 1D Lattices,” Phys. Rev. Lett. 84, 2144.
  67. Gong, Y., J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, and B. I. Yakobson, 2014, “Vertical and in-plane heterostructures from WS2/MoS2 monolayers,” Nat. Mater. 13, 1135.
  68. Goyal, V., D. Teweldebrhan, and A. A. Balandin, 2010, “Mechanically-Exfoliated Stacks of Thin Films of Bismuth Telluride Topological Insulators with Enhanced Thermoelectric Performance,” Appl. Phys. Lett., 97, 133117.
  69. Gu, X., B. Li, and R. G. Yang, 2016, “Layer thickness-dependent phonon properties and thermal conductivity of MoS2,” J. Appl. Phys. 119, 085106.
  70. Gu, X., and R. G. Yang, 2014, “Phonon transport in single-layer transition metal dichalcogenides: A first-principles study,” Appl. Phys. Lett. 105, 131903.
  71. Gu, X., and R. G. Yang, 2015, “First-principles prediction of phononic thermal conductivity of silicene: A comparison with graphene,” J. Appl. Phys. 117, 025102.
  72. Gu, X., and R. G. Yang, 2016, “Phonon transport in single-layer Mo1xWxS2 alloy embedded with WS2 nanodomains,” Phys. Rev. B 94, 075308.
  73. Guo, Z., D. Zhang, and X.-G. Gong, 2009, “Thermal conductivity of graphene nanoribbons,” Appl. Phys. Lett. 95, 163103.
  74. Gustafsson, M. V., T. Aref, A. F. Kockum, M. K. Ekström, G. Johansson, and P. Delsing, 2014, “Propagating phonons coupled to an artificial atom,” Science 346, 207.
  75. Han, H., et al., 2016, “Functionalization mediates heat transport in graphene nanoflakes,” Nat. Commun. 7, 11281.
  76. Hao, F., D. Fang, and Z. Xu, 2011, “Mechanical and thermal transport properties of graphene with defects,” Appl. Phys. Lett. 99, 041901.
  77. Haskins, J., A. Kınacı, C. Sevik, H. l. Sevinçli, G. Cuniberti, and T. Çağın, 2011, “Control of thermal and electronic transport in defect-engineered graphene nanoribbons,” ACS Nano 5, 3779.
  78. Henry, A., and G. Chen, 2008, “High thermal conductivity of single polyethylene chains using molecular dynamics simulations,” Phys. Rev. Lett. 101, 235502.
  79. Henry, A., and G. Chen, 2009, “Anomalous heat conduction in polyethylene chains: Theory and molecular dynamics simulations,” Phys. Rev. B 79, 144305.
  80. Hossain, M. S., F. Al-Dirini, F. M. Hossain, and E. Skafidas, 2015, “High performance graphene nano-ribbon thermoelectric devices by incorporation and dimensional tuning of nanopores,” Sci. Rep. 5, 11297.
  81. Hsieh, W.-P., B. Chen, J. Li, P. Keblinski, and D. G. Cahill, 2009, “Pressure tuning of the thermal conductivity of the layered muscovite crystal,” Phys. Rev. B 80, 180302.
  82. Hsieh, W.-P., M. D. Losego, P. V. Braun, S. Shenogin, P. Keblinski, and D. G. Cahill, 2011, “Testing the minimum thermal conductivity model for amorphous polymers using high pressure,” Phys. Rev. B 83, 174205.
  83. Hu, J., X. Ruan, and Y. P. Chen, 2009, “Thermal conductivity and thermal rectification in graphene nanoribbons: a molecular dynamics study,” Nano Lett. 9, 2730.
  84. Hu, J., S. Schiffli, A. Vallabhaneni, X. Ruan, and Y. P. Chen, 2010, “Tuning the thermal conductivity of graphene nanoribbons by edge passivation and isotope engineering: A molecular dynamics study,” Appl. Phys. Lett. 97, 133107.
  85. Huang, W., Q.-X. Pei, Z. Liu, and Y.-W. Zhang, 2012, “Thermal conductivity of fluorinated graphene: A non-equilibrium molecular dynamics study,” Chem. Phys. Lett. 552, 97.
  86. Imai, H., Y. Shimakawa, and Y. Kubo, 2001, “Large thermoelectric power factor in TiS 2 crystal with nearly stoichiometric composition,” Phys. Rev. B 64, 241104.
  87. Inyushkin, A. V. e., and A. Taldenkov, 2007, “On the phonon Hall effect in a paramagnetic dielectric,” JETP Lett. 86, 379.
  88. Issi, J.-P., J. Heremans, and M. S. Dresselhaus, 1983, “Electronic and lattice contributions to the thermal conductivity of graphite intercalation compounds,” Phys. Rev. B 27, 1333.
  89. Jackson, H. E., C. T. Walker, and T. F. McNelly, 1970, “Second sound in NaF,” Phys. Rev. Lett. 25, 26.
  90. Jain, A., and A. J. McGaughey, 2015, “Strongly anisotropic in-plane thermal transport in single-layer black phosphorene,” Sci. Rep. 5, 8501.
  91. Jang, H., J. D. Wood, C. R. Ryder, M. C. Hersam, and D. G. Cahill, 2015, “Anisotropic thermal conductivity of exfoliated black phosphorus,” Adv. Mater. 27, 8017.
  92. Jang, W., W. Bao, L. Jing, C. Lau, and C. Dames, 2013, “Thermal conductivity of suspended few-layer graphene by a modified T-bridge method,” Appl. Phys. Lett. 103, 133102.
  93. Jiang, J.-W., H. S. Park, and T. Rabczuk, 2013, “Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-Weber parametrization, mechanical properties, and thermal conductivity,” J. Appl. Phys. 114, 064307.
  94. Jiang, J.-W., B.-S. Wang, and J.-S. Wang, 2011a, “First principle study of the thermal conductance in graphene nanoribbon with vacancy and substitutional silicon defects,” Appl. Phys. Lett. 98, 113114.
  95. Jiang, J.-W., J.-S. Wang, and B.-S. Wang, 2011b, “Minimum thermal conductance in graphene and boron nitride superlattice,” Appl. Phys. Lett. 99, 043109.
  96. Jing, L., M. Hu, and L. Guo, 2013, “Thermal conductivity of hybrid graphene/silicon heterostructures,” J. Appl. Phys. 114, 153518.
  97. Jo, I., M. T. Pettes, J. Kim, K. Watanabe, T. Taniguchi, Z. Yao, and L. Shi, 2013, “Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride,” Nano Lett. 13, 550.
  98. Jo, I., M. T. Pettes, E. Ou, W. Wu, and L. Shi, 2014, “Basal-plane thermal conductivity of few-layer molybdenum disulfide,” Appl. Phys. Lett. 104, 201902.
  99. Ju, Y., and K. Goodson, 1999, “Phonon scattering in silicon films with thickness of order 100 nm,” Appl. Phys. Lett. 74, 3005.
  100. Katcho, N., J. Carrete, W. Li, and N. Mingo, 2014, “Effect of nitrogen and vacancy defects on the thermal conductivity of diamond: An ab initio Green’s function approach,” Phys. Rev. B 90, 094117.
  101. Kim, J. Y., J.-H. Lee, and J. C. Grossman, 2012, “Thermal transport in functionalized graphene,” ACS Nano 6, 9050.
  102. Kim, P., L. Shi, A. Majumdar, and P. L. McEuen 2001, “Thermal Transport Measurements of Individual Multiwalled Nanotubes,” Phys. Rev. Lett. 87, 215502.
  103. Kim, W., J. Zide, A. Gossard, D. Klenov, S. Stemmer, A. Shakouri, and A. Majumdar, 2006, “Thermal conductivity reduction and thermoelectric figure of merit increase by embedding nanoparticles in crystalline semiconductors,” Phys. Rev. Lett. 96, 045901.
  104. Kınacı, A., J. B. Haskins, C. Sevik, and T. Çağın, 2012, “Thermal conductivity of BN-C nanostructures,” Phys. Rev. B 86, 115410.
  105. Kittel, C., 2005, Introduction to Solid State Physics (Wiley, Hoboken, NJ).
  106. Klemens, P. G., 1955, “The scattering of low-frequency lattice waves by static imperfections,” Proc. Phys. Soc. London Sect. A 68, 1113.
  107. Klemens, P. G., 2000, “Theory of the a-plane thermal conductivity of graphite,” J. Wide Bandgap Mater. 7, 332.
  108. Klemens, P. G., and D. F. Pedraza, 1994, “Thermal conductivity of graphite in the basal plane,” Carbon 32, 735.
  109. Koh, Y. K., A. S. Lyons, M.-H. Bae, B. Huang, V. E. Dorgan, D. G. Cahill, and E. Pop, 2016, “Role of remote interfacial phonon (RIP) scattering in heat transport across graphene/SiO2 interfaces,” Nano Lett. 16, 6014.
  110. Koreeda, A., R. Takano, and S. Saikan, 2007, “Second sound in SrTiO3,” Phys. Rev. Lett. 99, 265502.
  111. Kuang, Y., L. Lindsay, and B. Huang, 2015, “Unusual enhancement in intrinsic thermal conductivity of multilayer graphene by tensile strains,” Nano Lett. 15, 6121.
  112. Kuang, Y., L. Lindsay, S. Shi, X. Wang, and B. Huang, 2016, “Thermal conductivity of graphene mediated by strain and size,” Int. J. Heat Mass Transfer 101, 772.
  113. Kuang, Y. D., L. Lindsay, S. Q. Shi, and G. Zheng, 2016, “Tensile strains give rise to strong size effects for thermal conductivities of silicene, germanene and stanene,” Nanoscale 8, 3760.
  114. Kundu, A., N. Mingo, D. Broido, and D. Stewart, 2011, “Role of light and heavy embedded nanoparticles on the thermal conductivity of SiGe alloys,” Phys. Rev. B 84, 125426.
  115. Lee, J.-U., D. Yoon, H. Kim, S. W. Lee, and H. Cheong, 2011, “Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy,” Phys. Rev. B 83, 081419.
  116. Lee, S., D. Broido, K. Esfarjani, and G. Chen, 2015, “Hydrodynamic phonon transport in suspended graphene,” Nat. Commun. 6, 6290.
  117. Lee, S., K. Hippalgaonkar, F. Yang, J. Hong, C. Ko, J. Suh, K. Liu, K. Wang, J. J. Urban, and X. Zhang, 2017, “Anomalously low electronic thermal conductivity in metallic vanadium dioxide,” Science 355, 371.
  118. Lee, S., et al., 2015, “Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K,” Nat. Commun. 6, 8573.
  119. Lepri, S., 1998, “Relaxation of classical many-body Hamiltonians in one dimension,” Phys. Rev. E 58, 7165.
  120. Lepri, S., R. Livi, and A. Politi, 1998, “On the anomalous thermal conductivity of one-dimensional lattices,” Europhys. Lett. 43, 271.
  121. Lepri, S., R. Livi, and A. Politi, 2003, “Thermal conduction in classical low-dimensional lattices,” Phys. Rep. 377, 1.
  122. Lepri, S., R. Livi, and A. Politi, 2016, Thermal Transport in Low Dimensions, Lecture Notes in Physics Vol. 921 (Springer, Berlin), pp. 1–37.
  123. Li, H., H. Ying, X. Chen, D. L. Nika, A. I. Cocemasov, W. Cai, A. A. Balandin, and S. Chen, 2014, “Thermal conductivity of twisted bilayer graphene,” Nanoscale 6, 13402.
  124. Li, H., Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and D. Baillargeat, 2012, “From bulk to monolayer MoS2: evolution of Raman scattering,” Adv. Funct. Mater. 22, 1385.
  125. Li, Q.-Y., K. Takahashi, H. Ago, X. Zhang, T. Ikuta, T. Nishiyama, and K. Kawahara, 2015, “Temperature dependent thermal conductivity of a suspended submicron graphene ribbon,” J. Appl. Phys. 117, 065102.
  126. Li, T., 2012, “Ideal strength and phonon instability in single-layer MoS 2,” Phys. Rev. B 85, 235407.
  127. Li, W., J. Carrete, and Natalio Mingo, 2013, “Thermal conductivity and phonon linewidths of monolayer MoS2 from first principles,” Appl. Phys. Lett. 103, 253103.
  128. Li, W., L. Lindsay, D. Broido, D. A. Stewart, and N. Mingo, 2012, “Thermal conductivity of bulk and nanowire   Mg2SixSn1x alloys from first principles,” Phys. Rev. B 86, 174307.
  129. Li, W., N. Mingo, L. Lindsay, D. A. Broido, D. A. Stewart, and N. A. Katcho, 2012, “Thermal conductivity of diamond nanowires from first principles,” Phys. Rev. B 85, 195436.
  130. Li, X., K. Maute, M. L. Dunn, and R. Yang, 2010, “Strain effects on the thermal conductivity of nanostructures,” Phys. Rev. B 81, 245318.
  131. Li, Z. Y., Y. Z Liu, L. Lindsay, Y. Xu, W-H. Duan, and E. Pop, 2017, “Size Dependence and Ballistic Limits of Thermal Transport in Anisotropic Layered Two-Dimensional Materials,” arXiv:1711.02772.
  132. Lindsay, L., and D. Broido, 2011, “Enhanced thermal conductivity and isotope effect in single-layer hexagonal boron nitride,” Phys. Rev. B 84, 155421.
  133. Lindsay, L., and D. Broido, 2012, “Theory of thermal transport in multilayer hexagonal boron nitride and nanotubes,” Phys. Rev. B 85, 035436.
  134. Lindsay, L., D. Broido, and N. Mingo, 2010a, “Diameter dependence of carbon nanotube thermal conductivity and extension to the graphene limit,” Phys. Rev. B 82, 161402.
  135. Lindsay, L., D. Broido, and N. Mingo, 2010b, “Flexural phonons and thermal transport in graphene,” Phys. Rev. B 82, 115427.
  136. Lindsay, L., D. Broido, and N. Mingo, 2011, “Flexural phonons and thermal transport in multilayer graphene and graphite,” Phys. Rev. B 83, 235428.
  137. Lindsay, L., W. Li, J. Carrete, N. Mingo, D. Broido, and T. Reinecke, 2014, “Phonon thermal transport in strained and unstrained graphene from first principles,” Phys. Rev. B 89, 155426.
  138. Lindsay, L. R., 2010, Ph.D. thesis (Boston College).
  139. Lippi, A., and R. Livi, 2000, “Heat conduction in two-dimensional nonlinear lattices,” J. Stat. Phys. 100, 1147.
  140. Liu, B., J. A. Baimova, C. D. Reddy, S. V. Dmitriev, W. K. Law, X. Q. Feng, and K. Zhou, 2014, “Interface thermal conductance and rectification in hybrid graphene/silicene monolayer,” Carbon 79, 236.
  141. Liu, B., F. Meng, C. D. Reddy, J. A. Baimova, N. Srikanth, S. V. Dmitriev, and K. Zhou, 2015, “Thermal transport in a graphene–MoS2 bilayer heterostructure: a molecular dynamics study,” RSC Adv. 5, 29193.
  142. Liu, B., C. Reddy, J. Jiang, J. A. Baimova, S. V. Dmitriev, A. A. Nazarov, and K. Zhou, 2012, “Morphology and in-plane thermal conductivity of hybrid graphene sheets,” Appl. Phys. Lett. 101, 211909.
  143. Liu, F., P. Ming, and J. Li, 2007, “Ab initio calculation of ideal strength and phonon instability of graphene under tension,” Phys. Rev. B 76, 064120.
  144. Liu, H., G. Qin, Y. Lin, and M. Hu, 2016, “Disparate Strain Dependent Thermal Conductivity of Two-dimensional Penta-Structures,” Nano Lett. 16, 3831.
  145. Liu, J., G.-M. Choi, and D. G. Cahill, 2014, “Measurement of the anisotropic thermal conductivity of molybdenum disulfide by the time-resolved magneto-optic Kerr effect,” J. Appl. Phys. 116, 233107.
  146. Liu, J., and R. Yang, 2012, “Length-dependent thermal conductivity of single extended polymer chains,” Phys. Rev. B 86, 104307.
  147. Liu, S., P Hänggi, N. Li, J. Ren, and B. Li, 2014, “Anomalous heat diffusion,” Phys. Rev. Lett. 112, 040601.
  148. Liu, T.-H., Y.-C. Chen, C.-W. Pao, and C.-C. Chang, 2014, “Anisotropic thermal conductivity of MoS2 nanoribbons: Chirality and edge effects,” Appl. Phys. Lett. 104, 201909.
  149. Liu, X., G. Zhang, Q.-X. Pei, and Y.-W. Zhang, 2013, “Phonon thermal conductivity of monolayer MoS2 sheet and nanoribbons,” Appl. Phys. Lett. 103, 133113.
  150. Luo, Z., J. Maassen, Y. Deng, Y. Du, R. P. Garrelts, M. S. Lundstrom, D. Y. Peide, and X. Xu, 2015, “Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus,” Nat. Commun. 6, 8572.
  151. Mai, T., and O. Narayan, 2006, “Universality of one-dimensional heat conductivity,” Phys. Rev. E 73, 061202.
  152. Majee, A. K. and Z. Aksamija, 2016, “Length divergence of the lattice thermal conductivity in suspended graphene nanoribbons,” Phys. Rev. B 93, 235423.
  153. Mak, K. F., C. H. Lui, and T. F. Heinz, 2010, “Measurement of the thermal conductance of the graphene/SiO2 interface,” Appl. Phys. Lett., 97, 221904.
  154. Malekpour, H., P. Ramnani, S. Srinivasan, G. Balasubramanian, D. L. Nika, A. Mulchandani, R. K. Lake, and A. A. Balandin, 2016, “Thermal conductivity of graphene with defects induced by electron beam irradiation,” Nanoscale 8, 14608.
  155. Mariani, E., and F. von Oppen, 2008, “Flexural phonons in free-standing graphene,” Phys. Rev. Lett. 100, 076801.
  156. Maruyama, S., 2002, “A molecular dynamics simulation of heat conduction in finite length SWNTs,” Physica B (Amsterdam) 323, 193.
  157. Mingo, N., and D. Broido, 2005, “Length dependence of carbon nanotube thermal conductivity and the “problem of long waves,” Nano Lett. 5, 1221.
  158. Mingo, N., K. Esfarjani, D. Broido, and D. Stewart, 2010, “Cluster scattering effects on phonon conduction in graphene,” Phys. Rev. B 81, 045408.
  159. Mohiuddin, T. M. G., et al., 2009, “Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation,” Phys. Rev. B 79, 205433.
  160. Morelli, D., and J. Heremans, 2002, “Thermal conductivity of germanium, silicon, and carbon nitrides,” Appl. Phys. Lett. 81, 5126.
  161. Mounet, N., and N. Marzari 2005, “First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives,” Phys. Rev. B 71, 205214.
  162. Mu, X., X. Wu, T. Zhang, D. B. Go, and T. Luo, 2014, “Thermal transport in graphene oxide-from ballistic extreme to amorphous limit,” Sci. Rep. 4, 3909.
  163. Narayan, O., and S. Ramaswamy, 2002, “Anomalous heat conduction in one-dimensional momentum-conserving systems,” Phys. Rev. Lett. 89, 200601.
  164. Narayanamurti, V., and R. Dynes, 1972, “Observation of second sound in bismuth,” Phys. Rev. Lett. 28, 1461.
  165. Nguyen, V. H., M. C. Nguyen, H. V. Nguyen, J. Saint-Martin, and P. Dollfus, 2014, “Enhanced thermoelectric figure of merit in vertical graphene junctions,” Appl. Phys. Lett., 105, 133105.
  166. Ni, Y., Y. Chalopin, and S. Volz, 2013, “Few layer graphene based superlattices as efficient thermal insulators,” Appl. Phys. Lett., 103, 141905.
  167. Nika, D. L., A. S. Askerov, and A. A. Balandin, 2012, “Anomalous size dependence of the thermal conductivity of graphene ribbons,” Nano Lett. 12, 3238.
  168. Nika, D. L., and A. A. Balandin, 2012, “Two-dimensional phonon transport in graphene,” J. Phys. Condens. Matter 24, 233203.
  169. Nika, D. L., and A. A. Balandin, 2017, “Phonons and thermal transport in graphene and graphene-based materials,” Rep. Prog. Phys. 80, 036502.
  170. Nika, D. L., A. I. Cocemasov, and A. A. Balandin, 2014, “Specific heat of twisted bilayer graphene: Engineering phonons by atomic plane rotations,” Appl. Phys. Lett. 105, 031904.
  171. Nika, D. L., S. Ghosh, E. P. Pokatilov, and A. A. Balandin, 2009, “Lattice thermal conductivity of graphene flakes: Comparison with bulk graphite,” Appl. Phys. Lett., 94, 203103.
  172. Nika, D. L., E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, 2009, “Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering,” Phys. Rev. B, 79, 155413.
  173. Omini, M., and A. Sparavigna, 1996, “Beyond the isotropic-model approximation in the theory of thermal conductivity,” Phys. Rev. B 53, 9064.
  174. Ong, Z.-Y., and E. Pop, 2011, “Effect of substrate modes on thermal transport in supported graphene,” Phys. Rev. B 84, 075471.
  175. Ouyang, T., Y. Chen, L.-M. Liu, Y. Xie, X. Wei, and J. Zhong, 2012, “Thermal transport in graphyne nanoribbons,” Phys. Rev. B 85, 235436.
  176. Ouyang, T., Y. Chen, Y. Xie, K. Yang, Z. Bao, and J. Zhong, 2010, “Thermal transport in hexagonal boron nitride nanoribbons,” Nanotechnology 21, 245701.
  177. Palomaki, T., J. Harlow, J. Teufel, R. Simmonds, and K. Lehnert, 2013, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature (London) 495, 210.
  178. Park, M., S.-C. Lee, and Y.-S. Kim, 2013, “Length-dependent lattice thermal conductivity of graphene and its macroscopic limit,” J. Appl. Phys. 114, 053506.
  179. Parrish, K. D., A. Jain, J. M. Larkin, W. A. Saidi, and A. J. McGaughey, 2014, “Origins of thermal conductivity changes in strained crystals,” Phys. Rev. B 90, 235201.
  180. Pei, Q.-X., Z.-D. Sha, and Y.-W. Zhang, 2011, “A theoretical analysis of the thermal conductivity of hydrogenated graphene,” Carbon 49, 4752.
  181. Peimyoo, N., J. Shang, W. Yang, Y. Wang, C. Cong, and T. Yu, 2015, “Thermal conductivity determination of suspended mono-and bilayer WS2 by Raman spectroscopy,” Nano Res. 8, 1210.
  182. Peng, B., H. Zhang, H. Shao, Y. Xu, X. Zhang, and H. Zhu, 2016, “Low lattice thermal conductivity of stanene,” Sci. Rep. 6, 20225.
  183. Pereira, L. F. C., and D. Donadio, 2013, “Divergence of the thermal conductivity in uniaxially strained graphene,” Phys. Rev. B 87, 125424.
  184. Pereverzev, A., 2003, “Fermi-Pasta-Ulam β lattice: Peierls equation and anomalous heat conductivity,” Phys. Rev. E 68, 056124.
  185. Pettes, M. T., I. Jo, Z. Yao, and L. Shi, 2011, “Influence of polymeric residue on the thermal conductivity of suspended bilayer graphene,” Nano Lett. 11, 1195.
  186. Pettes, M. T., J. Maassen, I. Jo, M. S. Lundstrom, and L. Shi, 2013, “Effects of surface band bending and scattering on thermoelectric transport in suspended bismuth telluride nanoplates,” Nano Lett. 13, 5316.
  187. Pettes, M. T., M. R. Sadeghi, H. Ji, I. Jo, W. Wei, R. S. Ruoff, and L. Shi, 2015, “Scattering of phonons by high-concentration isotopic impurities in ultrathin graphite,” Phys. Rev. B, 91, 035429.
  188. Picu, R., T. Borca-Tasciuc, and M. Pavel, 2003, “Strain and size effects on heat transport in nanostructures,” J. Appl. Phys. 93, 3535.
  189. Pohl, D. W., and V. Irniger, 1976, “Observation of second sound in NaF by means of light scattering,” Phys. Rev. Lett. 36, 480.
  190. Pop, E., V. Varshney, and A. K. Roy, 2012, “Thermal properties of graphene: Fundamentals and applications,” MRS Bull. 37, 1273.
  191. Poudel, B., et al., 2008, “High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys,” Science 320, 634.
  192. Prosen, T., and D. K. Campbell, 2000, “Momentum conservation implies anomalous energy transport in 1D classical lattices,” Phys. Rev. Lett. 84, 2857.
  193. Qian, X., X. Gu, M. S. Dresselhaus, and R. G. Yang, 2016, “Anisotropic Tuning on Graphite Thermal Conductivity by Lithium Intercalation,” J. Phys. Chem. Lett. 7, 4744.
  194. Qian, X., P. Q. Jiang, Y. Peng, X. Gu, Z. Liu, and R. G. Yang, 2018, “Anistropic Thermal Transport in van der Waals Layered Alloys WSe2(1x)Te2x,” Appl. Phys. Lett. 112, 241901.
  195. Qin, G., and M. Hu, 2016, in Diverse Thermal Transport Properties of Two-Dimensional Materials: A Comparative Review, edited by P. K. Nayak (InTech, Rijeka, Croatia).
  196. Qin, G., Z. Qin, W.-Z. Fang, L.-C. Zhang, S.-Y. Yue, Z.-B. Yan, M. Hu, and G. Su, 2016, “Diverse anisotropy of phonon transport in two-dimensional IV-VI compounds: A comparative study,” Nanoscale 8, 11306.
  197. Qin, G., X. Zhang, S.-Y. Yue, Z. Qin, H. Wang, Y. Han, and M. Hu, 2016, “Resonant bonding driven giant phonon anharmonicity and low thermal conductivity of phosphorene,” Phys. Rev. B 94, 165445.
  198. Qin, T., J. Zhou, and J. Shi, 2012, “Berry curvature and the phonon Hall effect,” Phys. Rev. B 86, 104305.
  199. Qiu, B., and X. Ruan, 2010, “Thermal conductivity prediction and analysis of few-quintuple Bi2Te3 thin films: A molecular dynamics study,” Appl. Phys. Lett. 97, 183107.
  200. Qiu, B., and X. Ruan, 2012, “Reduction of spectral phonon relaxation times from suspended to supported graphene,” Appl. Phys. Lett. 100, 193101.
  201. Ratsifaritana, C. A., and P. G. Klemens, 1987, “Scattering of phonons by vacancies,” Int. J. Thermophys. 8, 737.
  202. Ross, R. G., P. Andersson, B. Sundqvist, and G. Backstrom, 1984, “Thermal conductivity of solids and liquids under pressure,” Rep. Prog. Phys. 47, 1347.
  203. Sadeghi, M. M., I. Jo, and L. Shi, 2013, “Phonon-interface scattering in multilayer graphene on an amorphous support,” Proc. Natl. Acad. Sci. U.S.A. 110, 16321.
  204. Sadeghi, M. M., M. T. Pettes, and L. Shi, 2012, “Thermal transport in graphene,” Solid State Commun. 152, 1321.
  205. Sahoo, S., A. P. Gaur, M. Ahmadi, M. J.-F. Guinel, and R. S. Katiyar, 2013, “Temperature-dependent Raman studies and thermal conductivity of few-layer MoS2,” J. Phys. Chem. C 117, 9042.
  206. Sato, D. S., 2016, “Pressure-induced recovery of Fourier’s law in one-dimensional momentum-conserving systems,” Phys. Rev. E 94, 012115.
  207. Savin, V., and Y. A. Kosevich, 2014, “Thermal conductivity of molecular chains with asymmetric potentials of pair interactions,” Phys. Rev. E 89, 032102.
  208. Schmidt, A. J., X. Chen, and G. Chen, 2008, “Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance,” Rev. Sci. Instrum. 79, 114902.
  209. Seol, J. H., et al., 2010, “Two-dimensional phonon transport in supported graphene,” Science 328, 213.
  210. Sevik, C., A. Kinaci, J. B. Haskins, and T. Çağın, 2011, “Characterization of thermal transport in low-dimensional boron nitride nanostructures,” Phys. Rev. B 84, 085409.
  211. Sevinçli, H., W. Li, N. Mingo, G. Cuniberti, and S. Roche, 2011, “Effects of domains in phonon conduction through hybrid boron nitride and graphene sheets,” Phys. Rev. B 84, 205444.
  212. Shi, L., D. Li, C. Yu, W. Jang, D. Kim, Z. Yao, P. Kim, and A. Majumdar, 2003, “Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device,” J. Heat Transfer 125, 881.
  213. Singh, D., J. Y. Murthy, and T. S. Fisher, 2011, “Mechanism of thermal conductivity reduction in few-layer graphene,” J. Appl. Phys. 110, 044317.
  214. Singh, V., S. Bosman, B. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. Steele, 2014, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9, 820.
  215. Slack, G. A., 1973, “Nonmetallic crystals with high thermal conductivity,” J. Phys. Chem. Solids 34, 321.
  216. Song, J., and N. V. Medhekar, 2013, “Thermal transport in lattice-constrained 2D hybrid graphene heterostructures,” J. Phys. Condens. Matter 25, 445007.
  217. Strohm, C., G. Rikken, and P. Wyder, 2005, “Phenomenological evidence for the phonon Hall effect,” Phys. Rev. Lett. 95, 155901.
  218. Sullivan, S., A. Vallabhaneni, I. Kholmanov, X. Ruan, J. Murthy, and L. Shi, 2017, “Optical generation and detection of local non-equilibrium phonons in suspended graphene,” Nano Lett. 17, 2049.
  219. Sun, B., X. Gu, Q. Zeng, X. Huang, Y. Yan, Z. Liu, R. Yang, and Y. K. Koh, 2017, “Temperature Dependence of Anisotropic Thermal-Conductivity Tensor of Bulk Black Phosphorus,” Adv. Mater. 29, 1603297.
  220. Tamura, S.-i., 1983, “Isotope scattering of dispersive phonons in Ge,” Phys. Rev. B 27, 858.
  221. Tan, Z. W., J.-S. Wang, and C. K. Gan, 2011, “First-principles study of heat transport properties of graphene nanoribbons,” Nano Lett. 11, 214.
  222. Tang, X., S. Xu, J. Zhang, and X. Wang, 2014, “Five orders of magnitude reduction in energy coupling across corrugated graphene/substrate interfaces,” ACS Appl. Mater. Interfaces 6, 2809.
  223. Taube, A., J. Judek, A. Łapińska, and M. Zdrojek, 2015, “Temperature-dependent thermal properties of supported MoS2 monolayers,” ACS Appl. Mater. Interfaces 7, 5061.
  224. Teweldebrhan, D., V. Goyal, and A. A. Balandin, 2010, “Exfoliation and characterization of bismuth telluride atomic quintuples and quasi-two-dimensional crystals,” Nano Lett. 10, 1209.
  225. Tian, L., 2015, “Optoelectromechanical transducer: Reversible conversion between microwave and optical photons,” Ann. Phys. (Berlin) 527, 1.
  226. Tran, V. T., J. Saint-Martin, P. Dollfus, and S. Volz, 2017, “Optimizing the thermoelectric performance of graphene nano-ribbons without degrading the electronic properties,” Sci. Rep., 7, 2313.
  227. Vallabhaneni, A. K., D. Singh, H. Bao, J. Murthy, and X. Ruan, 2016, “Reliability of Raman measurements of thermal conductivity of single-layer graphene due to selective electron-phonon coupling: A first-principles study,” Phys. Rev. B 93, 125432.
  228. Venkatasubramanian, R., E. Siivola, T. Colpitts, and B. O’quinn, 2001, “Thin-film thermoelectric devices with high room-temperature figures of merit,” Nature (London) 413, 597.
  229. Wan, C., et al., 2015, “Flexible n-type thermoelectric materials by organic intercalation of layered transition metal dichalcogenide TiS2,” Nat. Mater. 14, 622.
  230. Wan, C., Y. Kodama, M. Kondo, R. Sasai, X. Qian, X. Gu, K. Koga, K. Yabuki, R. Yang, and K. Koumoto, 2015, “Dielectric mismatch mediates carrier mobility in organic-intercalated layered TiS2,” Nano Lett. 15, 6302.
  231. Wan, C., Y. Wang, W. Norimatsu, M. Kusunoki, and K. Koumoto, 2012, “Nanoscale stacking faults induced low thermal conductivity in thermoelectric layered metal sulfides,” Appl. Phys. Lett. 100, 101913.
  232. Wan, C., Y. Wang, N. Wang, and K. Koumoto, 2010, “Low-thermal-conductivity (MS)1+x(TiS2)2 (M=Pb, Bi, Sn) misfit layer compounds for bulk thermoelectric materials,” Materials 3, 2606.
  233. Wan, C., Y. Wang, N. Wang, W. Norimatsu, M. Kusunoki, and K. Koumoto, 2010, “Development of novel thermoelectric materials by reduction of lattice thermal conductivity,” Sci. Technol. Adv. Mater. 11, 044306.
  234. Wan, C., Y. Wang, N. Wang, W. Norimatsu, M. Kusunoki, and K. Koumoto, 2011, “Intercalation: building a natural superlattice for better thermoelectric performance in layered Chalcogenides,” J. Electron. Mater. 40, 1271.
  235. Wang, F. Q., S. Zhang, J. Yu, and Q. Wang, 2015, “Thermoelectric properties of single-layered SnSe sheet,” Nanoscale 7, 15962.
  236. Wang, H., and M. S. Daw, 2016, “Anharmonic renormalization of the dispersion of flexural modes in graphene using atomistic calculations,” Phys. Rev. B 94, 155434.
  237. Wang, J. Y., 2013, Ph.D. thesis (National University of Singapore).
  238. Wang, L., B. Hu, and B. Li, 2012, “Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices,” Phys. Rev. E 86, 040101.
  239. Wang, Li, B. Hu, and B. Li, 2013, “Validity of Fourier’s law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions,” Phys. Rev. E 88, 052112.
  240. Wang, Y., B. Qiu, and X. Ruan, 2012, “Edge effect on thermal transport in graphene nanoribbons: A phonon localization mechanism beyond edge roughness scattering,” Appl. Phys. Lett. 101, 013101.
  241. Wang, Y., A. K. Vallabhaneni, B. Qiu, and X. Ruan, 2014, “Two-dimensional thermal transport in graphene: a review of numerical modeling studies,” Nanoscale Micro. Thermophys. Eng. 18, 155.
  242. Wang, Y., N. Xu, D. Li, and J. Zhu, 2017, “Thermal Properties of Two Dimensional Layered Materials,” Adv. Funct. Mater. 27, 1604134.
  243. Ward, A., D. Broido, D. A. Stewart, and G. Deinzer, 2009, “Ab initio theory of the lattice thermal conductivity in diamond,” Phys. Rev. B 80, 125203.
  244. Wei, N., L. Xu, H.-Q. Wang, and J.-C. Zheng, 2011, “Strain engineering of thermal conductivity in graphene sheets and nanoribbons: a demonstration of magic flexibility,” Nanotechnology 22, 105705.
  245. Wei, Y., B. Wang, J. Wu, R. Yang, and M. L. Dunn, 2013, “Bending rigidity and Gaussian bending stiffness of single-layered graphene,” Nano Lett. 13, 26.
  246. Wei, Z., Y. Chen, and C. Dames, 2012, “Wave packet simulations of phonon boundary scattering at graphene edges,” J. Appl. Phys. 112, 024328.
  247. Wei, Z., Z. Ni, K. Bi, M. Chen, and Y. Chen, 2011, “In-plane lattice thermal conductivities of multilayer graphene films,” Carbon 49, 2653.
  248. Wei, Z., J. Yang, K. Bi, and Y. Chen, 2014, “Mode dependent lattice thermal conductivity of single layer graphene,” J. Appl. Phys. 116, 153503.
  249. Wei, Z., J. Yang, W. Chen, K. Bi, D. Li, and Y. Chen, 2014, “Phonon mean free path of graphite along the c-axis,” Appl. Phys. Lett. 104, 081903.
  250. Whittingham, M. S., and A. J. Jacobson, 1982, Intercalation Chemistry (Academic Press, New York).
  251. Wilson, J., and A. Yoffe, 1969, “The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties,” Adv. Phys. 18, 193.
  252. Xie, G., Y. Shen, X. Wei, L. Yang, H. Xiao, J. Zhong, and G. Zhang, 2014, “A Bond-order Theory on the Phonon Scattering by Vacancies in Two-dimensional Materials,” Sci. Rep. 4, 5085.
  253. Xie, H., L. Chen, W. Yu, and B. Wang, 2013, “Temperature dependent thermal conductivity of a free-standing graphene nanoribbon,” Appl. Phys. Lett. 102, 111911.
  254. Xie, H., T. Ouyang, É. Germaneau, G. Qin, M. Hu, and H. Bao, 2016, “Large tunability of lattice thermal conductivity of monolayer silicene via mechanical strain,” Phys. Rev. B 93, 075404.
  255. Xiong, D., J. Wang, Y. Zhang, and H. Zhao, 2010, “Heat conduction in two-dimensional disk models,” Phys. Rev. E 82, 030101.
  256. Xu, X., J. Chen, and B. Li, 2016, “Phonon thermal conduction in novel 2D materials,” J. Phys. Condens. Matter 28, 483001.
  257. Xu, X., L. F. Pereira, Y. Wang, J. Wu, K. Zhang, X. Zhao, S. Bae, C. T. Bui, R. Xie, and J. T. Thong, 2014, “Length-dependent thermal conductivity in suspended single-layer graphene,” Nat. Commun. 5, 3689.
  258. Xu, Y., X. Chen, B.-L. Gu, and W. Duan, 2009, “Intrinsic anisotropy of thermal conductance in graphene nanoribbons,” Appl. Phys. Lett. 95, 233116.
  259. Xu, Y., and G. Li, 2009, “Strain effect analysis on phonon thermal conductivity of two-dimensional nanocomposites,” J. Appl. Phys. 106, 114302.
  260. Xu, Y., Z. Li, and W. Duan, 2014, “Thermal and thermoelectric properties of graphene,” Small 10, 2182.
  261. Xu, Z., and M. J. Buehler, 2009, “Strain controlled thermomutability of single-walled carbon nanotubes,” Nanotechnology 20, 185701.
  262. Yan, J.-A., W. Y. Ruan, and M. Y. Chou, 2008, “Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene: Density-functional perturbation theory,” Phys. Rev. B 77, 125401.
  263. Yan, R., J. R. Simpson, S. Bertolazzi, J. Brivio, M. Watson, X. Wu, A. Kis, T. Luo, A. R. Hight Walker, and H. G. Xing, 2014, “Thermal conductivity of monolayer molybdenum disulfide obtained from temperature-dependent Raman spectroscopy,” ACS Nano 8, 986.
  264. Yan, X.-J., Y.-Y. Lv, L. Li, X. Li, S.-H. Yao, Y.-B. Chen, X.-P. Liu, H. Lu, M.-H. Lu, and Y.-F. Chen, 2017, “Composition dependent phase transition and its induced hysteretic effect in the thermal conductivity of WxMo1xTe2,” Appl. Phys. Lett. 110, 211904.
  265. Yan, Z., C. Jiang, T. Pope, C. Tsang, J. Stickney, P. Goli, J. Renteria, T. Salguero, and A. Balandin, 2013, “Phonon and thermal properties of exfoliated TaSe2 thin films,” J. Appl. Phys. 114, 204301.
  266. Yang, J., E. Ziade, C. Maragliano, R. Crowder, X. Wang, M. Stefancich, M. Chiesa, A. K. Swan, and A. J. Schmidt, 2014, “Thermal conductance imaging of graphene contacts,” J. Appl. Phys. 116, 023515.
  267. Yang, L., P. Grassberger, and B. Hu, 2006, “Dimensional crossover of heat conduction in low dimensions,” Phys. Rev. E 74, 062101.
  268. Yang, N., X. Xu, G. Zhang, and B. Li, 2012, “Thermal transport in nanostructures,” AIP Adv. 2, 041410.
  269. Yang, N., G. Zhang, and B. Li, 2010, “Violation of Fourier’s law and anomalous heat diffusion in silicon nanowires,” Nano Today 5, 85.
  270. Yang, R., and G. Chen, 2004, “Thermal conductivity modeling of periodic two-dimensional nanocomposites,” Phys. Rev. B 69, 195316.
  271. Yang, R., G. Chen, and M. S. Dresselhaus, 2005, “Thermal conductivity of simple and tubular nanowire composites in the longitudinal direction,” Phys. Rev. B 72, 125418.
  272. Ye, Z.-Q., B.-Y. Cao, W.-J. Yao, T. Feng, and X. Ruan, 2015, “Spectral phonon thermal properties in graphene nanoribbons,” Carbon 93, 915.
  273. Zabel, H., 2001, “Phonons in layered compounds,” J. Phys. Condens. Matter 13, 7679.
  274. Zeraati, M., S. M. V. Allaei, I. A. Sarsari, M. Pourfath, and D. Donadio, 2016, “Highly anisotropic thermal conductivity of arsenene: An ab initio study,” Phys. Rev. B 93, 085424.
  275. Zhang, G., and B. Li, 2005, “Thermal conductivity of nanotubes revisited: Effects of chirality, isotope impurity, tube length, and temperature,” J. Chem. Phys. 123, 114714.
  276. Zhang, G., and Y.-W. Zhang, 2017, “Thermal properties of two-dimensional materials,” Chin. Phys. B 26, 034401.
  277. Zhang, H., X. Chen, Y.-D. Jho, and A. J. Minnich, 2016, “Temperature-Dependent Mean Free Path Spectra of Thermal Phonons Along the c-Axis of Graphite,” Nano Lett. 16, 1643.
  278. Zhang, H., G. Lee, and K. Cho, 2011, “Thermal transport in graphene and effects of vacancy defects,” Phys. Rev. B 84, 115460.
  279. Zhang, H., C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, 2009, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5, 438.
  280. Zhang, J., Y. Hong, and Y. Yue, 2015, “Thermal transport across graphene and single layer hexagonal boron nitride,” J. Appl. Phys. 117, 134307.
  281. Zhang, L., J. Ren, J.-S. Wang, and B. Li, 2010, “Topological nature of the phonon Hall effect,” Phys. Rev. Lett. 105, 225901.
  282. Zhang, X., D. Sun, Y. Li, G.-H. Lee, X. Cui, D. Chenet, Y. You, T. F. Heinz, and J. C. Hone, 2015, “Measurement of lateral and interfacial thermal conductivity of single-and bilayer MoS2 and MoSe2 using refined optothermal raman technique,” ACS Appl. Mater. Interfaces 7, 25923.
  283. Zhang, Z.-W., S.-Q. Hu, J. Chen, and B. Li, 2017, “Hexagonal Boron nitride: A promising substrate for graphene with high heat dissipation,” Nanotechnology 28, 226704.
  284. Zhong, W.-R., M.-P. Zhang, B.-Q. Ai, and D.-Q. Zheng, 2011, “Chirality and thickness-dependent thermal conductivity of few-layer graphene: a molecular dynamics study,” Appl. Phys. Lett. 98, 113107.
  285. Zhong, Y., Y. Zhang, J. Wang, and H. Zhao, 2012, “Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions,” Phys. Rev. E 85, 060102.
  286. Zhu, G., J. Liu, Q. Zheng, R. Zhang, D. Li, D. Banerjee, and D. G. Cahill, 2016, “Tuning thermal conductivity in molybdenum disulfide by electrochemical intercalation,” Nat. Commun. 7, 13211.
  287. Zhu, J., et al., 2016, “Revealing the Origins of 3D Anisotropic Thermal Conductivities of Black Phosphorus,” Adv. Electron. Mater. 2, 1600040.
  288. Zhu, L., G. Zhang, and B. Li, 2014, “Coexistence of size-dependent and size-independent thermal conductivities in phosphorene,” Phys. Rev. B 90, 214302.
  289. Zhu, T., and E. Ertekin, 2014, “Phonon transport on two-dimensional graphene/boron nitride superlattices,” Phys. Rev. B 90, 195209.
  290. Ziman, J. M., 1960, Electrons and phonons: the theory of transport phenomena in solids (Oxford University Press, New York).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation