Crossover to Quantized Thermal Conductance in Nanotubes and Nanowires

Abstract

Using the non-equilibrium Green’s function techniques with interatomic potentials, we study the temperature dependence and the crossover of thermal conductance from the usual behavior proportional to the cross-sectional area at room temperature to the universal quantized behavior at low temperature for carbon nanotubes, silicon nanowires, and diamond nanowires. We find that this crossover of thermal conductance occurs smoothly for the quasi-one-dimensional materials and its universal behavior is well reproduced by the simplified model characterized by two parameters.

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K. Yamamoto, H. Ishii, N. Kobayashi and K. Hirose, "Crossover to Quantized Thermal Conductance in Nanotubes and Nanowires," Open Journal of Composite Materials, Vol. 3 No. 2A, 2013, pp. 48-54. doi: 10.4236/ojcm.2013.32A007.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. I. Boukai, Y. Bunimovich, J. T. Kheli, J.-K. Yu, W. A. Goddard III and J. R. Heath, “Silicon Nanowires as Efficient Thermoelectric Materials,” Nature, Vol. 451, 2008, pp. 168-171. doi:10.1038/nature06458
[2] L. G. C. Rego and G. Kirczenow, “Fractional Exclusion Statistics and the Universal Quantum of Thermal Conductance: A Unifying Approach,” Physical Review B, Vol. 59, No. 20, 1999, pp. 13080-13086. doi:10.1103/PhysRevB.59.13080
[3] K. Schwab, E. A. Henriksen, J. M. Worlock and L. Roukes, “Letters to Nature,” Nature, Vol. 404, 2000, pp. 974-977. doi:10.1038/35010065
[4] O. Chiatti, J. T. Nicholls, Y. Y. Proskuryakov, N. Lumpkin, I. Farrer and D. A. Ritchie, “Quantum Thermal Conductance of Electrons in a One-Dimensional Wire,” Physical Review Letters, Vol. 97, 2006, Article ID: 056601. doi:10.1103/PhysRevLett.97.056601
[5] M. Meschke, W. Guichard and J. P. Pekola, “Single-Mode Heat Conduction by Photons,” Nature, Vol. 444, 2006, pp. 187-190. doi:10.1038/nature05276
[6] Y. Dubi and M. Di Ventra, “Colloquium: Heat Flow and Thermoelectricity in Atomic and Molecular Junctions,” Reviews of Modern Physics, Vol. 83, No. 1, 2011, pp. 131-156.
[7] M. Büttiker, Y. Imry, R. Landauer and S. Pinhas, “Generalized Many-Channel Conductance Formula with Application to Small Rings,” Physical Review B, Vol. 31, 1985, pp. 6207-6215. doi:10.1103/PhysRevB.31.6207
[8] L. V. Keldysh, “Diagram Technique for Nonequilibrium Processes,” Soviet Physics—JETP, Vol. 20, No. 4, 1965, pp. 1018-1026.
[9] C. Caroli, R. Combescot, P. Nozieres and D. Saint-James, “Direct Calculation of the Tunneling Current,” Journal of Physics C: Solid State Physics, Vol. 4, No. 8, 1971, p. 916. doi:10.1088/0022-3719/4/8/018
[10] Y. Meir and N. S. Wingreen, “Landauer Formula for the Current through an Interacting Electron Region,” Physical Review Letters, Vol. 68, No. 16, 1992, pp. 2512-2515. doi:10.1103/PhysRevLett.68.2512
[11] A. Ozpineci and S. Ciraci, “Quantum Effects of Thermal Conductance through Atomic Chains,” Physical Review B, Vol. 63, No. 12, 2001, Article ID: 125415. doi:10.1103/PhysRevB.63.125415
[12] N. Mingo and L. Yang, “Phonon Transport in Nanowires Coated with an Amorphous Material: An Atomistic Green’s Function Approach,” Physical Review B, Vol. 68, No. 24, 2003, Article ID: 245406. doi:10.1103/PhysRevB.68.245406
[13] T. Yamamoto and K. Watanabe, “Nonequilibrium Green’s Function Approach to Phonon Transport in Defective Carbon Nanotubes,” Physical Review Letters, Vol. 96, No. 25, 2006, Article ID: 255503. doi:10.1103/PhysRevLett.96.255503
[14] K. Yamamoto, H. Ishii, N. Kobayashi and K. Hirose, “Effects of Vacancy Defects on Thermal Conduction of Silicon Nanowire: Nonequilibrium Green’s Function Approach,” Applied Physics Express, Vol. 4, 2011, Article ID: 085001. doi:10.1143/APEX.4.085001
[15] M. P. Lopez-Sancho, J. M. Lopez-Sancho and J. Rubio, “Quick Iterative Scheme for the Calculation of Transfer Matrices: Application to Mo (100),” Journal of Physics F: Metal Physics, Vol. 14, No. 5, 1984, p. 1205. doi:10.1088/0305-4608/14/5/016
[16] J. Tersoff, “Empirical Interatomic Potential for Silicon with Improved Elastic Properties,” Physical Review B, Vol. 38, No. 14, 1988, pp. 9902-9905. doi:10.1103/PhysRevB.38.9902
[17] D. W. Brenner, “Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films,” Physical Review B, Vol. 42, No. 15, 1990, pp. 9458-9471. doi:10.1103/PhysRevB.42.9458
[18] D. Li, Y. Wu, P. Kim, L. Shi, P. Yang and A. Majumdar, “Thermal Conductivity of Individual Silicon Nanowires,” Applied Physics Letters, Vol. 83, No. 14, 2003, p. 2934.

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