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Full counting statistics of phonon transport in disordered systems

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Abstract

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.

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References

  1. Z. Liu, X. Yu, and K. Chen, Thermal transport associated with ballistic phonons in asymmetric quantum structures, Front. Phys. China 4(3), 420 (2009)

    Article  ADS  Google Scholar 

  2. R. Su, Z. Yuan, J. Wang, and Z. G. Zheng, Interface-facilitated energy transport in coupled Frenkel-Kontorova chains, Front. Phys. 11(2), 114401 (2016)

    Article  ADS  Google Scholar 

  3. T. Yamamoto, S. Watanabe, and K. Watanabe, Universal features of quantized thermal conductance of carbon nanotubes, Phys. Rev. Lett. 92(7), 075502 (2004)

    Article  ADS  Google Scholar 

  4. C. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Breakdown of Fourier’s law in nanotube thermal conductors, Phys. Rev. Lett. 101(7), 075903 (2008)

    Article  ADS  Google Scholar 

  5. X. Chen, Y. Xu, J. Wang, and H. Guo, Valley filtering effect of phonons in graphene with a grain boundary, Phys. Rev. B 99(6), 064302 (2019)

    Article  ADS  Google Scholar 

  6. P. Wang, L. Lu, and K. Bertoldi, Topological phononic crystals with one-way elastic edge waves, Phys. Rev. Lett. 115(10), 104302 (2015)

    Article  ADS  Google Scholar 

  7. S. H. Mousavi, A. B. Khanikaev, and Z. Wang, Topologically protected elastic waves in phononic metamaterials, Nat. Commun. 6(1), 8682 (2015)

    Article  ADS  Google Scholar 

  8. R. Süsstrunk and S. D. Huber, Observation of phononic helical edge states in a mechanical topological insulator, Science 349(6243), 47 (2015)

    Article  ADS  Google Scholar 

  9. Z. Y. Ong and C. H. Lee, Transport and localization in a topological phononic lattice with correlated disorder, Phys. Rev. B 94(13), 134203 (2016)

    Article  ADS  Google Scholar 

  10. H. B. Zhou, G. Zhang, J. S. Wang, and Y. W. Zhang, Phonon transport in a one-dimensional harmonic chain with long-range interaction and mass disorder, Phys. Rev. E 94(5), 052123 (2016)

    Article  ADS  Google Scholar 

  11. Y. Q. Ke, K. Xia, and H. Guo, Disorder scattering in magnetic tunnel junctions: Theory of nonequilibrium vertex correction, Phys. Rev. Lett. 100(16), 166805 (2008)

    Article  ADS  Google Scholar 

  12. Y. Q. Ke, K. Xia, and H. Guo, Oxygen-vacancy-induced diffusive scattering in Fe/MgO/Fe magnetic tunnel junctions, Phys. Rev. Lett. 105(23), 236801 (2010)

    Article  ADS  Google Scholar 

  13. P. Soven, Coherent-potential model of substitutional disordered alloys, Phys. Rev. 156(3), 809 (1967)

    Article  ADS  Google Scholar 

  14. D. W. Taylor, Vibrational properties of imperfect crystals with large defect concentrations, Phys. Rev. 156(3), 1017 (1967)

    Article  ADS  Google Scholar 

  15. X. X. Ni, M. L. Leek, J. S. Wang, Y. P. Feng, and B. W. Li, Anomalous thermal transport in disordered harmonic chains and carbon nanotubes, Phys. Rev. B 83(4), 045408 (2011)

    Article  ADS  Google Scholar 

  16. J. X. Zhai, Q. Y. Zhang, Z. H. Cheng, J. Ren, Y. Q. Ke, and B. W. Li, Anomalous transparency induced by cooperative disorders in phonon transport, Phys. Rev. B 99(19), 195429 (2019)

    Article  ADS  Google Scholar 

  17. Z. H. Cheng, J. X. Zhai, Q. Y. Zhang, and Y. Q. Ke, Auxiliary coherent medium theory for lattice vibrations in random binary alloys with mass and force-constant disorders, Phys. Rev. B 99(13), 134202 (2019)

    Article  ADS  Google Scholar 

  18. W. R. Mondal, T. Berlijn, M. Jarrell, and N. S. Vidhyadhiraja, Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green’s function approach, Phys. Rev. B 99(13), 134203 (2019)

    Article  ADS  Google Scholar 

  19. B. Fu, L. Zhang, Y. Wei, and J. Wang, Full counting statistics of conductance for disordered systems, Phys. Rev. B 96(11), 115410 (2017)

    Article  ADS  Google Scholar 

  20. J. A. Young and J. U. Koppel, Phonon spectrum of graphite, J. Chem. Phys. 42(1), 357 (1965)

    Article  ADS  Google Scholar 

  21. R. A. Jishi, L. Venkataraman, M. S. Dresselhaus, and G. Dresselhaus, Phonon modes in carbon nanotubules, Chem. Phys. Lett. 209(1–2), 77 (1993)

    Article  ADS  Google Scholar 

  22. L. G. C. Rego and G. Kirczenow, Quantized thermal conductance of dielectric quantum wires, Phys. Rev. Lett. 81(1), 232 (1998)

    Article  ADS  Google Scholar 

  23. M. P. Blencowe, Quantum energy flow in mesoscopic dielectric structures, Phys. Rev. B 59(7), 4992 (1999)

    Article  ADS  Google Scholar 

  24. J. S. Wang, J. Wang, and J. T. Lü, Quantum thermal transport in nanostructures, Eur. Phys. J. B 62(4), 381 (2008)

    Article  ADS  Google Scholar 

  25. X. Chen, Y. Liu, and W. Duan, Thermal engineering in low-dimensional quantum devices: A tutorial review of nonequilibrium Green’s function methods, Small Methods 2(6), 1700343 (2018)

    Article  Google Scholar 

  26. M. P. Lopez Sancho, J. M. Lopez Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F: Met. Phys. 15, 851 (1985)

    Article  ADS  Google Scholar 

  27. Z. Yu, G. M. Tang, and J. Wang, Full-counting statistics of transient energy current in mesoscopic systems, Phys. Rev. B 93(19), 195419 (2016)

    Article  ADS  Google Scholar 

  28. G. M. Tang, Z. Yu, and J. Wang, Full-counting statistics of energy transport of molecular junctions in the polaronic regime, New J. Phys. 19(8), 083007 (2017)

    Article  ADS  Google Scholar 

  29. G. M. Tang and J. Wang, Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green’s function approach, Phys. Rev. B 90(19), 195422 (2014)

    Article  ADS  Google Scholar 

  30. G. M. Tang, Y. Xing, and J. Wang, Short-time dynamics of molecular junctions after projective measurement, Phys. Rev. B 96(7), 075417 (2017)

    Article  ADS  Google Scholar 

  31. J. S. Wang, B. K. Agarwalla, H. Li, and J. Thingna, Nonequilibrium Green’s function method for quantum thermal transport, Front. Phys. 9(6), 673 (2014)

    Article  ADS  Google Scholar 

  32. L. Zhang, B. Fu, B. Wang, Y. Wei, and J. Wang, Frequency-dependent transport properties in disordered systems: A generalized coherent potential approximation approach, Phys. Rev. B 99(15), 155406 (2019)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 12034014) and the Natural Science Foundation of Guangdong Province (Grant No. 2020A1515011418).

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Authors and Affiliations

  1. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China

    Chao Zhang, Fuming Xu & Jian Wang

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  1. Chao Zhang
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  2. Fuming Xu
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  3. Jian Wang
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Corresponding authors

Correspondence to Fuming Xu or Jian Wang.

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This article can also be found at http://journal.hep.com.cn/fop/EN/https://doi.org/10.1007/s11467-020-1027-8.

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Zhang, C., Xu, F. & Wang, J. Full counting statistics of phonon transport in disordered systems. Front. Phys. 16, 33502 (2021). https://doi.org/10.1007/s11467-020-1027-8

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  • DOI: https://doi.org/10.1007/s11467-020-1027-8

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