Full counting statistics of phonon transport in disordered systems

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.

Keywords

phonon transport / disordered systems / coherent potential approximation / full counting statistics

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)

[2] R. Su, Z. Yuan, J. Wang, and Z. G. Zheng, Interfacefacilitated energy transport in coupled Frenkel–Kontorova chains, Front. Phys. 11(2), 114401 (2016)

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

[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)

[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)

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

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

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

[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)

[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)

[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)

[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)

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

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

[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)

[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)

[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)

[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)

[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)

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

[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)

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

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

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

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

RIGHTS & PERMISSIONS

Higher Education Press