Full counting statistics of phonon transport in disordered systems
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Front. Phys. 16(3), 33502 (2021)
Research article Full counting statistics of phonon transport in disordered systems Chao Zhang, Fuming Xu† , Jian Wang‡ College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China Corresponding authors. E-mail: † [email protected], ‡ [email protected] Received October 2, 2020; accepted October 27, 2020
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
1 Introduction Due to the advancement of nanotechnology, the feature size of electronic devices has reached nanoscale. Power dissipation of nano-devices increases as they become smaller which may limit device size and density. Hence it is important to study how power dissipation especially Joule heat is dissipated in nano-devices. Since phonon transport is one of the primary dissipation mechanisms, investigating phonon transport through nano-devices [1, 2] can obtain important information in order to design low power devices. From scientific point of view, phonon quantum transport has shown a number of interesting phenomena such as the quantized thermal conductance [3], breakdown of Fourier’s law in nanoscale systems [4], phonon filtering [5], and topological phononic crystals [6–8], to name just a few. Impurities are always present in nano-devices giving rise to disorders for phonon transport, which has been studied for various disordered systems. For topological phononic systems, it was found that the topological edge state is intact in the presence of uncorrelated disorder and is gradually destroyed when the disorder is spatially correlated [9]. For one-dimensional harmonic chain with mass disorders, the effect of long-range interaction on phonon transport was examined and found to enhance (reduce) ∗ arXiv:
2011.04231. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467020-1027-8.
the transmission of high (low) frequency phonon [10]. To avoid huge computational burden of the brute force calculation of disorder average, the non-equilibrium vertex correction (NVC) theory [11, 12] within coherent potential appr
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