Quantum mechanical analyses of nanoscale phonon transport

2019 Fiscal Year Annual Research Report

• Project/Area Number: 19F19353
• Research Institution: The University of Tokyo
• Principal Investigator: 野村 政宏 東京大学, 生産技術研究所, 准教授 (10466857)
• Co-Investigator(Kenkyū-buntansha): GUO YANGYU 東京大学, 生産技術研究所, 外国人特別研究員
• Project Period (FY): 2019-11-08 – 2022-03-31
• Keywords: Anharmonic phonon NEGF / Fourier’s representation / MPI parallelization / heat transport

Outline of Annual Research Achievements

Within the past half year since the support of JSPS fellowship, I have been mainly focused on the theoretical foundation and numerical implementation of the anharmonic phonon NEGF (non-equilibrium Green’s function) for quantum mechanical modeling of heat transport at nanoscale. The research achievements mainly include the following three aspects:
(1) Derivation and clarification of the previously ambiguous theoretical formula of phonon-phonon scattering self-energy in the anharmonic NEGF formalism through a rigorous perturbative expansion to the contour-ordered phonon Green’s function by Feynman’s diagrammatic technique.
(2) We further introduce the Fourier’s representation of the anharmonic phonon NEGF formalism for heat transport through layered nanostructures with transverse periodicity. This technique is crucial for quantum mechanical modeling of coherent and incoherent heat transport through interface and superlattices.
(3) We have built an efficient anharmonic NEGF FORTRAN code with MPI parallelization scheme for heat transport through interface. The anharmonic NEGF code has been tested on the supercomputer in the University of Tokyo and achieves good parallelization efficiency.

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

We have been mainly focused on the development of the methodology and computational framework as the code from our collaborator in ETH Zurich has big problem in both principle and numerical aspects. In the future, we will focus more on the modeling and physics of coherent and incoherent heat transport through interfaces and superlattices.

Strategy for Future Research Activity

In the future, our research will be mainly focused on:
(1) The influence of temperature and anharmonic phonon-phonon scattering on heat transport through interface will be studied based on our present parallelized FORTRAN code. The discrimination between previous harmonic NEGF result and experimental data of thermal boundary conductance will be explained by our new anharmonic NEGF formalism. The unclear physics of phonon mode conversion and the debated role of anharmonicity at the interface will be declared.
(2) Extend our present code to heat transport through larger nanostructures like superlattices by introducing the recursive algorithm. The recursive algorithm is very efficient as the computational cost is linearly proportional to the system size. On the other hand, as the present formalism is still too computationally intensive, some reasonable approximations must be introduced as well to simulate large nano-systems.
(3) Once the whole numerical framework is established, we will investigate the transition from coherent to incoherent heat transport in superlattices. The influence of anharmonicity on the wave nature of phonons will be elucidated.