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Ab initio real-time quantum dynamics of charge carriers in momentum space

Nature Computational Science volume 3, pages 532–541 (2023)Cite this article

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Abstract

Application of the non-adiabatic molecular dynamics (NAMD) approach is limited to studying carrier dynamics in the momentum space, as a supercell is required to sample the phonon excitation and electron–phonon (e–ph) interaction at different momenta in a molecular dynamics simulation. Here we develop an ab initio approach for the real-time charge carrier quantum dynamics in the momentum space (NAMD_k) by directly introducing e–ph coupling into the Hamiltonian based on the harmonic approximation. The NAMD_k approach maintains the zero-point energy and includes memory effects of carrier dynamics. The application of NAMD_k to the hot carrier dynamics in graphene reveals the phonon-specific relaxation mechanism. An energy threshold of 0.2 eV—defined by two optical phonon modes—separates the hot electron relaxation into fast and slow regions with lifetimes of pico- and nanoseconds, respectively. The NAMD_k approach provides an effective tool to understand real-time carrier dynamics in the momentum space for different materials.

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Fig. 1: Hot electron relaxation in graphene with Eini = 1.0 eV using 150 × 150 × 1k-point grid.
Fig. 2: Hot electron relaxation in graphene with different Eini.
Fig. 3: Time-dependent phonon excitation during the hot electron relaxation dynamics.
Fig. 4: Electron temperature evolution in graphene.
Fig. 5: Comparison of NAMD_r and NAMD_k simulations.

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Data availability

These data are obtained by NAMD_k simulations using our homemade code56,57. The source data for Figs. 1–5, Supplementary Figs. 1–3 and input files for NAMD_k simulations have been deposited in the Materials Cloud Archive at https://doi.org/10.24435/materialscloud:2n-3j. Source Data are provided with this paper.

Code availability

The code for our algorithm and a guide to reproducing the results is available at GitHub56 and Code Ocean57. In the calculation, e–ph coupling is calculated by the package Perturbo58, which can be obtained at https://perturbo-code.github.io.

Change history

  • 15 June 2023

    In the version of this article initially published, a reference (https://doi.org/10.1016/j.cpc.2021.107970) for the Perturbo software package listed in the Code availability section was missing and has now been amended in the HTML and PDF versions of the article.

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Acknowledgements

J.Z. acknowledges the support of the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0303306); the National Natural Science Foundation of China (NSFC, grant nos. 12125408 and 11974322); and the informatization plan of Chinese Academy of Sciences (grant no. CAS-WX2021SF-0105). Q.Z. acknowledges the support of the NSFC (grant no. 12174363). O.V.P. acknowledges funding of the US National Science Foundation (grant no. CHE-2154367). Calculations were performed at the Hefei Advanced Computing Center, the Supercomputing Center at USTC, and the ORISE Supercomputer. We received no specific funding for this work.

Author information

Authors and Affiliations

  1. Department of Physics, ICQD/Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, China

    Zhenfa Zheng, Yongliang Shi, Qijing Zheng & Jin Zhao

  2. Center for Spintonics and Quantum Systerms, State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an, China

    Yongliang Shi

  3. State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China

    Yongliang Shi

  4. School of Physics, Beijing Institute of Technology, Beijing, China

    Jin-Jian Zhou

  5. Departments of Chemistry, Physics, and Astronomy, University of Southern California, Los Angeles, CA, USA

    Oleg V. Prezhdo

  6. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA

    Jin Zhao

  7. Hefei National Laboratory, University of Science and Technology of China, Hefei, China

    Jin Zhao

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Contributions

Y.S. contributed to this work before March 2022. J.Z. supervised the research project. Y.S. conceived the original idea. J.Z., Q.Z., Y.S. and Z.Z. developed the method, whereas J.-J.Z. and O.V.P. provided suggestions to improve the method. Q.Z. constructed the original Hefei-NAMD code. Z.Z. developed the NAMD_k version of Hefei-NAMD on the basis of the original Hefei-NAMD code, performed the NAMD_k simulation of graphene, and data analysis, with help from Q.Z. J.-J.Z. provided the patch of PERTURBO package for outputting e–ph matrix elements data. J.Z., Q.Z. and Z.Z. wrote the manuscript. The manuscript reflects the contributions of all authors.

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Correspondence to Yongliang Shi, Qijing Zheng or Jin Zhao.

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Nature Computational Science thanks Jun Yin, Sergei Tretiak, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Proof of zero non-adiabatic coupling for Bloch states with different momenta, and Supplementary Figs. 1–3.

Supplementary Data 1

Source data for Supplementary Fig. 1.

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Source Data Fig. 2

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Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

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Source Data Fig. 5

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Zheng, Z., Shi, Y., Zhou, JJ. et al. Ab initio real-time quantum dynamics of charge carriers in momentum space. Nat Comput Sci 3, 532–541 (2023). https://doi.org/10.1038/s43588-023-00456-9

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