Ab initio real | Shandong Forgingss Group

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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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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.

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 Perturbo, which can be obtained at https://perturbo-code.github.io.

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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.

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

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

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

Yongliang Shi

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

Jin-Jian Zhou

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

Oleg V. Prezhdo

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

Jin Zhao

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

Jin Zhao

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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.

Correspondence to Yongliang Shi, Qijing Zheng or Jin Zhao.

The authors declare no competing interests.

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

Source data for Supplementary Fig. 1.

Source data for Supplementary Fig. 2.

Source data for Supplementary Fig. 3.

Statistical source data.

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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 (2023). https://doi.org/10.1038/s43588-023-00456-9

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Received: 09 November 2022

Accepted: 21 April 2023

Published: 01 June 2023

DOI: https://doi.org/10.1038/s43588-023-00456-9

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