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  Theory for all-optical responses in topological materials: The velocity gauge picture

Kim, D., Shin, D., Landsman, A. S., Kim, D. E., & Chacón, A. (2022). Theory for all-optical responses in topological materials: The velocity gauge picture. Physical Review B, 106(21): 214314. doi:10.1103/PhysRevB.106.214314.

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PhysRevB.106.214314.pdf (Publisher version), 7MB
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https://doi.org/10.1103/PhysRevB.106.214314 (Publisher version)
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https://arxiv.org/abs/2105.12294 (Preprint)
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 Creators:
Kim, D.1, 2, Author
Shin, D.3, 4, 5, Author           
Landsman, A. S.2, 6, Author
Kim, D. E.1, 2, Author
Chacón, A.1, 2, Author
Affiliations:
1Department of Physics and Center for Attosecond Science and Technology, POSTECH, ou_persistent22              
2Max Planck POSTECH/KOREA Research Initiative, ou_persistent22              
3Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
4Center for Free-Electron Laser Science, ou_persistent22              
5Department of Physics and Photon Science, Gwangju Institute of Science and Technology (GIST), ou_persistent22              
6Department of Physics, Ohio State University, ou_persistent22              

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 Abstract: High-order harmonic generation (HHG), which has been widely studied in atomic gas, has recently been expanded to solids to study the highly nonlinear electronic response in condensed matter and produce coherent high-frequency radiation. Recently, attention has turned to topological materials and the use of HHG to characterize topological bands and invariants. However, the theoretical interpretation of the nonlinear electronic response in topological materials presents many challenges. In particular, the Bloch wavefunction phase of topological materials has undefined points in the Brillouin zone. This leads to singularities in the calculation of the interband and intraband transition dipole matrix elements of the semiconductor Bloch equations (SBEs). Here, we use the laser-electromagnetic velocity gauge p⋅A(t) to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra with better numerical efficiency and more straightforward implementation. We used a prototype of Chern insulators (CIs), the Haldane model, to demonstrate our approach. The validity of the velocity gauge approach is demonstrated in the following way: for topologically trivial materials such as MoS2, qualitative agreement is achieved with the results of the length gauge approach and the time-dependent density functional theory. For the application of the velocity gauge approach to topological materials, Chern insulator is taken, using the two-band Haldane model. We found a good qualitative agreement between the velocity gauge and the length gauge approach in view of (i) the selection rules, (ii) the linear cutoff law scaling, and (iii) anomalous circular dichroism. We conclude that the velocity-gauge approach for HHG provides a theoretical tool to investigate topological materials.

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Language(s): eng - English
 Dates: 2022-11-022021-05-272022-12-152022-12-262022-12-01
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevB.106.214314
arXiv: 2105.12294
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Project name : We thank professor Angel Rubio's group for calculating the TDDFT result for MoS2. We also thank professor Misha Ivanov from the Max Born Institute for sharing computational data related to the Wannier approach in order to compare it with our model. D.K., D.E.K., and A.C. acknowledge support by the National Research Foundation of Korea (NRF) Grants (Grants No. 2016K1A4A4A01922028, No. 2022M3H4A1A04074153, No. 2020R1A2C2103181, and No. RS-2022-00154676) funded by the Ministry of Science, ICT, and by Korea Institute for Advancement of Technology(KIAT) grant funded by the Korea Government(MOTIE) (P0008763, HRD Program for Industrial Innovation). D.S. is supported by the Alexander von Humboldt Foundation. A.S.L. acknowledges support from the Center for Emergent Materials through NSF grant number DMR-2011876.
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Source 1

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Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 106 (21) Sequence Number: 214314 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008