Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material

Journal Article · 09 October 2022 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.2204804119 · OSTI ID:2471419

Shao, Zhibin ^[1]; Li, Shaojian ^[2]; Liu, Yanzhao ^[3]; Li, Zi  ^[4]; Wang, Huichao ^[5]; Bian, Qi ^[2]; Yan, Jiaqiang ^[6]; Mandrus, David ^[7]; Liu, Haiwen  ^[8]; Zhang, Ping  ^[9]; Xie, X. C. ^[10]; Wang, Jian  ^[10]; Pan, Minghu  ^[11]

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1. Shaanxi Normal University, Xi’an (China)
2. Huazhong University of Science and Technology, Wuhan (China)
3. Peking University, Beijing (China)
4. Institute of Applied Physics and Computational Mathematics (IAPCM), Beijing (China)
5. Sun Yat-sen University, Guangzhou (China)
6. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
7. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); University of Tennessee, Knoxville, TN (United States)
8. Beijing Normal University, Beijing (China)
9. Institute of Applied Physics and Computational Mathematics (IAPCM), Beijing (China); Qufu Normal University (China)
10. Peking University, Beijing (China); Collaborative Innovation Center of Quantum Matter, Beijing (China); University of Chinese Academy of Sciences, Beijing (China); Beijing Academy of Quantum Information Sciences (China)
11. Shaanxi Normal University, Xi’an (China); Huazhong University of Science and Technology, Wuhan (China)

Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe₅) and hafnium pentatelluride (HfTe₅), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe₅ can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the “orbitals” surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (E_F). These features are consistent with the theoretical prediction of a magnetic field–induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: Beijing Natural Science Foundation; China Postdoctoral Science Foundation; Chinese Academy of Sciences (CAS); Fundamental Research Funds for the Central Universities; National Key R&D Program of China; National Natural Science Foundation of China (NSFC); Postdoctoral Innovative Talent Support Program of China; USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 2471419
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 42 Vol. 119; ISSN 0027-8424
• Publisher: National Academy of SciencesCopyright Statement
• Country of Publication: United States
• Language: English