Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5

Huichao Wang, Yanzhao Liu, Yongjie Liu, Chuanying Xi, Junfeng Wang, Jun Liu, Yong Wang, Liang Li, Shu Ping Lau, Mingliang Tian, Jiaqiang Yan, David Mandrus, Ji Yan Dai, Haiwen Liu, Xincheng Xie, Jian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρxx) and the Hall traces (ρyx) of HfTe5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρxx and ρyx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.

Original languageEnglish
Pages (from-to)914-920
Number of pages7
JournalNational Science Review
Issue number5
Publication statusPublished - 6 Aug 2019


  • Dirac materials
  • discrete-scale invariance
  • Hall resistance
  • log-periodic oscillations
  • magnetoresistance
  • topological materials

ASJC Scopus subject areas

  • General


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