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arXiv · 1807.02459

Discrete Scale Invariance in Topological Semimetals

Haiwen Liu·Hua Jiang·Ziqiang Wang·Robert Joynt·X. C. Xie
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Abstract

The discovery of Weyl and Dirac semimetals has produced a number of dramatic physical effects, including the chiral anomaly and topological Fermi arc surface states. We point out that a very different but no less dramatic physical effect is also to be found in these materials: discrete scale invariance. This invariance leads to bound state spectra for Coulomb impurities that repeat when the binding energy is changed by a fixed factor, reminiscent of fractal behavior. We show that this effect follows from the peculiar dispersion relation in Weyl and Dirac semimetals. It is observed when such a material is placed in very strong magnetic field B: there are oscillations in the magnetoresistivity somewhat similar to Shubnikov-de Haas oscillations but with a periodicity in ln B rather than 1/B. These oscillations should be present in other thermodynamic and transport properties. The oscillations have now been seen in three topological semimetals: ZrTe$_{5}$, TaAs, and Bi.

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Haiwen Liu, Hua Jiang, Ziqiang Wang, Robert Joynt, X. C. Xie. 2018-07-06. Discrete Scale Invariance in Topological Semimetals. https://arxiv.org/abs/1807.02459

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