  Discrete scale invariance (DSI) is a phenomenon featuring intriguing
log-periodicity which can be rarely observed in quantum systems. Here we report
the log-periodic quantum oscillations in the magnetoresistance (MR) and the
Hall traces of HfTe5 crystals, which reveals the appearance of DSI. The
oscillations show the same logB-periodicity in the behavior of MR and Hall,
indicating an overall effect of the DSI on the transport properties. Moreover,
the DSI feature in the Hall resistance signals its close relation to the
carriers. Combined with theoretical simulations, we further clarify the origin
of the log-periodic oscillations and the DSI in the topological materials. Our
work evidences the universality of the DSI in the Dirac materials and paves way
for the full understanding of the novel phenomenon.
