Discovery of log-periodic oscillations in ultraquantum topological materials

Quantum oscillations are usually the manifestation of the underlying physical nature in condensed matter systems. Here we report a new type of log-periodic quantum oscillations in ultra-quantum three-dimensional topological materials. Beyond the quantum limit (QL), the log-periodic oscillations involving up to five oscillating cycles (5 peaks and 5 dips) are observed on the magnetoresistance (MR) of high quality single-crystal ZrTe5, virtually showing the clearest feature of discrete scale invariance (DSI). Further theoretical analyses show that the two-body quasi-bound states can be responsible for the DSI feature. Our work provides a new perspective on the ground state of topological materials beyond the QL.