It is well known that there are two classes of quantum oscillations. One is magnetic field B periodic oscillations, such as Aharonov-Bohm effect for mesoscopic system and Little Parks oscillations for superconducting systems. The other one is 1/B periodic Shubnikov-deHaas and deHaas van-Alphen oscillations from quantized Landau levels. We discover a new class of quantum oscillations beyond quantum limit in topological materials by magnetoresistance measurements up to ultrahigh magnetic field, which show exotic log B periodic oscillations, i.e. discrete scale invariance.  The log B quantum oscillations are further confirmed in different topological materials and revealed in Hall traces. 
Jian Wang, Changjiang Distinguished Professor of China's Ministry of Education, received his bachelor’s degree in Physics from Shandong University in 2001, and PhD degree in condensed matter physics from Institute of Physics, Chinese Academy of Sciences in 2007. From 2006 to 2011, he worked as a Postdoc and Research Associate at Penn State University, USA. He became a Professor at Peking University in 2017. He was selected to Changjiang Distinguished Professor of China's Ministry of Education in 2016 and Chief Scientist for National Key R&D Program of China in 2018. He won Sir Martin Wood China Prize in 2015. His current research interests are qauntum transport properties of low dimensional superconductors and topological materials. Jian Wang with collaborators discovered quantum Griffiths singularity in 2D superconductors, firstly demonstrated high Tc in one unit cell thick FeSe films by direct transport and Meissner evidences, for the first time found interface-modulated Ising superconductivity, developed a new method to detect topological superconductivity (tip-induced unconventional superconductivity in topological materials), was first to reveal eletron-electron interaction in topological materials, and studied the heterostructures of topological/ferromagnetic materials and superconductors etc as one of the pioneers. In recent years, he has authored more than 70 papers including Science, Science Advances, Nature Materials, Nature Physics, Nature Nanotechnology, Nature Communications, Physical Review X, Physical Review Letters, Nano Letters, JACS, Advanced Materials etc. Jian Wang’s lab at Peking University possesses low temperature scanning tunneling microcopy/spectroscopy-molecular beam epitaxy combined ultrahigh vacuum system, ultralow temperature-high magnetic field measurement system etc.
 Science Advances 4, eaau5096 (2018)