Quantum Hall State Reincarnated (IMAGE) Rice University Caption The rugged landscapes in these illustrations depict the electric potential on the surface of 2D materials that exhibit the quantum Hall effect. The level of ruggedness corresponds to impurities in the system, and the water level represents the "Fermi energy," or filling level of electrons. In the quantum Hall effect (left), the percolation threshold (middle) is a fine-tuned energy state that marks the transition to topological order. New research by physicists at Rice University, the University of California Berkeley and the Karlsruhe Institute of Technology has found "stacks" of this special 2D state that protect patterns of quantum entanglement (right) throughout the surface energy spectrum of 3D topological materials. (Graphic courtesy of M. Foster/Rice University) Credit M. Foster/Rice University Usage Restrictions Must credit: "M. Foster/Rice University" License Licensed content Disclaimer: AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert system.