Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including nontrivial topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.

Observation of topological valley transport of sound in sonic crystals

Subject Code:A04 Supported by the National Natural Science Foundation of China,a research group from Wuhan University,led by Profs.Liu Zhengyou(刘正猷)and Qiu Chunyin(邱春印),demonstrated the topological valley transport of sound in sonic crystals,which was published in Nature Physics(2017,13:369—374).