The laws of quantum physics tell us that electrons behave like waves; and in some materials, these electron waves can take on complicated shapes. So-called “topological materials” produce electron states that can be useful, but it is difficult to identify these materials and their associated electronic states. To identify these “topological materials,” scientists from TU Wien (Vienna University of Technology) and the University of Science and Technology of China created a “crystal” made of light waves. The crystal was used to hold atoms in a geometric pattern. With the help of interfering light waves, the atoms could be held in predefined places, creating a regular pattern, similar to a crystal grid. The team said that in this “crystal grid,” the role of the atoms can be compared to the role of the electrons in a solid-state crystal. The spin structure in the atoms in the crystal made of light. It is possible to switch between simple and complex states. Courtesy of TU Wien. The crystal could also be used to drive the system (that is, the pattern of atoms) out of equilibrium. By changing the light wavelength, the geometry of the atomic arrangement could be switched. The new arrangement could be used to investigate how the electron states would behave in an actual solid-state material. By switching the atomic arrangement between simple and complicated states, topologically interesting states in the system were revealed. “With this change, a massive imbalance is suddenly being generated,” said professor Jörg Schmiedmayer. “The quantum states must rearrange and approach a new equilibrium, much like balls rolling down a hill until they find equilibrium in the valley. And during this process we can see clear signatures that tell us whether topologically interesting states are to be found or not.” A topologically trivial band structure (left), much like a valley in which a rolling ball approaches the lowest point. The structure on the right is more complex. Courtesy of TU Wien. The results could help further studies on topological states of matter — an area of research that was awarded the Nobel Prize in Physics in 2016. The artificial light crystals could even be adapted to simulate certain crystal structures in order to find new topological materials, suggest the researchers. It is still considered extremely difficult to determine whether or not a certain material allows topologically interesting quantum states. “Quantum states that are not in equilibrium, are changing rapidly,” said Schmiedmayer. “This dynamic is notoriously difficult to understand, but as we have shown, it is a great way to obtain extremely interesting information about the system. The research was published in Physical Review Letters (https://doi.org/10.1103/PhysRevLett.121.250403).