Unexpected emergent states of matter created out of equilibrium in tantalum disulphide.*

The idea that many body systems in complex materials may self-organise into long range order under highly non-equilibrium conditions suggests that entirely new emergent states with new and unexpected functionalities might be created in this way. The route for creation of such states is not limited to symmetry-breaking phase transitions, and entirely novel mechanisms may come into play. I will discuss recent experimental findings of mesoscopically textured metastable states with long range order created through density-driven non-equilibrium transitions. Combining ultrafast optical pulse excitation with scanning tunneling microscopy under moderate non-equilibrium conditions we find unambiguous evidence for long range electronic order appearing through a topological transition. Further out of equilibrium, under warm dense matter conditions we observe an entirely new metastable state of hyperuniform electronic matter. These discoveries open the way to new mechanisms for the creation of new states of matter created under highly non-equilibrium conditions.