Nematicity in iron-based superconductors: emergent symmetry at transitions between composite electronic orders

The phase diagram of iron-based superconductors contains various electronic orders, which are intimately connected with the superconducting phase. Among the electronic states are nematic and related composite electronic orders. Here we analyze the fluctuations of one type of orders in the other. This analysis leads to an emergent U(1) symmetry at the first-order transition between a nematic phase and a C₄-symmetric charge-ordered phase. We also discuss this emergent symmetry in terms of certain hidden algebra that links the different orders. The enriched continuous symmetry leads to a Goldstone mode at the transition and causes softening of excitations in the nematic and charge sectors when the system is tuned towards the transition. We address the experimental means to probe these effects and discuss the implications of our results for the iron-based superconductors and other correlated systems.