Breaking Translational Invariance by Population Imbalance: The Fulde-Ferrell-Larkin-Ovchinnikov States

An overview is given of our present understanding of superconductivity with spontaneously broken translation symmetry in polarized Fermi systems. The existence of “crystalline” superconducting phases is considered in a wide range of systems, prominent examples being conduction electrons in metals, ultra-cold atoms in a trap, nuclear matter and dense quark systems. The underlying physics is delineated and theoretical approaches to the inhomogeneous phases and their properties are discussed. From the experimental side, it is argued that superconductivity with imbalance-induced order parameters is realized in layered organic compounds and potentially in heavy-fermion systems.