Helical phases in broken parity superconductors

The recently discovered broken inversion superconductors, CePt$_3$Si, Li$_2$Pt$_3$B, and Li$_2$Pd$_3$B, have provided a unique opportunity to study the role of broken parity in the superconducting state. In these superconductors, a magnetic field leads to a novel inhomogeneous superconducting state, a helical phase. Although the origin of the helical phase is quite different from another well known inhomogeneous superconducting phase, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, the consequences of both phases are similar, for example; a relative enhancement of transition temperature as a function of magnetic field over that of a uniform state. FFLO states are quite unstable and hard to observe experimentally as that exist only in the low temperature and high field regime. Until now, the FFLO state has only been identified in CeCoIn$_5 $ as an unusual magnetic field enhanced superconducting state near a quantum critical point. We argue that the helical phases is more stable than the FFLO state and will exist in all broken parity superconductors. We present results on the microscopic quasiparticle structure and the stability of the helical phase in broken inversion superconductors.