The Kerr effect can arise in a time-reversal invariant dissipative medium that is gyrotropic, i.e. one that breaks inversion ($mathcal I$) and all mirror symmetries. Examples of such systems include electron analogs of cholesteric liquid crystals, an
d their descendants, such as systems with chiral charge ordering. We present arguments that the striking Kerr onset seen in the pseudogap phase of a large number of cuprate high temperature superconductors is evidence of chiral charge ordering. We discuss additional experimental consequences of a phase transition to a gyrotropic state, including the appearance of a zero field Nernst effect.
The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the
weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at u=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.
