After a brief introduction to crystalline organic superconductors and metals,we shall describe two recently-observed exotic phases that occur only in highmagnetic fields. The first involves measurements of the non-linear electricalresistance of single crystals of the charge-density-wave (CDW) system(Per)$_2$Au(mnt)$_2$ in static magnetic fields of up to 45 T and temperaturesas low as 25 mK. The presence of a fully gapped CDW state with typical CDWelectrodynamics at fields higher that the Pauli paramagnetic limit of 34 Tsuggests the existence of a modulated CDW phase analogous to theFulde-Ferrell-Larkin-Ovchinnikov state. Secondly, measurements of the Hallpotential of single crystals of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$, made usinga variant of the Corbino geometry in quasistatic magnetic fields, showpersistent current effects that are similar to those observed in conventionalsuperconductors. The longevity of the currents, large Hall angle, fluxquantization and confinement of the reactive component of the Hall potential tothe edge of the sample are all consistent with the realization of a new stateof matter in CDW systems with significant orbital quantization effects instrong magnetic fields.
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