The Quantum Hall Effect of Field Induced Spin Density Wave Phases: the Physics of the Ultra Quantum Crystal

The Quantum Hall Effect of Field Induced Spin Density Waves is accounted for within a weak coupling theory which assumes that in the relevant low temperature part of the phase diagram the quasi one dimensional conductor is well decribed by Fermi liquid theory. Recent experimental results show that sign inversion of the Hall plateaux takes place all the way down from the instability line of the normal state. The Quantum Nesting Model, when it takes into account small perturbations away from perfect nesting, describes well, not only the usual sequence of Hall Plateaux, but also the anomalies connected with sign inversion of the Hall Effect. Experimental observation of de-doubling of sub-phase to subphase transition lines suggests that superposition of SDW order parameters occurs in some parts of the phase diagram. The collective elementary excitations of the Ultra Quantum Crystal have a specific magneto-roton structure. The SDW case exhibits, apart from the usual spin waves, topological excitations which are either skyrmions or half skyrmions. It is suggested that magneto-rotons may have been observed some years ago in specific heat experiments. Pacs numbers 72.15.Nj 73.40.Hm 75.30.Fv. 75.40.Gb