Underdoped cuprates, manifestations of boson-fermion crossover, `quantum   oscillations' and the robust fractional quantum Hall state nu = 2/5
  The quantum oscillation data from a whole variety of underdoped HTSC systems and physical measurements has almost universally been presented in very classical terms following the Lifshitz-Kosevich formulation for Fermi-Landau quasiparticles, quantized into vortices and Landau levels under the high applied magnetic fields. The Fermi surface always emerges as a very small fraction of the large parent Fermi surface detected at higher doping. This then calls for some Fermi surface reconstruction to have occurred, as from a charged density wave, etc.. The paper refutes this reciprocal space approach, and shows that many of the more recent detailed works taking this line are not consistent with the data. The present author developed an alternative real-space interpretation of these matters a couple of years ago. This was in terms of interaction of the vortex array with the stripe array, using a 2D modelling for the latter. This approach has here been revised slightly and copes well with addressing the wide variety of new data. The paper pursues and justifies the BEC/BCS, negative-U based, two-subsystem modelling advocated earlier, along with the strength and geometry of the striping acquired in a strong magnetic field. A wide variety of recent experiments are expounded to produce an overall appreciation of a situation far from being appropriately treated within a Fermi-Landau quasiparticle framework. Indeed it is demonstrated that the universality of the 'QO' observations ensues from the fractional quantum Hall effect. The data all point to FQHE state with filling factor nu = 2/5. This state in its genesis and expression finds a much greater alignment with the BEC/BCS crossover condition and the proximity of the HTSC materials to Mott-Anderson localization than does any model for this highly correlated material appealing to well-metallized Fermi-Landau quasiparticle physics. 
John A. Wilson
cond-mat.supr-con