Abstract
We argue that the low-frequency quantum oscillations observed recently in the vortex state of underdoped ortho-II YBa${}_{2}$Cu${}_{3}$O${}_{6,5}$ have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several leading Fermi surfaces creates the proximity gaps on the other. The gap that is transferred on a small-sized pocket from larger Fermi surfaces is small. In the case of unconventional pairing symmetry the induced gap is proportional to the ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to the mass enhancement on the latter. We share the view that small pockets in and of themselves exist as a certain band feature among all Fermi surfaces.
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