New magnetic-field-induced macroscopic quantum phenomenon in a superconductor with gap nodes

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High-Tc superconductivity is unconventional because the gap is not isotropic as in simple metals but has dₓ₂₋y₂ symmetry with lines of nodes. In a fascinating thermal transport experiment on a high-Tc superconductor, Krishana et al Krishana have reported mysterious magnetic field induced first order transitions from a superconducting state with gap nodes to a state without gap nodes. We show here that this is an experimental manifestation of a novel macroscopic quantum phenomenon induced by the magnetic field, qualitatively different from the usual quantum Hall effects. It corresponds to the quantization of the superfluid density in a superconductor with gap nodes due to the generation of Confined Field Induced Density Waves (CFIDW) in the node regions of the Fermi surface. The Landau numbers L are not sufficient to index these macroscopic quantum states and the addition of a new quantum number ζ is necessary. Distinct qualitative implications of this non-integer |L,ζ> quantization are also evident in a number of recent unexplained experimental reports in the cuprates.