  We reveal a novel macroscopic quantum phenomenon induced by a magnetic field.
It corresponds to the {\it non-integer quantization of the superfluid density}
in a superconductor with gap nodes due to the generation of confined
field-induced density waves (CFIDW) over a portion of the Fermi surface (FS).
The Landau numbers $L$ are not sufficient to index these macroscopic quantum
states and new quanrum numbers $\zeta$ must be added. Distinct qualitative
implications of this $|L,\zeta >$ quantization are evident in a number of
puzzling experiments in high-$T_c$ cuprates including the plateaus behavior in
the field profile of thermal conductivity, field induced magnetic moments,
charge textures around the vortices, and field induced vortex-solid to cascade
vortex glass transitions.
