Confined field induced density waves in unconventional superconductors

We demonstrate that a magnetic field may induce a first order transition from a d-wave superconducting (SC) state to a state in which SC coexists and competes with confined field induced spin (or charge) density waves (CFIDW) that develop over a portion of the Fermi surface (FS) centred in the node regions. The extension of the CFIDW states over the FS is fixed by their competition with SC and shows a non-integer quantization. Novel macroscopic quantum phenomena like the non-integer quantization of the superfluid density are therefore generated. We argue that CFIDW states may be the origin of the numerous puzzling field induced phenomena reported in high-T, cuprates and as an example we analyse the field induced plateaus observed in thermal transport data in connection with the field induced reduction of the superfluid density.