Role of disorder in the multi-critical region of d-wave superconductivity and antiferromagnetism

We investigate the disorder-induced microscopic inhomogeneity in the multi-critical region of d-wave superconductivity and antiferromagnetism on the basis of the microscopic t-t'-U-V model. We find that a small amount of point disorder induces the nanoscale inhomogeneity of spin and superconducting fluctuations when the coherence length of superconductivity is remarkably short as in the under-doped cuprates. Then, the two fluctuations spatially segregate to avoid their competition. We show the remarkable electron-hole asymmetry in high-T-c cuprates where the quite different spatial structure is expected in the electron-doped materials. (c) 2006 Elsevier B.V. All rights reserved.