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We present analytic analyses for the joint density of states (JDOS) and theelastic scattering susceptibility (ESS) for d-wave superconductors under thelinear dispersion approximation. The profile of the JDOS, determined by thecurves on which the JDOS diverges, is found to be the envelope function relatedto the contour of constant energy of the Bogoliubov quasiparticles. We derivethe explicit form of the envelope functions. The intrinsic relationship of theJDOS patten and the octet model of ESS is clearly revealed. It is also foundthat apexes of the envelope function coincide with the octet vectors when theDirac-cone anisotropy is strong, which is relevant to the d-wave cuprates.

Joint density of states and its relationship with quasiparticle interference pattern of d-wave superconductors