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

TL;DR

This paper analytically explores the joint density of states and elastic scattering susceptibility in d-wave superconductors, revealing their relationship and implications for quasiparticle interference patterns, especially in strongly anisotropic cases.

Contribution

It provides explicit analytic forms of the envelope functions of JDOS and clarifies their connection with the octet model of ESS in d-wave superconductors.

Findings

Envelope functions coincide with octet vectors under strong anisotropy.

JDOS diverges along specific curves related to constant energy contours.

The relationship between JDOS and ESS patterns is explicitly derived.

Abstract

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