Exact analysis on the singularity of the joint density of states and its relationship to the quasiparticle interference

TL;DR

This paper provides an exact analysis of the singularities in the joint density of states and their relation to quasiparticle interference, classifying types and revealing their geometric nature and divergence behavior.

Contribution

It offers a precise classification of JDOS singularities, identifies their geometric origins, and links them to FT-LDOS features, advancing understanding of quasiparticle interference patterns.

Findings

Three types of JDOS singularities classified.

Third type are envelopes of constant energy contours.

JDOS and FT-LDOS share the same singular points.

Abstract

Singularities of the joint density of states (JDOS) and Fourier-transformed local density of states (FT-LDOS) correspond to the hot spots in quasiparticle interference patterns. In this paper the singularity of JDOS is analyzed exactly, with three types of singularities being classified. In particular, the third type of singularities are found exactly to be envelopes of the contours of constant energy. Remarkably, we show that JDOS and FT-LDOS have the same singular points. Approaching to the singular points, both quantities diverge complementarily in an inverse-square-root manner if the joint curvature is nonzero. The relative magnitude of divergence is governed by the joint curvature as well as the product of the quasiparticle velocities. If the joint curvature of certain singularity is zero, the divergence has a higher order than -1/2.