The wave-vector power spectrum of the local tunnelling density of states: ripples in a d-wave sea

TL;DR

This paper analyzes the wave-vector power spectrum of the local tunneling density of states in cuprate superconductors, relating it to quasiparticle interference patterns and the scattering potential structure, with implications for understanding superconducting states.

Contribution

It provides a theoretical framework connecting the wave-vector power spectrum to quasiparticle spectra and scattering potential structures in d-wave superconductors.

Findings

Structure of the power spectrum is related to quasiparticle interference.

Analysis of normal metals and s- and d-wave superconductors.

Insights into the effects of weak scattering potentials.

Abstract

A weak scattering potential imposed on a $CuO_2$ layer of a cuprate superconductor modulates the local density of states $N(x,\omega)$. In recently reported experimental studies scanning-tunneling maps of $N(x,\omega)$ have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasi-particle spectrum and the structure factor of the scattering potential. Examples of quasi-particle interferences in normal metals and $s$- and d-wave superconductors are discussed.