Charge modulations vs. strain waves in resonant x-ray scattering

TL;DR

This paper introduces a resonant x-ray scattering method to distinguish and quantify charge modulations and strain waves in charge density waves, enabling better characterization of their nature.

Contribution

It presents a novel approach to separate and measure charge and strain modulations in CDWs using atomic form factor decomposition, applicable to various materials.

Findings

The method allows independent quantification of charge and strain modulations.

It can distinguish Peierls-like from Wigner-like charge density waves.

Illustrated with a one-dimensional chain model.

Abstract

A method is described for using resonant x-ray scattering to separately quantify the charge (valence) modulation and the strain wave associated with a charge density wave. The essence of the method is a separation of the atomic form factor into a "raw" amplitude, fR(w), and a valence-dependent amplitude, fD(w), which in many cases may be determined independently from absorption measurements. The advantage of this separation is that the strain wave follows the quantity |fR(w) + <v> fD(w)|^2 whereas the charge modulation follows only |fD(w)|^2. This allows the two distinct modulations to be quantified separately. A scheme for characterizing a given CDW as Peierls-like or Wigner-like naturally follows. The method is illustrated for an idealized model of a one-dimensional chain.