  The concept of a Charge Density Wave (CDW) permeates much of condensed matter
physics and chemistry. Conceptually, CDWs have their origin rooted in the
instability of a one-dimensional system described by Peierls. The extension of
this concept to reduced dimensional systems has led to the concept of Fermi
surface nesting (FSN), which dictates the wave vector q_cdw of the CDW and the
corresponding lattice distortion. The idea is that segments of the Fermi
contours are connected by q_cdw, resulting in the effective screening of
phonons inducing Kohn Anomalies in their dispersion at q_cdw, driving a lattice
restructuring at low temperatures. There is growing theoretical and
experimental evidence that this picture fails in many real systems and in fact
it is the momentum dependence of the electron-phonon coupling (EPC) matrix
element that determines the characteristic of CDW phase (q_cdw). Here, based on
the published results for the prototypical CDW system 2H-NbSe2, we show how
well the q-dependent EPC matrix element, but not the FSN, can describe the
origin of CDW. We further demonstrate a procedure of combing electronic band
and phonon (dispersion and linewidth) measurements to extract the EPC matrix
element, allowing the electronic states involved in the EPC to be identified.
Thus we show that a large EPC does not necessarily induce the CDW phase, with
Bi2Sr2CaCu2O8 (Bi2212) as the example, and the charge ordered phenomena
observed in various cuprates are not driven by FSN or EPC. To experimentally
resolve the microscopic picture of EPC will lead to a fundamental change in the
way we think about, write about, and classify Charge Density Waves.
