Charge density waves in transition metal di-chalcogenides: A comparison of fermi surface nesting and electron-phonon coupling

Abstract

Charge density waves are ordered phases of matter in condensed matter physics. It is like a standing wave floating above the lattice which also has a phenomenon called periodic lattice distortion. A charge density wave and a periodic lattice distortion might come together on a material since electrical charges make the system come to a new ground state due to lattice-driven effects and the coupling between lattice and the electrons. A thought experiment made by Peierls pave the way going to the charge density waves. According to the Peierls, a 1-dimensional half filled band will go under a transition if the system is probed with a momentum of two times its wavevector. This is called Peierls instability. After several years, another scientist named Fröchlich wrote down a microscopic theory of electron-phonon coupling, which has the similar types of instability with the charge density waves. According to Peierls, an instability pave the way for a mechanism called Fermi surface Nesting. It says that when there is a q vector connecting the opposite edges of the Fermi surface there will be a instability just like the as in the earlier idea of Peierls distortion/instability. This idea of Fermi surface nesting is feasible in 1-dimensional materials but as one uses higher dimensional materials Fermi surface nesting starts to fail. The reason for that, in two dimensional Fermi surfaces it is not easy to connect any point on the edges os the Fermi surface directly. The geometrical shapes of the Fermi surfaces are much more complex than their 1-dimensional counterparts. The amount of points that can manage the connect with CDW vectors a not enough to create an instability and hence, a CDW. A good measure of Fermi surface nesting in a material is a function called static Lindhard susceptibility. If there is a divergence in this function at some q point, that q point would be a good candidate for charge density wave instability. At higher dimension, with Fermi surface nesting not working any more, new mechanisms are searched for since the first two dimensional observation of charge density waves in 1970s. To this day, there is still not any mechanism ideal for all cases or for all materials. Still, one has to run experiments or simulations for which mechanism is stronger in a specific material. The problem of determining fundamental mechanism between two candidates, which are Fermi surface nesting and electron-phonon coupling, will be the motivation of this study. We have a candidate material called NbSe2 , a member of the transition-metal di-chalcogenides family. After neutron and x-ray scattering experiments, we know that there is a q vector of charge density wave in the path Γ-M of the Brillouin zone. We run simulations to observe the Lindhard susceptibility and electron-phonon coupling constant on this path. For these simulations we use DFT programs called Quantum Espresso and Electron-Phonon Wannier. After the calculations, we see that the electronic effects observed by searching for a peak value of Lindhard susceptibility, is not very effective or distinctive. Whereas, the electron-phonon coupling constant has a mighty peak just above the searched q vector. This gives the hint that for instabilities about that q point, electron-phonon coupling effects are much more effective, and materials NbSe2 is identified as a q-dependent electron-phonon coupling material. For some researchers this corresponds to the type 2 CDW. The judgment of the which effect has more influence on the resultant instability is decided o their behavior on the ⃗qCDW = 0.66(Γ − M). The peaks in graphs are quantitatively measured according to their elevation from the mean of their respective datasets. The peak of the electron-phonon coupling effect has showed %865 peak values, where the electronics effects which are probed with the Lindhard susceptibility has showed only %38 peak behavior.