# A Matter of Definitions

When one unearths a new superconductor, there exist three experimental signatures one hopes to observe to verify this discovery. These are:

1. D.C. resistance is zero
2. Meissner Effect (expulsion of magnetic field)
3. Zero Peltier coefficient or thermopower

The last item is a little finical, but bear with me for a second. The Peltier coefficient effectively measures the transport of heat current that accompanies the transport of electric current. So in a superconductor, there is no heat transport (condensate carries zero entropy!), when there is electrical transport. For instance, here is a plot of the thermopower for a few iron pnictides:

Let us ask a similar, seemingly benign, question: what are the experimental signatures one hopes to observe when one discovers a charge density wave (CDW) material?

If we are to use the superconductor as a guide, one would probably say the following:

1. Non-linear conductivity
2. CDW satellite reflections in a diffraction pattern
3. An almost zero Peltier coefficient or thermopower once the CDW has been depinned

I have posted about the non-linear I-V characteristics of CDWs previously. Associated with the formation of a charge density wave is, in all known cases to my knowledge, a periodic lattice distortion. This can be observed using X-rays, neutrons or electrons. Here is an image from 1T-TaS$_2$ taken from here:

Now, startlingly, once the charge density wave is depinned in a large enough electric field, the thermopower decreases dramatically. This is plotted below as a function of electric field along with the differential conductivity:

This indicates that there is very little entropy transport associated with the charge density wave condensate. Personally, I find this result to be quite stunning. I suspect that this was one of the several signatures that led John Bardeen to suggest that the origin of the charge density wave in low-dimensional materials was essentially quantum mechanical in origin.

Having outlined these three criteria, one should ask: do many of the materials we refer to as charge density waves actually exhibit these experimental signatures?

For many of the materials we refer to as charge density waves today, notably the transition metal dichalcogenides, such as 1T-TaS$_2$, 2H-NbSe$_2$, and 2H-TaSe$_2$, items (1) and (3) have not been observed! This is because it has not been possible to definitively depin the charge density wave. This probably has to do with the triple-q structure of the charge density wave in many of these materials, which don’t select a preferential direction.

There exist many clues that the latter materials do indeed exhibit a charge density wave transition similar to others where a depinning has been observed. It is interesting to note, though, that there are some glaring experimental absences in the transition metal dichalcogenides,  which are often considered prototypical examples of a charge density wave transition.