I just saw the summary for a feature story on “Physics”, the online journal highlighting what the APS considers exciting developments
Weyl semimetals are definitely a hot subject lately. These are electronic materials in which non-degenerate (i.e. spin-split) conduction and valence bands touch at a single point (called a Weyl point) in three dimensions. Anton Burkov and I actually were one of the first groups to predict these things some years ago (see this paper), hot on the heels of Ashvin Vishwanath’s group (here). Well full disclosure requires me to point out that Herring discovered them in 1937! Anyway, like the related topological insulators, these things are not actually all that rare, and are pretty easy to find using very standard DFT methods, so the subject is booming.
One of the latest twists is the discovery of “type II” Weyl semimetals (if you buy into this, you now call the original ones type I). I’m of II minds myself about this. On the one hand, the type II Weyl point is no different from a type I Weyl point, the only distinction is that in the type II case, the dispersion away from the point goes only in one direction of energy, in some directions in k space. On the other hand, because of this type of slope, such a type II Weyl point cannot be isolated: there are always states at the same energy elsewhere in k space. And those other states form a Fermi surface, which has much more density of states than the vicinity of the point itself. So I would have thought type II Weyl points are mainly special in that they by construction are less able to influence electronic properties than the type I Weyl point (which can be isolated in energy and in that case would control all the physics).
But I’ve been wrong before about what becomes big. Type II Weyl points…sure!
Nevertheless, I found the summary of this Physics piece crazy. Type II Weyl semimetals would be (what does “would be” mean here, anyway? In some hypothetical world?) both conducting and insulating in different directions? Certainly not! As cool as Weyl fermions are, whatever type they are, they are extremely well-described by non-interacting quasiparticle theory. According to this cornerstone of the theory of solids, electrons travel in directions determined by their group velocity, and because they certainly disperse in three dimensions, they also move in all directions. So the statement, at face value, is pretty much absurd.
When I read the actual feature, a few paragraphs down there is some discussion where a magnetic field is mentioned in this context, which might allow for some speck of truth in the summary. Actually it has been known for decades that any low density electron system becomes, in high magnetic field, much more conducting along the field than normal to it. This is a called the ultra-quantum limit. If conditions are right, ultra-quantum electrons can be conducting along the field and insulating normal to it. This does not depend much upon the nature of the band dispersion.
So, well, I don’t know what the writer had in mind, and maybe there is some way it could make sense here. Yet…I doubt it.
I should say that there certainly are materials that are conducting in some directions and insulating in others. Usually this is related to structure: they are built from linear chains or planes, that are weakly coupled. The disparity between conducting in different directions can be magnified by magnetic fields, by strong interactions, by disorder, or all of the above. I don’t think this is particularly rare.