="Warren D Smith" <warren.wds@gmail.com> http://arxiv.org/abs/1310.0391 --what good is this stuff? Can anybody explain?
I recalled that my colleague Josh Parks once had done some work on graphene and asked him. He very kindly provided the following explanation. He even pasted in some PNG graphics that are removed here--let me know if you want them and perhaps we can find some way to share them "out of band"... --MLB ---------- Forwarded message ---------- From: Joshua Parks <jparks@tagged.com> Hi Marc! Interesting article -- and the scientific community thought so as well -- it's coming out in the journal Science! I am no longer particularly an expert in this field, but I'll give it a shot. At the end of the day, it's a first step, and mostly a fundamental work of science rather than the triumph of technology, so I'll treat it that way. So in the past 10 years, there have been 2 materials that have been the subject of intense research by Physicists. The first is graphene and the second is topological insulators. In the case of graphene, there are lots of interesting properties in addition to their fascinating electronic structure which drives fundamental Physics research -- for example, electrons in graphene can move 100x faster than they do in silicon (high-frequency applications); they are conducting and transparent and elastic (touch screens); they are incredibly strong mechanically (stronger than diamond); they have nice thermal properties (best thermal conductor known); and at the same time, the tiniest atoms can't seem to penetrate a graphene layer. Basically, they're ripe for potential applications and have properties that are highly appealing for interdisciplinary research. Topological insulators are materials that have a remarkable property: they are insulating on the inside but are conducting on the outside. They are also a triumph of theoretical physics, which predicted this new class of materials, and experiment actually confirmed the predictions. Just like how a doughnut being morphed into the shape of a coffee mug is homeomorphic, similar topological properties can actually appear when electrons are confined so that they can only move in 2 dimensions. In the case of topological insulators, the electrons sitting on the surface of an insulator are topologically protected from disorder. The marriage of topology with physical materials is something that has been appreciated only recently. In terms of the electronic properties of graphene and topological insulators, it basically boils down to this. Whereas typical semiconductors have a gap between the valence and conduction bands (quadratic in form, see e.g., the blue curves below -- the existence of this gap is how we can control current flow in a device like the transistor: by using a gate electrode to tune the number of electrons we can adjust the device between states of current flow and no current flow)... graphene and topological insulators are instead 1) gapless and 2) have a linear relationship between energy and momentum (see the dotted line below). [snip pix] Well, let's think about that again. gapless and linear. This suggests that electrons in graphene and topological insulators are very different than those in other materials. For example, in an introductory physics class, we've always learned that kinetic energy is proportional to the square of the velocity (or the square of the momentum). But here, we see that electron energies go linearly with momentum. An entity we know that also has this linear relationship are massless photons. In fact, electrons in graphene are well described by "massless Dirac fermions" -- they really act as if they have no mass. An interesting tidbit about topological insulators is that in addition to these properties, the spin orientation of an electron at the surface of a topological insulator is locked to the direction that the electron is moving. Very neat stuff. For graphene, this gapless and linear bandstructure is not particularly robust: by making the material more 3-D, e.g. by adding consecutive layers on top to make stacked sheets, this linear relationship between energy and momentum is destroyed in the material; the electrons acquire mass, and no longer behave as massless Dirac Fermions. In this paper, the authors follow up on a series of theoretical predictions that a linear energy-momentum relationship can be observed in all directions within a new class of topological 3D semimetals (topological in the sense that the electronic structure is topologically protected), in stark contrast to what happens in graphene as we move away from 2 dimensions. They use doping to probe different parts of the energy bands to establish that the band structure is gapless and linear [snip pix] And they establish this linearity across all 3 dimensions: [snip pix] Will we be treated to some cool applications in the very near future? Probably not. This 3D topological material used in the experiment was already incredibly sensitive to air, and in order to make electrical devices out of them, we'd need something more robust. But the work establishes that there exists a class of materials in which all the interesting electronic properties of graphene are topologically protected and which exist in 3 dimensions, and not just in 2 dimensions. -Josh