Every APS March meeting I try to get my head around something new. Last year in Pittsburgh it was supersolids. Now that I’m on the return trek home from this year’s meeting in Portland, I’m trying to work out how far I have managed to get with this year’s challenge, topological insulators.
By all accounts, topological insulators are set to be the next big thing in physics. Though theymade a splash like graphene at the 2006 meeting in Baltimore, but if the increase in submissions to Nature and Nature Physics in this area are anything to go by, it may soon come close. Even graphene took a few years to become stratospheric. And a colleague of mine suggested that ‘topological’ is the new ‘nano’ as the favorite buzzword that authors are adding to their papers to try to make them sound more sexy.
There are good reasons for the excitement. They could enable low-loss spin currents to be harnessed for high-speed, low-power electronics. There is much talk about their use in high-efficiency thermoelectric systems for power generation and heat management. But most exciting is their potential to generate exotic quantum states — from Majorana fermions, which behave analogously to dark matter candidate particles known as axions, to braiding states, which could finally enable us to build quantum computers that don’t fall down the minute anyone thinks about sneezing.
But enough of the hype. What about the nuts and bolts?
I’m not going to pretend that I have anything close to a coherent understanding of what topological insulators are or how they work. The site in the press room after the APS press conference on the subject was one of a half-dozen journalists on the table trying to find a way to parse what the hell they were about to their readers. Of all so far, I think my colleague Geoff Brumfiel from Nature came the closest to getting the balance right.
First, the easy bit. A topologically insulator in fact isn’t really much of an insulator at all. By definition, its surface is conducting. And although an ideal topological insulator has a bulk that is insulating, in practice many materials that people are working on aren’t bulk insulators at all, but semiconductors or semimetals. Thankfully, this needn’t be a problem. That’s because you can modify the bulk with doping (or similar) without affecting the all important surface states, because these states are robust — one of the unique selling points of a topological insulator… actually, arguably the unique selling point.
Yulin Chen, from Stanford showed some pretty compelling angle resolved photoelectron spectra that show that when you dope bismuth telluride (Bi2Te3) — one of the materials that several groups are working on — with tin, you can switch it from an n-type semiconductor to an insulator while leaving the impotant topological surface states unchanged. This occurs at a doping concentration of 0.67% — which is freakin’ huge! It’s remarkable that the surface states are not utterly destroyed at such a level — to compare, parts per million doping turns silicon into garbage.
Anyway, I (and all my colleagues) have been throwing the word ‘topological’ around with gay abandon. Do we know what this means? Probably not. I certainly don’t — not in a deep way. anyway. But I might have an idea.
HEALTH WARNING: The explanation that follows (and what precedes, as well) is subject to change without warning. At best, it’s likely tangential to anything that resembles reality. Really, it’s just an exercise in me thinking out loud.
Image credit: Ali Yazdani, Princeton University
I’ve heard many explanations but none really resonate. It is often said that topological insulators are materials whose surface states are ‘topologically protected’. Okay, well that’s helpful, like, not at all!
The closest I think I’ve come to getting a feel for what it means for a state to be topologically protected comes from some things that Laurens Molenkamp (University of Würzburg) said in a press conference on Monday. Molenkamp was the first to demonstrate the existence of topologically protected surface states experimentally, in mercury telluride. In the press conference, he began by saying that in normal insulators, the geometry (or did he say topology?) of the conduction band states are s-like (like a Bohr atom), and of the valence band states are p-like (like the states of the electrons in the outer shell of a carbon atom).
Now, the electronic behaviour of an insulator or semiconductor is sensitively dependant on the distance in energy between the bottom of the conduction band, which always curves up in density of states of a material, and the top of the valence band, which always curves down. And any perturbation to the material — such as impurities (deliberate or otherwise), defects, strain, changes in temperature, even magnetic or electric fields — tends to frig with the distance between them.
Sometimes this is useful. Most times it’s a pain in the ass. And for things like quantum computing, this sort of thing is a deal-killer. So what do to topological insulators bring to the table?
According to Molenkamp, in certain materials made from heavy elements, the geometry (s-like and p-like) of the conduction and valence bands flip. And at the surface of some materials, they cross. And this is the key, I think.
If you move the uncrossed conduction and valence bands of a conventional material, you change the distance between their nearest points — that is, you change the thing that controls their behaviour.
But if you move the crossed conduction and valence at the surface of a topological insulator, they still remain crossed. The point where they cross might move a bit in k-space (that’s momentum-space — the inverse of normal space, which physicists like to describe electronic materials in, because makes this simpler). But they’re not going to move further apart — they’re crossed!
And it is this crossing, apparently (I think), that not only makes topologically protected states robust, it also makes them wacky, and gives rise to the panoply of exotic behaviour that physicists are excited about.
So there you go. I didn’t promise that’d you’d be able to write a paper on topological insulators after reading all this. I certainly wouldn’t claim that I could. But if I can pick up more bits and pieces at future meetings, perhaps by the time topological insulators are really huge, I might.
(Image credit: Ali Yazdani, Princeton University.)
