Sunday, August 14, 2011

Topological insulator question

I have a question, and I'm hoping one of my reader experts might be able to answer it for me.  Let me set the stage.  One reason 3d topological insulators are a hot topic these days is the idea that they have special 2d states that live at their surfaces.  These surface states are supposed to be "topologically protected" - in lay terms, this means that they are very robust; something deep about their character means that true back-scattering is forbidden.  What this means is, if an electron is in such a state traveling to the right, it is forbidden by symmetry for simple disorder (like a missing atom in the lattice) to scatter the electron into a state traveling to the left.  Now, these surface states are also supposed to have some unusual properties when particle positions are swapped around.  These unconventional statistics are supposed to be of great potential use for quantum computation.  Of course, to do any experiments that are sensitive to these statistics, one needs to do quantum interference measurements using these states.   The lore goes that since the states are topologically protected and therefore robust, this should be not too bad.

Here's my question.  While topological protection suppresses 180 degree backscattering, it does not suppress (as far as I can tell) small angle scattering, and in the case of quantum decoherence, it's the small angle scattering that actually dominates.  It looks to me like the coherence of these surface states shouldn't necessarily be any better than that in conventional materials.  Am I wrong about this?  If so, how?  I've now seen multiple papers in the literature (here, here, and here, for example) that show weak antilocalization physics at work in such materials.  In the last one in particular, it looks like the coherence lengths in these systems (a few hundred nanometers at 1 K) are not even as good as what one would see in a conventional metal film (e.g., high purity Ag or Au) at the same temperatures.  That doesn't seem too protected or robust to me....  I know that the situation is likely to be much more exciting if superconductivity is induced in these systems.  Are the normal state coherence properties just not that important?


Anonymous said...

Should be relevant:

Anonymous said...

Previous link is broken.

Heidar said...

I am a little confused about which particles you are referring to. I think that low energy excitations on the surface of a 3D (T-invariant) topological insulator have (almost) always fermionic statistics.**** Therefore there is nothing interesting as far as quantum computation (QC) is concerned.

In order to get something relevant for QC(such as non-abelian statistics), complications are necessarily. Such as inducing p-wave superconductivity on the surface by proximity effects. This might change the stability analysis.

By the way, I am NO expert.

**** Well, there is an exception. One can induce magnetic monopoles on the surface, which by the Witten effect will also have (fractional) electric charge (they are called dyons in particle physics). Aharonov-Bohm effect can give rise to non-trivial statistics, but that is abelian statistics and not relevant for quantum computation. For more info see >>Science 323, 1184 (2009)<< and >>Phys. Rev. B 82, 035105 (2010)<<.

Olaf said...

It might be a good thing to point out that as of yet we do not know of any (conjectured) (3+1)D topological insulators that exhibit fractional statistics (to my knowledge at least). The most prominent candidate for a topological quantum computer at the moment are certain plateaus in the Fractional Quantum Hall regime -- which is a (2+1)D effect. The edge of a FQH state is 1 dimensional.

Furthermore, the degrees of freedom associated with the qubit are topological, meaning they are "stored" non-locally in the system. This is what makes these topological qubits potentially interesting, since no local operator (e.g. an impurity) couples to these degrees of freedom.

I'm no expert on decoherence of the edge current, but the point I'm trying to make is that it's actually not the edge current which stores the qubit. The qubit is a bulk property of the system, and is associated with non-local (topological!) degrees of freedom.

Douglas Natelson said...

Heidar, Olaf - I guess my impressions were shaped by this paper:
The authors argue that the nontrivial Berry's phase carried by the carriers in the surface state "is known, theoretically, to protect an electron system against the almost universal weak localization behavior in their low-temperature transport (11, 13) and is expected to form the key element for fault-tolerant quantum computation schemes (13, 28, 29)."

Even in the exciting idea of using proximity-induced superconductivity to create Majorana fermions, the normal state coherence length should be important. If that coherence length is short, that seems like bad news. I know it's early days yet, and I still feel like I must be missing something here. I'm not working on these systems, so I haven't had to learn the details yet.

Peter Armitage said...


You are right in the sense that there is only a weak suppression of normal small angle scattering. Normal scattering should be suppressed by an additional factor of something like 1 - cos(theta). But since 2D is a marginal dimension for weak localization anyway, this is apparently enough to keep particles from weak-localizing. There are also special issues to consider vis a vis these being Dirac electons and localization, but this is a bit of separate issue.

These states are only "protected" in the sense that there have to be states at the chemical potential on the surface. This is the aspect which is protected. No reasonable amount of non-magnetic disorder can gap them away, even if the mobility is going to hell in process.

Peter Armitage said...

I wrote" suppressed by an additional factor of something like 1 - cos(theta)."

Oops. Sorry shoulda been 1 + cos(theta).

Anonymous said...

Ya'll should check out:

k_f*l = 41 and fractional filling of 13/3, 9/2, etc...

Impressive for a 1st gen material (Bi2Te2Se).

-Marc Ulrich, ARO. [Note I'm competing a MURI on 3d TI with interactions. Check out the BAA and join the competition to snag a few research $!]

Unknown said...

what if I said that ideal topological insulator was created in 1992 by Russian scientists?
It's called "oriented carbyne":
"Superinjection from Oriented Carbyne as the Result of Landau Quantization in Giant Pseudo-Magnetic Field" doi: 10.4236/jmp.2013.47134.

Unknown said...
This comment has been removed by the author.