Thursday, April 26, 2007

This week in cond-mat

Briefly emerging from my end-of-semester fog, here are some interesting preprints from the past week.

The graphene craze continues unabated. Remember how the superconductivity community descended upon MgB2 and made every superconductivity-related measurement under the sun on the new material in a feeding frenzy? A similar phenomena is taking place with the 2d electron community and graphene. Fortunately, graphene seems to be pretty neat stuff! For example:
arxiv:0704.3165 - Hill et al., Graphene spin valve devices
People have done normal metal contacts to graphene, and superconducting contacts to graphene, so what's left but ferromagnetic contacts to graphene? Unsurprisingly you can use ferromagnetic electrodes to inject spin into graphene, and its such a low-Z material of high purity that both spin-orbit scattering and spin flip scattering from impurities are minimal, leading to real spintronic possibilities in this stuff.

Further exploiting the robustness of graphene even under significant processing:
arxiv:0704.2626 - Huard et al., Transport measurements across a tunable potential barrier in graphene
arxiv:0704.3487 - Williams et al., Quantum Hall Effect in a graphene pn junction
arxiv:0704.3608 - Abanin and Levitov, Quantized transport in graphene pn junctions in magnetic field
Because graphene is a high quality 2d material and can be shifted readily from n and p carriers via doping or gating, it is possible to set up sophisticated structures (npn or pnp junctions; pn junctions) while preserving long mean free paths. The result is rich phenomenology, as seen in the first two (experimental) papers listed here, and analyzed in detail in the third (theory) paper. I'm still waiting for a really unexpected graphene result that isn't readily explained.

Two other papers that involve tunable model systems to examine strong correlation physics:
arxiv:0704.3011 - Bloch et al., Many-body physics with ultracold gases
This is a review article about using cold atoms to look at nontrivial correlation effects. One holy grail in this business is to use strongly interacting cold fermions in a 2d optical lattice to explicitly simulate the Hubbard model (relevant to high-Tc superconductivity), a topic of much interest to one of my faculty colleagues.

arxiv:0704.2614 - Walsh et al., Screening of excitons in single, suspended carbon nanotubes
Carbon nanotubes have 1d band structures, and therefore are subject to strong electron-electron interaction effects and poor screening. The consequence of these interactions is the demise of Fermi liquid theory, and therefore the onset of the fractionalized quasiparticles (spinons and holons) of Luttinger liquid theory. Excitons are also strongly modified in these systems. One way to probe these effects is to change the effective interaction; this is done by using immersion in dielectric media to change the screening of charges, and the effects are probed spectroscopically.


Anonymous said...

Funny how carbon physics works. First people cared about fullerene (ostensibly 0-D), then moved on to nanotubes (1-D), and now to graphene (2-D). I can't wait for people to start researching graphite again! Or, better yet is when they invent 4-D graphite. The 4th dimension is hype (get it? it's "hype"rdimensional).

Actually, in light of the recent Columbia work, one thing I always wondered is at what point does graphene become graphite. For example, did that paper (Philip Kim, I want to say) ever note how many layers it takes to lost any measurable fractional quantum hall effect? I thought that'd be a good metric to separate the two systems, but I'm probably missing something obvious.

Anonymous said...

Do you suppose that graphene emits terahertz radiation?

Douglas Natelson said...

Graph-fiend - It depends on what you mean. As soon as you have more than one layer you lose the perfect linear dispersion at the Fermi points. On the other hand, the work by deHeer on few-layer systems shows that when transport is dominated by one layer (because the bottom layer in their structures is effectively doped by charge transfer from the substrate), the 2d picture is pretty good. Of course, they don't see the quantum Hall effect in that experiment. Generically I would think that this wouldn't be different than other confined 2d systems: as long as the z motion is quenched (that is, you're in the first z subband), quantum hall physics should work. The fractional stuff is trickier - in graphene you get even denominator fractions because of the symmetry of the lattice. In GaAs 2deg, for example, you get odd-denominator fractions because of strong electronic correlation effects. As far as I know, no one has seen that kind of fractional quantum Hall physics in graphene yet, probably because the mobility isn't high enough.

Dan, doesn't everything either emit THz or have interesting conductivity features in the THz? You've pretty much convinced me of that....

Douglas Natelson said...

I just spoke to Walt deHeer at this NSF grantees meeting that I'm attending, and his take is that the cleanliness of the material is integral to the question of quantum Hall physics in graphene. He's got a preprint coming out soon on this, so i should probably just wait for that and then write more.

Anonymous said...


In multisubband systems (e.g. multilayer graphene), you get a combination of Landau levels (LLs) arising from the different subbands. If the number of subbands is small enough, you can still resolve the levels, and observe the QH effect. See, e.g., bilayer or trilayer GaAs 2DEGs. So technically, you do not need to have only one z subband to see the QH effect.

Too many subbands will cause partial overlap of the LLs, which are always broadened by disorder. The critical graphite thickness below which the QH effect can be seen should thus depend on disorder.

Anonymous said...


I just want to add some clarifications to your comments about the fractional QH effect:

In GaAs 2DEGs, you get odd-denominator fractions because electrons are fermions, i.e. their many-body wavefunction is antisymmetric with respect to particle interchange, yielding odd power-law dependencies on spatial coordinates. This in itself results in odd-denominator fractionally charged quasiparticles.

Some even-denominator states do exist in GaAs, but only in multicomponent systems (bilayers).

I don't think you really need "strong" correlation effects as much as very low disorder to observe the FQHE. Correlation effects should be just as strong (or weak) in graphene as in GaAs.

It's worth pointing out that the even-denominator "fractions" in graphene have nothing to do with the FQH effect or with many-electron states, but come out of plain old quantum Hall physics. Their origin is simply the electron-hole degeneracy at the Dirac point, or, in other words, the fact that the n=0 Landau level has energy zero (thus, half-filled by electrons, and half-filled by holes, QED!). Or, in the fancy language some physicists like to use, they come out of the 180-degree "Berry phase".

The mobility in graphene is still too low to see any FQH states, as you say.

Anonymous said...

Oops... I forgot to mention the nu=5/2 FQHE state in GaAs, of course. The basis of our future quantum computers! ;-)

Douglas Natelson said...

fqhe and qhe - Thanks for your points. What I was trying to convey is that the integer QHE is a disorder effect more than a correlation effect. My understanding is that you need extended states in the middle of the Landau levels and localized states on the wings of the Landau levels, and that interactions are not particularly relevant. Regarding deHeer's graphene work, the interesting thing is that his material is cleaner than that of Geim and Kim, at least as inferred from mobility. The fact that he hasn't seen the qhe in his samples is therefore rather interesting....

I also think that the key to the FQHE is that the correlation physics that leads to the Laughlin liquid can't be overcome by the disorder potential. That is, you need some disorder so that the quantum hall physics still works for the composite fermions, but not too much disorder, or you kill the whole effect (the quasiparticles scatter before completing a cyclotron orbit in their effective magnetic field). Am I misunderstanding the physics here?

As you say, the 5/2 state is special, and there is something of a race on among experimental groups to demonstrate the exotic nonAbelian statistics that are supposed to be there.

Thanks again - I'd enjoy having more discussions like this on here.

Csaba said...

graphene is amazing already in the view of the fact, that you can make electrical contact to one single layer of atoms without distroying it, and send a considerable electric current through it. We have gone up to 80 microamps (over a few kohms!! calculate the voltage...) at which point one of the contact interfaces, a pinholed AlOx tunnel barrier, gave it up and exploded. The graphene sheet itself was UNAFFECTED except right at the place where the contact was damaged! This was done after we've measured the spin transport through it, see Nature 448, 571-574 ;)

It is indeed a hype but at least it is a hype about something really cool.

Csaba Jozsa
Groningen, NL