- 2d metal-insulator transition - What is the mechanism for the apparent metal-insulator transition in 2d electron and hole systems at low densities? Is it profound or not? I admit, I haven't followed this as closely as I should have. The old argument had been that the scaling theory of localization (a theory that essentially neglects electron-electron interactions) says that any 2d electronic system becomes an insulator at zero temperature in the presence of arbitrarily weak (but nonzero) disorder.
- High-Tc - what is the mechanism of high temperature superconductivity? What is the ultimate limit of Tc? What is the "bad metal", and what is the pseudogap, really? How important are stripes and checkerboards? Is the phrase "doped Mott insulator" really a generic description of these systems? We still don't have a definitive, broadly agreed answer to these questions, though progress has been made, in large part due to continually improving sample material quality. It sure looks like there can be other phases (including ones involving spatial patterns of charge like stripes and checkerboards) that compete with superconductivity. It also looks like high temperature superconductivity often "dies" as T is increased due to loss of global phase coherence. That is, there are still paired electrons above the (bulk) critical temperature, but the pairs lack the coordinated quantum mechanical evolution that gives what we think of as the hallmarks of the superconducting state (the perfect expulsion of magnetic flux at low magnetic fields; zero electrical resistance). Since I wrote the above, a whole new class of superconducting materials, the iron pnictides, has been discovered. While in their normal state they are generally not Mott insulators, electronic correlations and the competition between different correlated ground states do seem to be important, something broadly similar to what is seen in the cuprates.
- Quantum criticality and heavy fermions - Do we really understand these systems? What are the excitations in the "local moment" phase? What is the connection to high-Tc, if any? My faculty colleague who is an expert on quantum criticality would give a definite, though qualified "yes" to that last question. I think (and please correct me in the comments if you disagree) that how to properly describe low energy electronic excitations of systems when the quasiparticle picture breaks down (that is, when the carriers don't act roughly like ordinary electrons, but instead are "incoherent") is still up in the air.
- Manganites - What sets the length scale for inhomogeneities in these materials? I believe this is still up for discussion, though it's known that the effects of disorder and strain can make it very challenging to pull out truly intrinsic physics.
- Quantum coherence and mesoscopics - Do we really have a complete understanding of mesoscopic physics and decoherence at this point? What about in correlated materials? In normal ("boring") metals at low temperatures and in ordinary semiconductors, it looks like we do have a pretty good handle on what's going on, though there are still some systems where the details can get very complicated. As for strongly correlated materials (when electron-electron interactions are very important), I still have not seen a lot of work directly looking at the issue. This is related to the point above about quantum criticality - if you can't readily describe the low energy excitations of the system as particle-like, then it can be tricky to think about their quantum coherent properties.
- Quantum Hall systems - Are there really non-Abelian states at certain filling factors? In bilayers, is there excitonic condensation? Cautious answers on both these counts appear to be "yes". There has been quite a bit of lovely work looking at the 5/2 fractional quantum Hall state (including very cute stuff by my postdoctoral mentor) that seems entirely consistent with non-Abelian physics. Likewise, the recent work making the case for Majorana fermions in semiconductor/superconductor hybrid systems shows that there is hope of really studying systems with non-Abelian excitations. In the case of the quantum Hall bilayers, work by Jim Eisenstein's group at Cal Tech looks very exciting (if I'm leaving out someone, my apologies - I haven't followed the area that closely).
- 1d systems - Is there conclusive evidence of spin-charge separation and Luttinger liquid behavior in semiconductor nanowires? Nanotubes? I think the case for spin-charge separation is better now than it was six years ago, due to very nice work by multiple groups (Yacoby now at Harvard; the gang at Cavendish in Cambridge, for example).
- Mixed valence compounds - Is there or is there not charge ordering at low temperatures in Fe3O4, something that's been argued about for literally 60 years now? This seems to have been settled in the Fe3O4 case: the system has some amount of charge disproportionation, orbital ordering, and the electron-phonon coupling is not negligible in looking at the physics here.
- Two-channel Kondo physics - Is there firm evidence for the two-channel Kondo effect and non-Fermi liquid behavior in some physical system? A qualified "yes", in that the Goldhaber-Gordon group at Stanford made a tunable quantum dot system that can sit at a point that looks like 2-channel Kondo physics is relevant. However, I haven't seen anyone else following up on this, probably in part b/c it's very hard.
- Molecular electronics - Is there really improving agreement between experiment and theory? Can novel correlation physics be studied in molecular systems? Can molecules exhibit intrinsic (to the molecule) electronic functionality? In order, "yes", "yes" (interesting underscreened Kondo physics and other quantum impurity problems, for example), and "yes" (e.g., optically driven switching between isomers with different conductances), though as I've said for years, we're not going to be building computers out of these things - they're tools for looking at physics and chemistry at the nanometer scale.
- Organic semiconductors - What is the ultimate limit of charge mobility in these materials? Are there novel electronic correlation effects to be seen? Can one see a metal-insulator transition in these systems? In order, "it still remains to be seen" (though mobilities on the order of 10-100 cm^2/Vs have been shown); "maybe" (if one counts experiments looking at charge transfer salts, Mott transitions, etc.), and "yes" (if one uses, e.g., ionic liquids to obtain exceedingly high carrier densities).
- Nanomechanical systems - Can we demonstrate true "quantum mechanics", in the sense of a mechanical system that acts quantum mechanically? Yes - see Science's breakthrough of the year in 2010, for example.
- Micro/nano systems to address "fundamental physics" - Can we measure gravity on the 100 nm length scale? Are there experiments with Josephson junctions that can probe "dark energy"? "Not yet" and "Not yet", though like atomic physics I think it would not be surprising if condensed matter produced some systems that could be used in precision measurement tests looking at these kinds of issues.
Wednesday, September 19, 2012
Controversies/hot topics in condensed matter, revisited
A little over six years ago (!), I wrote this post, where I listed a whole series of topics that were hot/exciting/controversial at the time. While I'm traveling for a NSF site visit and working on a couple of proposals, I thought that now might be a good time to bring up this list again. Here is a too-brief update/scorecard, with current statements in blue. In a followup post I will try to add some new topics, and I invite suggestions/submissions in the comments. The previous list was:
Posted by Douglas Natelson at 3:34 PM