The hottest off-shoot of topological insulators these days is the study of nodal electronic structures.  By this I mean the situation in which two different bands touch along some locus in momentum space.  This started a few years ago with the re-discovery of Weyl points – I wrote a commentary some time ago with the poetic title, “Weyl electrons kiss”, using kissing as a metaphor for band touching.  The actual contact for Weyl fermions is linear in energy versus momentum, so a bit angular compared to lips.  The kissing image seems more apt for quadratic band touching, which also occurs and is interesting in its own right.

The contact locus between bands can be extended, and form for example a loop in momentum space.  This is often called a “nodal loop”.  An exotic phenomena that happens in such cases is that there can be a branch of surface bound states which exists only for surface momenta which project inside the nodal loop.  If one plots the energy of the surface state versus the two dimensional momentum of the surface, it forms a “drumhead” that stretches across the projection of the nodal loop into the 2d surface Brillouin zone.  I think this drumhead surface state was first pointed out by Volovik, though I do not recall the reference at the moment.

To a good approximation such a drumhead state is “flat”, i.e. its energy is nearly constant. A flat band has no kinetic energy, so one might think it should be susceptible to interactions.  With Jianpeng Liu, a postdoc at KITP, we studied this and indeed found various instabilities due to electron-electron forces.   Here is a phase diagram from our paper, for a simple limit of our simple model:

You can see in the inset the charge density wave pattern that forms in our simple model – it looks a bit like the drumhead surface state is “ringing”, though this is really oscillation of the charge density as a function of distance into the material.

This sort of tendency to form ordered states means that nodal loop semimetals should be an interesting place to study two-dimensional electronic surface phase transitions.    A neat feature of this situation is that the nodal loop means there are gapless states in the bulk, and that the surface bound states become bulk-like as they approach the momenta of the loop.  These attributes mean that surface quantum criticality in this situation is different from the criticality of a purely 2d system, and is instead inextricably tied to the 3d nature of the system.

You can read our paper if you want to know the details.

I feel a certain sense of unreality lately.  Science in general, and my own scientific situation, seems in a strange state.  The administration just released its proposed budget, and it is awfully bad news for science.  The huge cuts to the EPA were expected, and get the most press, but the situation is uniformly grim for basic science.  A 20 percent cut to the NIH and 17 percent to the DOE office of science are also massive, and the latter, if it happens, is likely to be devastating to physics.  The National Science Foundation (NSF) is not even mentioned in the budget document, but probably it is considered one of a set of “other agencies” slated for a 10 percent cut.  Those percentages might not seem large, but they are bound to be distributed unevenly: these agencies have various commitments that have already been made, and need to be prioritized.  This level of cut could easily translate into many programs not being renewed, complete cancellation of any new grants, etc.. I wonder how many jobs will be lost at national labs and universities, and how many students and postdocs will lose their support.   I can only hope that congress does not follow these recommendations.

It is interesting to make some comparisons internationally, but hard to find very recent data.  According to wikipedia as of 2014, the US ranked 11th in the world in its research and development spending as a fraction of GDP.   Anyone in my field has had the experience of traveling to Germany, Switzerland, South Korea, Japan, etc., and being overwhelmed by the availability and level of research funding there.  American science is still strong on any scale, but for how long can it remain so under these terms?  It is hard to imagine a great country making these decisions.

There’s a personal side to it for me.  Our KITP grant is up for renewal this year from the NSF.  The KITP is without a doubt the most successful visiting center for theoretical physics in the world.  Among other things, the KITP’s postdoctoral program has trained some huge fraction of the leaders in theoretical physics, who have gone on to become faculty at all the top institutions.  The KITP’s scientific programs chart the future of physics.  It has become a model for other institutes worldwide, though the competition doesn’t come close to its level of productivity despite in many cases significantly more financial support in these imitators.  The KITP’s budget has been stagnant for many years, even before the change of administration.  I’ll be attending a “reverse site visit” in D.C. to present the case for renewal of the KITP’s grant to the NSF in May.

The KITP’s NSF grant does not support my own group’s research.  For that I rely on my own grants.  This year my DOE grant from the office of Basic Energy Sciences is up for renewal.  A 17% cut  does not bode well for that.  This DOE grant supported nearly all of our group’s work on quantum spin ice and pyrochlores, which has been probably the most influential part of my research in the past decade.  It supported my (former) graduate student Dr. Lucile Savary, who received a permanent CNRS research position in France, and has been winning a lot of prizes lately.

In mid-April, I’ll be traveling to New York City to present a proposal to the Simons Foundation, a private philanthropic organization that funds mathematics and science.  My team is competing for what they call a “Simons Collaboration”: the goal being to bring a group of researchers together to attack some major scientific challenge that needs the combined efforts of a team, and which cannot be supported by governmental means.  With the proposed budget changes, the latter criteria should not be too hard to satisfy.  It seems that private support for science may become especially crucial given the governmental trends.  Already nearly all of our postdocs in condensed matter at the KITP are funded by the Betty and Gordon Moore Foundation, another fantastic philanthropic foundation.

In order not to end on a low note, let me say that these thoughts about funding are the backdrop for my main concern, which is the science itself.  That is flourishing!  It’s an exciting time to do physics.  This has been a great year for the recognition of the topological revolution.  I’m amazed by the talent of young minds in the field: I’ve been working with an undergraduate on non-Fermi liquids, hydrodynamics, and disorder – research that crosses the boundaries between condensed matter physics and quantum gravity, which I myself would not have been close to understanding at that age!  At the Boulder summer school for condensed matter and materials physics last July, the students were simply incredible.  Our KITP postdocs are doing breakthrough work on their own at the cutting edge of topological matter. Experiments on quantum materials are rich and varied (though increasingly the ones I care about are done outside of the US), and it seems likely we will see increasing technological impacts of these basic research areas soon.  I don’t think my own research has ever been as diverse as it is now.  So it is a great time to do physics, even though I worry about being able to afford it.