## Saturday, May 28, 2022

### Brief items - reviews, videos, history

Here are some links from the past week:

• I spent a big portion of this week attending Spin Caloritronics XI at scenic UIUC, for my first in-person workshop in three years.  (The APS March Meeting this year was my first conference since 2019.)  It was fun and a great way to get to meet and hear from experts in a field where I'm a relative newbie.  While zoom and recorded talks have many upsides, the in-person environment is still tough to beat when the meeting is not too huge.
• Topical to the meeting, this review came out on the arxiv this week, all about the spin Seebeck effect and how the thermally driven transport of angular momentum in magnetic insulators can give insights into all sorts of systems, including ones with exotic spin-carrying excitations.
• Another article on a topic near to my heart is this new review (to appear in Science) about strange metals.  It makes clear the distinction between strange and bad metals and gives a good sense of why these systems are interesting.
• On to videos.  While at the meeting, Fahad Mahmood introduced me to this outreach video, by and about women in condensed matter at UIUC.
• On a completely unrelated note, I came across this short film from 1937 explaining how differential steering works in cars.  This video is apparently well known in car enthusiast circles, but it was new to me, and its clarity was impressive.
• Finally, here is the recording of the science communication symposium that I'd mentioned.  The keynote talk about covid by Peter Hotez starts at 1h49m, and it's really good.
• In terms of history (albeit not condensed matter), this article (written by the founding chair) describes the establishment of the first (anywhere) Space Science department, at Rice University,  In 1999 the SPAC department merged with Physics to become the Department of Physics and Astronomy, where I've been since 2000.

## Sunday, May 15, 2022

### Flat bands: Why you might care, and one way to get them

When physicists talk about the electronic properties of solids, we often talk about "band theory".  I've written a bit about this before here.  In classical mechanics, a free particle of mass $m$ and momentum $\mathbf{p}$ has a kinetic energy given by $p^2/2m$.  In a crystalline solid, we can define a parameter, the crystal momentum, $\hbar \mathbf{k}$, that acts a lot like momentum (accounting for the ability to transfer momentum to and from the whole lattice).  The energy near the top or bottom of a band is often described by an effective mass $m_{*}$, so that $E(\mathbf{k}) = E_{0} + (\hbar^2 k^2/2m_{*})$.  The whole energy band spans some range of energies called the bandwidth, $\Delta$. If a band is "flat", that means that its energy is independent of $\mathbf{k}$ and $\Delta = 0$.  In the language above, that would imply an infinite effective mass; in a semiclassical picture, that implies zero velocity - the electrons are "localized", stuck around particular spatial locations.

Why is this an interesting situation?  Well, the typical band picture basically ignores electron-electron interactions - the assumption is that the interaction energy scale is small compared to $\Delta$.  If there is a flat band, then interactions can become the dominant physics, leading potentially to all kinds of interesting physics, like magnetism, superconductivity, etc.  There has been enormous excitement in the last few years about this because twisting adjacent layers of atomically thin materials like graphene by the right amount can lead to flat bands and does go along with a ton of cool phenomena.

How else can you get a flat band?  Quantum interference is one way.  When worrying about quantum interference in electron motion, you have to add the complex amplitudes for different electronic trajectories.  This is what gives you the interference pattern in the two-slit experiment.   When trajectories to a certain position interfere destructively, the electron can't end up there.

It turns out that destructive interference can come about from lattice symmetry. Shown in the figure is a panel adapted from this paper, a snapshot of part of a 2D kagome lattice.  For the labeled hexagon of atoms there, you can think of that rather like the carbon atoms in benzene, and it turns out that there are states such that the electrons tend to be localized to that hexagon.  Within a Wannier framework, the amplitudes for an electron to hop from the + and - labeled sites to the nearest (red) site are equal in magnitude but opposite in sign.  So, hopping out of the hexagon does not happen, due to destructive interference of the two trajectories (one from the + site, and one from the - site).

Of course, if the flat band is empty, or if the flat band is buried deep down among the completely occupied electronic states, that's not likely to have readily observable consequences.  The situation is much more interesting if the flat band is near the Fermi level, the border between filled and empty electronic states.  Happily, this does seem to happen - one example is Ni3In, as discussed here showing "strange metal" response; another example is the (semiconducting?) system Nb3Cl8, described here.  These flat bands are one reason why there is a lot of interest these days in "kagome metals".

## Saturday, May 14, 2022

I'm working on a physics post about flat bands, but in the meantime I thought I would appeal to the greater community.  Our physics and astronomy graduate student association is spinning up a mentoring program, wherein senior grad students will mentor beginning grad students.  It would be interesting to get a sense of best practices in this.  Do any readers have recommendations for resources about this kind of mentoring, or examples of departments that do this particularly well?  I'm aware of the program at UCI and the one at WUSTL, for example.

## Sunday, May 01, 2022

### The multiverse, everywhere, all at once

The multiverse (in a cartoonish version of the many-words interpretation of quantum mechanics sense - see here for a more in-depth writeup) is having a really good year.  There's all the Marvel properties (Spider-Man: No Way Home; Loki, with its Time Variance Authority; and this week's debut of Doctor Strange in the Multiverse of Madness), and the absolutely wonderful film Everything, Everywhere, All at Once, which I wholeheartedly recommend.

While it's fun to imagine alternate timelines, the actual many-worlds interpretation of quantum mechanics (MWI) is considerably more complicated than that, as outlined in the wiki link above.  The basic idea is that the apparent "collapse of the wavefunction" upon a measurement is a misleading way to think about quantum mechanics.  Prepare an electron so that its spin is aligned along the $+x$ direction, and then measure $s_{z}$.  The Copenhagen interpretation of quantum would say that prior to the measurement, the spin is in a superposition of $s_{z} = +1/2$ and $s_{z}=-1/2$, with equal amplitudes.  Once the measurement is completed, the system (discontinuously) ends up in a definite state of $s_{z}$, either up or down.  If you started with an ensemble of identically prepared systems, you'd find up or down with 50/50 probability once you looked at the measurement results.

The MWI assumes that all time evolution of quantum systems is (in the non-relativistic limit) governed by the Schrödinger equation, period.  There is no sudden discontinuity in the time evolution of a quantum system due to measurement.  Rather, at times after the measurement, the spin up and spin down results both occur, and there are observers who (measured spin up, and $s_{z}$ is now +1/2) and observers who (measured spin down, and $s_{z}$ is now -1/2).  Voila, we no longer have to think about any discontinuous time evolution of a quantum state; of course, we have the small issues that (1) the universe becomes truly enormously huge, since it would have to encompass this idea that all these different branches/terms in the universal superposition "exist", and (2) there is apparently no way to tell experimentally whether that is actually the case, or whether it is just a way to think about things that makes some people feel more comfortable.  (Note, too, that exactly how the Born rule for probabilities arises and what it means in the MWI is not simple.)

I'm not overly fond of the cartoony version of MWI.  As mentioned in point (2), there doesn't seem to be an experimental way to distinguish MWI from many other interpretations anyway, so maybe I shouldn't care.  I like Zurek's ideas quite a bit, but I freely admit that I have not had time to sit down and think deeply about this (I'm not alone in that.).  That being said, lately I've been idly wondering if the objection of the "truly enormously huge" MWI multiverse is well-founded beyond an emotional level.  I mean, as a modern physicist, I already have come to accept (because of observational evidence) that the universe is huge, possibly infinite in spatial extent, appears to have erupted into an inflationary phase 13.6 billion years ago from an incredibly dense starting point, and contains incredibly rich structure that only represents 5% of the total mass of everything, etc.  I've also come to accept that quantum mechanics makes decidedly unintuitive predictions about reality that are borne out by experiment.  Maybe I should get over being squeamish about the MWI need for a zillion-dimensional hilbert space multiverse.  As xkcd once said, the Drake Equation should include a factor for "amount of bullshit you're willing to buy from Frank Drake".  Why should MWI's overhead be a bridge too far?

It's certainly fun to speculate idly about roads not taken.  I recommend this thought-provoking short story by Larry Niven about this, which struck my physics imagination back when I was in high school.  Perhaps there's a branch of the multiverse where my readership is vast :-)