Friday, June 24, 2022

Implementing a model of polyacetylene

An impressive paper was just published in Nature, in which atomically precisely fabricated structures in Si were used as an analog model of a very famous problem in physics, the topological transition in trans-polyacetylene. 

Actual trans-polyacetylene is an aromatic organic chain molecule, consisting of sp2 hybridized carbons, as shown.  This is an interesting system, because you could imagine swapping the C-C and C=C bonds, and having domains where the (bottom-left to top-right) links are double bonds, and other domains where the (top-left to bottom-right) links are double bonds.  The boundaries between domains are topological defects ("solitons").  As was shown by Su, Schrieffer, and Heeger, these defects are spread out over a few bonds, are energetically cheap to form, and are mobile.  

(Adapted from Fig 1 here)
The Su-Schrieffer-Heeger model is a famous example of a model that shows a topological transition.  Label site-to-site hopping along those two bond directions as \(v\) and \(w\).  If you have a finite chain, as shown here, and \(v > w\), there are no special states at the ends of the chain.  However, \(v < w\) for the system as shown, it is favorable to nucleate two "surface states" at the chain ends, with the topological transition happening at \(v = w\).  

The new paper that's just been published takes advantage of the technical capabilities developed over the last two decades by the team of Michelle Simmons at UNSW.  I have written about this approach here.  They have developed and refined the ability to place individual phosphorus dopant atoms on Si with near-atomic precision, leading them to be able to fabricate "dots" (doped islands) and gate electrodes, and then wire these up and characterize them electrically.  The authors made two devices, each  a chain of islands analogous to the C atoms, and most importantly were able to use gate electrodes to tune the charge population on the islands.  One device was designed to be in the topologically trivial limit, and the other (when population-tuned) in the limit with topological end states.  Using electronic transport, they could perform spectroscopy and confirm that the energy level structure agrees with expectations for these two cases.

(Adapted from Fig 2 here)

This is quite a technical accomplishment.  Sure, we "knew" what should happen, but the level of control demonstrated in the fabrication and measurement are very impressive.  These bode well for the future of using these tools to implement analog quantum simulators for more complicated, much harder to solve many-body systems.  

Sunday, June 12, 2022

Quasiparticles and what is "real"

This week a paper was published in Nature about the observation via Raman scattering of a particular excitation in the charge density wave materials RTe3 (R = La, Gd) that is mathematically an example of an "amplitude mode" that carries angular momentum that the authors identify as an axial Higgs mode.  (I'm not going to get into the detailed physics of this.)

The coverage of this paper elicited a kerfuffle on blogs (e.g here and here) for two main reasons that I can discern.  First, there is disagreement in the community about whether calling a mode like this "Higgs" is appropriate, given the lack of a gauge field in this system (this is in the comments on the second blog posting).  That has become practice in the literature, but there are those who strongly disapprove.  Second, some people are upset because some of the press coverage of the paper, with references to dark matter, hyped up the result to make it sound like this was a particle physics discovery, or at least has implications for particle physics. 

This does give me the opportunity, though, to talk about an implication that I see sometimes from our high energy colleagues in discussions of condensed matter, that "quasiparticles" are somehow not "real" in the way of elementary particles.  

What are quasiparticles?  In systems with many degrees of freedom built out of large numbers of constituents, amazingly it is often possible to look at the low energy excitations above the ground state and find that those excitations look particle-like - that is, there are discrete excitations that, e.g., carry (crystal) momentum \(\hbar \mathbf{k}\), have an energy that depends on the momentum in a clear way \(\epsilon(\mathbf{k})\), and also carry spin, charge, etc.  These excitations are "long lived" in the sense that they propagate many of their wavelengths (\(2 \pi/|\mathbf{k}|\)) before scattering and have lifetimes \(\tau\) such that their uncertainty in energy is small compared to their energy above the ground state, (\(\hbar/\tau << \epsilon(\mathbf{k})\)).  The energy of the many-body system can be well approximated as the sum of the quasiparticle excitations:  \(E \approx \Sigma n(\mathbf{k})\epsilon(\mathbf{k})\).  

There are many kinds of quasiparticles in condensed matter systems.  There are the basic ones like (quasi)electrons and (quasi)holes in metals and semiconductors, phonons, magnons, polarons, plasmons, etc.  While it is true that quasiparticles are inherently tied to their host medium, these excitations are "real" in all practical ways - they can be detected experimentally and their properties measured.  Indeed, I would argue that it's pretty incredible that complicated, many-body interacting systems so often host excitations that look so particle-like.  That doesn't seem at all obvious to me a priori.  

What has also become clear over the last couple of decades is that condensed matter systems can (at least in principle) play host to quasiparticles that act mathematically like a variety of ideas that have been proposed over the years in the particle physics world.  You want quasiparticles that mathematically look like massless fermions described by the Dirac equationGraphene can do that.  You want more exotic quasiparticles described by the Weyl equationTaAs can do that.  You want Majorana fermions?  These are expected to be possible, though challenging to distinguish unambiguously.  Remember, the Higgs mechanism started out in superconductors, and the fractional quantum Hall system supports fractionally charged quasiparticles.  (For a while it seemed like there was a cottage industry on the part of a couple of teams out there:  Identify a weird dispersion relation \(\epsilon(\mathbf{k})\) predicted in some other context; find a candidate material whose quasiparticles might show this according to modeling; take ARPES data and publish on the cover of a glossy journal.)

Why are quasiparticles present in condensed matter, and why to they "look like" some models of elementary particles?  Fundamentally, both crystalline solids and free space can be usefully described using the language of quantum field theory.  Crystalline solids have lower symmetry than free space (e.g. the lattice gives discrete rather than continuous translational symmetry), but the mathematical tools at work are closely related.  As Bob Laughlin pointed out in his book, given that quasiparticles in condensed matter can be described in very particle-like terms and can even show fractional charge, maybe its worth wondering whether everything is in a sense quasiparticles.  

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

Grad students mentoring grad students - best practices?

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 :-)

Monday, April 25, 2022

Science Communications Symposium

 I will be posting more about science very soon, but today I'm participating in a science communications symposium here in the Wiess School of Natural Sciences at Rice.  It's a lot of fun and it's great to hear from some amazing colleagues who do impressive work.   For example, Lesa Tran Lu and her work on the chemistry of cooking, Julian West and his compelling scientific story-telling, Scott Solomon and his writing about evolution, and Kirsten Siebach and her work on Mars rovers and geology.

(On a side note, I've now been blogging for almost 17 years - that makes me almost 119 blog-years old.)

UPDATE:  Here is a link to a video of the whole symposium.