## 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.

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.

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.