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 equation? Graphene can do that. You want more exotic quasiparticles described by the Weyl equation? TaAs 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.

## 12 comments:

Technically speaking, we will never be able to tell whether a particle/excitation is truly 'fundamental' or is just a 'low-energy' quasiparticle, low being defined by the highest energy resolution of our experiments. Since we can never reach infinite energy resolution, we can always build a bigger machine, which could in principle redefine our notion of fundamental. It may not (if the quantum field theory describing your current most fundamental particles is renormalizable). But you can never know for sure...

I tend to think one should not overdo this kind of thing too much. As many of the commenters posted in the linked blogs write, conflating these kinds of things too much can be confusing. I think this analogy making can be useful, and it can be interesting, but it is not always useful. I like Tony Leggett's commentary on this now almost 30 years ago in a review in Physics Today of a Volovik book on He3.

https://physicstoday.scitation.org/doi/10.1063/1.2808980?journalCode=pto

Leggett wrote, "As to the correspondences with particle physics, being the kind of philistine who does not feel that, for example, his understanding of the Bloch equations of nmr is particularly improved by being told that they are a consequence of Berry's phase, I have to confess to greeting the news that the "spin-orbit waves" of 3He-A are the analog of the W boson and the "clapping" modes the analog of the graviton with less than overwhelming excitement. These analogies no doubt display a certain virtuosity, but it is not clear that they actually help our concrete understanding of either the condensed matter or the particle-physics problems very much, especially when they have to be qualified as heavily as is done here."

Actually, I tend to think these analogies are usually more interesting than they are useful. But I do think it is interesting to think a bit as to why these analogies exist. I do not want to toot my own horn too much, but this was the subject of an Aspen lecture I gave some years ago. Its level may be better matched to readers of this blog than the "general audience" it was supposed to be for.

https://www.youtube.com/watch?v=cdam0l3A2uU

It is a shame that the controversy over the analogy making has taken attention away from what is a very nice result otherwise. An axial amplitude mode that gives insight into the nature of the CDW state in this compound and the manner it which is was measured (quantum interference) are super interesting by themselves.

Some texts distinguish collective excitations and quasiparticles. You’ve lumped them all together.

Peter, I agree w/ both of your comments, and thanks for the link to your fun and engaging talk!

Anon, yes, I was a bit sloppy. A bulk plasmon, for example, is a collective excitation (basically the zero-momentum mode), while a propagating surface plasmon polariton is more quasiparticle-like in the sense of transporting energy and momentum and having a well-defined dispersion. It is definitely worth thinking about how we define these things, to make sure we're not talking about a distinction without a difference. I admit that I have not tried to formulate a rigorous technical definition of a quasiparticle here.

I think generally quasiparticles refer to fermion-ic type modes, while collective modes are boson-ic. So a gapped magnon, phonon, or plasmon is a collective mode, but Weyl fermions are quasiparticles. So surface plasmon polariton is also a collective mode, not quasiparticle.

From the particle physics perspective, calling these condensed matter modes with the same terminology diminishes from the importance of the original particle physics version with no added insight (cf Leggett's comment reproduced above). For a particle physicist, it is totally unsurprising that you get all sorts of low-energy modes in condensed matter where you can realize basically any sort of Hamiltonian. So it doesn't make sense to capitalize on HEP phenomena when you aren't adding to the search but instead just desensitize the already disillusioned public.

Anon, I’ve read the Wikipedia page about quasiparticles, too, but I think you will find that definition doesn’t work well across the community as a whole. An exciton, for example, is considered a quasiparticle by many, and it’s a bosonic. There are also anyonic quasiparticles in 2D systems. See, too, https://www.cambridge.org/core/books/string-theory-methods-for-condensed-matter-physics/bosonic-quasiparticles-phonons-and-plasmons/1F9D4DD3ED338C53D2D8644FDCB3D369 as an example of a textbook that disagrees with that definition.

I also think that’s a pretty hot take to basically imply that all of CMP is rather trivial compared to HEP because you can get “basically any sort of Hamiltonian.” I think it’s pretty interesting that we can make a list of unobserved HEP ideas (one could argue that those ideas were unsuccessful from the HEP perspective, since the particles don’t seem to exist in free space in nature) that actually do show up in condensed matter embodiments. Peter’s talk linked above is a fun look at some of this.

One should not forget that there are condensed matter systems that do not have quasiparticles, like the bad and strange metals. It should be a surprise that this is not the case most often, but that it because of the unreasonable effectiveness of Landau Silin Fermi Liquid theory.

Re: quasiparticles vs. collective modes. I think a lot of the above discussion is making an apples to oranges comparison. I'd call a quasiparticle an excitation that is $almost$ an eigenstate of the system and which possibly becomes an eigenstate in the low energy limit. This implies at some arbitrarily low, but finite energy it can still be understood in terms of the non-interacting degrees of freedom, but with a finite lifetime. So the quasiparticle concept tells us that we don't need to know the exact eigenstates. Approximate ones can be OK. Landau fermonic quasiparticles are the canonical example because they become exact eigenstates as their energy approaches E_F and have a scattering rate that is small at not too large energies. Eps don't have to be fermions. One can imagine thinking of phonons in some very non-harmonic crystal as quasiparticles e.g. non-harmonicity allows phonon decay into multiple phonons, but for short enough times this decay is unlikely and its still useful to think of almost free phonons. In this regard anyons in FQHE systems or spinons in a QHE can be quasiparticles. The QP concept tells us it it useful to look for degrees of freedom (e.g. a basis) that make the residual interactions small, but they don't need to be zero. Particles with small, but not zero residual interactions are Eps.

In contrast collective modes refer to something else. Collective modes are excitations that are composed of "many" of some other degree of freedom that one could imagine being uncoupled. And when they are coupled new degrees of freedom result. A simple example would be a spin wave. One can imagine some state of uncoupled spins, where the excitations are individual localized spin flips. But if one includes spin-spin coupling, the elementary excitations are spin waves that exist throughout the crystal and include all spins. This is a somewhat trivial example because a localized spin slip has a lot of similar properties to a propagating spin flip. But one can also have examples where new collective modes appear that don't have an analog in the uncoupled problem. The amplitude modes of this Raman paper are example of this.

Frequently finding quasiparticles is a matter of finding the right basis to describe them. One could describe phonons entirely in terms of local vibrations and then include coupling as a interaction. But this will probably look like a very complicated strongly interacting problem in terms of original degrees of freedom. Whereas we know if we transform to the right basis (momentum space), then it is becomes an uncoupled (or weakly coupled) problem. For instance spin excitations can look simple if one picks the right direction for angular momentum basis that takes into account the relevant symmetries, but if you pick the wrong direction they excitations can look strongly coupled.

Moreover, I’d say that in realistic systems all collective modes are quasiparticles, but not all quasiparticles are collective modes eg landau QP with Z~< 1 are not collective modes, at least not in the basis of the non interacting k states.

That’s me immediately above.

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