# Monthly Archives: August 2015

## Thoughts on Consistency and Physical Approximations

Ever since the series of posts about the Theory of Everything (ToE) and Upward Heritability (see here, here, here and here), I have felt like perhaps my original perspective lacked some clarity of thought. I recently re-read the chapter entitled Physics on a Human Scale in A.J. Leggett’s The Problems of Physics. In it, he takes a bird’s eye view on the framework under which most of us in condensed matter physics operate, and in doing so, untied several of the persisting mental knots I had after that series of blog posts.

The basic message is this: in condensed matter physics, we create models that are not logically dependent on the underlying ToE. This means that one does not deduce the models in the mathematical sense, but the models must be consistent with the ToE. For example, in the study of magnetism, the models must be consistent with the microscopically-derived Bohr-van Leeuwen theorem.

When one goes from the ToE to an actual “physical” model, one is selecting relevant features, rather than making rigorous approximations (so-called physical approximations). This requires a certain amount of guesswork based on experience/inspiration. For example, in writing down the BCS Hamiltonian, one neglects all interaction terms apart from the “pairing interaction”.

Leggett then makes an intuitive analogy, which provides further clarity. If one is building a transportation map of say, Bangkok, Thailand, one could do this in two ways: (i) One could take a series of images from a plane/helicopter and then resize the images to fit on a map or (ii) one could draw schematically the relevant transportation features on a piece of paper that would have to be consistent with the city’s topography. Generally, scheme (ii) will give us a much better representation of the transportation routes in Bangkok than the complicated images in scheme (i). This is the process of selecting relevant features consistent with the underlying system.  This is usually the process undertaken in condensed matter physics. Note this process is not one of approximation, but one of selection while retaining consistency.

With respect to the previous posts on this topic, I stand by the following: (1) I do still think that Laughlin and Pines’ claim that certain effects (such as the Josephson quantum) cannot be derived from the ToE to be quite speculative. It is difficult to prove either (mine or L&P’s) viewpoint, but I  take the more conservative (and what I would think is the simpler) option and suggest that in principle one could obtain such effects from the ToE. (2) Upward heritability, while also speculative, is a hunch that claims that concepts in particle physics and condensed matter physics (such as broken symmetry) may result from a yet undiscovered connection between the two realms of physics. I still consider this a plausible idea, though it could be just a coincidence.

Previously, I was under the assumption that the views expressed in the L&P article and the Wilzcek article were somehow mutually exclusive. However, upon further reflection, I no longer think that this is so and have realized that in fact they are quite compatible with each other. This is probably where my main misunderstanding laid in the previous posts, and I apologize for any confusion this may have caused.

## Potential Women Nobelists

In the lead-up to the conferring of the 2014 Nobel Prize in Physics, Slate published an article asking why so few women have been endowed with the award. I don’t like many aspects of the Nobel Prize and other awards singling out individual scientists (even in circumstances where they may be deserved), but I agree with several aspects of the Slate piece. There are some interesting facts to consider from the article:

Women earned 20 percent of U.S. physics Ph.D.s in 2012, up from 2 percent in 1966; they hold 14 percent of U.S. physics faculty slots and have headed some of the nation’s top physics departments and major scientific agencies. Five women have been president of the American Physical Society (the sixth was just elected and will serve in 2017); the society’s current and previous executive officers are also women.

So it is surprising in light of these numbers that women have won exactly zero Nobel Prizes in Physics in the past 50 years. These numbers suggest that there likely exists some bias on the part of the Nobel selection committee. This claim does not seem so far-fetched when considering the blatant oversights of Rosalind Franklin for the Medicine and Physiology Nobel in 1962 and of Jocelyn Bell Burnell for the Physics Nobel in 1974. I have previously mentioned the difficult circumstances under which women must work in our physics departments due to these biases, citing the eloquent piece by Eileen Pollack in the New York Times.

The article goes on to highlight the work of 10 women, which it claims are deserving of the Nobel Prize in Physics:

1. Jocelyn Bell Burnell – Pulsars
2. Mildred Dresselhaus – Carbon Materials
3. Lene Hau – Stopping Light with a Bose-Einstein Condensate
4. Deborah Jin – Ultracold Fermionic Condensation
5. Vera Rubin – Calculation Galactic Rotational Speeds
6. Margaret Geller – Making a Map of the Known Universe
7. Fabiola Gianotti – Head of ATLAS Team that Discovered the Higgs Boson
8. Margaret Murnane – Ultrafast Pulsed Lasers on the Femtoscale
9. Helen Quinn – Prediction of the Axion
10. Lisa Randall – General Relativity and Quantum Field Theory

I’m not an expert (far from it!) in particle physics, so I have just regurgitated the Slate list. Even then, putting Lisa Randall on this list seems a little far-fetched. She may, though, be a candidate for the Fundamental Physics Prize, which again has only bestowed individual awards to men (Fabiola Gianotti shared an award for being a part of the team that discovered the Higgs).

In the field where I am more knowledgeable, Deborah Jin, Mildred Dresselhaus and Margaret Murnane would all be worthy recipients of the Nobel. They have all been recognized with numerous awards in their respective careers.

The Slate article does a great job of helping us get to know the listed women and their work a little better. Hopefully a woman (or several!) will be recognized for their scientific accomplishments soon by the Nobel committee and end this unwarranted drought.

## A Plea for More Plots of the Energy Loss Function

In the modern landscape of condensed matter physics, it seems like while it is important to get a well-rounded and comprehensive view of the experimental status within each topic, that most physicists are biased towards their favorite standard experimental probes. For me, I have to admit that when getting acquainted with a certain topic, that I tend to lean towards reading papers that use ARPES, inelastic neutron scattering and optical spectroscopy.

I especially like the latter two because of the very close relationship to the spin-spin correlation function and the current-current correlation function respectively. This means that these probes are constrained to satisfy certain sum-rules, which provide strong constraints on response functions regardless of the state of matter probed.

With regard to optical spectroscopy, I do have one complaint — it would be great if authors would plot the energy loss function, $-\textrm{Im}(1/\epsilon)$, more often. Recently, when trying to get an overview of the iron-arsenide superconductors, I found that I couldn’t find a paper that plotted the energy loss function for these compounds. Most papers plotted only the reflectivity and optical conductivity. A few plotted the deduced scattering rates, but none seemed to plot the energy loss function.

Below are a list of a few papers (some have paywalls) that I went through, many of which are great. However, I would love it if authors would plot the energy loss function in the future.

Why is the energy loss function important? Well, it gives one an idea of the effective Coulomb interaction in a solid. This is important considering that how the Coulomb interaction is modified by the lattice vibrations and electrons is often critical in the formation of a material’s ground state. Also, interesting collective modes that form in a ground state (usually because of these interactions) will exhibit peaks in the energy loss function.

For instance, this classic paper by Uchida et al. shows the energy loss function in LSCO as a  function of doping in Fig. 9(a), which one could view (perhaps!) as the development of a free carrier plasmon with increased doping. This information is not easily discernible from the other optical constants (except maybe the reflectivity, but even then the development of the plasmon is not clear).

The reflectivity and optical conductivity are extremely useful, but often the energy loss function has information buried that isn’t easily visualized in the other optical constants. So a plea to optical spectroscopists: please plot the energy loss function in the future when it is relevant.

## Bardeen, CDWs and Macroscopic Quantum Phenomena

There is a well-written 1990 Physics Today article by John Bardeen entitled Superconductivity and Other Macroscopic Quantum Phenomena (pdf!). For those who are unaware, Bardeen was a two-time Nobel Laureate in Physics for inventing the transistor and secondly for the BCS theory of superconductivity.

Later in his career, Bardeen focused on the theory of transport in quasi-1D charge density wave materials. Bardeen was vocal in advocating that the transport in these materials must be understood in a quantum mechanical manner whereas most other physicists working on the problem treated it as a classical one (see True Genius by Daitch and Hoddeson). In the Physics Today article, he describes why he believes that the CDW sliding in these quasi-1D materials must be viewed as a manifestation of a macroscopic quantum phenomenon similar to that in superconductors and superfluids.

While Bardeen seemed to have lost his battle against the mainstream condensed matter physics community on this point upon his death in 1991, some interesting work has taken place since his death that has started to provide evidence for his perspective. In 1997, Monceau and co-workers showed the presence of Aharonov-Bohm-like oscillations in the CDW compound NbSe$_3$, with an oscillation period of, interestingly, $hc/2e$. While his tunneling theory of CDW transport may have been incorrect, his view of CDW transport as a macroscopic quantum phenomenon may yet be vindicated.

A lot of interest in these problems dissipated as scientists shifted to work on the problem of high temperature superconductivity following the discovery of the cuprates in 1986. However, it seems to me that there are still many unresolved issues in these compounds that persist to the present day that were cast aside rather than figured out.

As Paul Valery once said:

A poem is never finished, only abandoned.

The same can aptly be said about scientific problems.

## Toyota, General Motors and the Quest for Quality

A couple weeks ago, This American Life, the podcast from which this blog derives its name, aired an episode entitled NUMMI. The episode covered several aspects that led to General Motors’ decline and Toyota’s increased market share among auto-makers in the United States in the 1990s.

One of the cited reasons for GM’s downfall stood out in my mind: the emphasis of quantity over quality. While Toyota stressed manufacturing reliable cars, GM was trying to maximize the number of cars it was able to produce behind the idea that repairs could be taken care of at a later time. Ultimately, the consumers lost confidence in GM’s product, GM went bankrupt, and it was bailed out by the US government with \$50 billion of taxpayer money.

Why did Toyota stress reliability and GM highlight volume? From the point of view of the podcast, it had to do with the management structure as well as labor relations between the auto-workers and upper management. Without getting mired in details, Toyota had a far superior management structure where workers felt like they could contribute ideas and wanted the product to succeed.

I bring these issues up because in today’s academic climate in the sciences, there are some apt parallels. Because of the structure put in place either by government funding agencies or by the administrators at universities, there is an ever-increasing pressure to publish papers. Of course, the added emphasis on volume does not necessarily have to lead to a decline in quality, but there does appear to be an inherent tension between quantity and quality. It is quite easy to intuit that in a world where publication quality reigns supreme, there would be far fewer publications in total.

There is a lot of fantastic science done in the present time, but because of the pressure to publish papers I am afraid that there is not enough time for a thorough education and proper scientific development. It is interesting to note that Richard Feynman published a moderate 85 refereed publications in his lifetime, but they were often of the highest quality. Truly remarkable breakthroughs take years of deep thought, synthesis and attention to detail, i.e. time.

It would be great to see a more concerted effort to manufacture more reliable cars, not just making many cars with the hope that a few will be manufactured well.

## Excitonic Insulator

The state of matter dubbed the excitonic insulator was first qualitatively discussed by Mott, Keldysh and Kopaev, and others and then expanded upon more systematically by Jerome, Rice and Kohn.

The excitonic insulating state can be considered from two normal states (pictured below). Either the system must be a small-gap semiconductor or a small indirect overlap semimetal. In fact, Mott had first considered the semimetallic limit, while Kohn and others had considered the semiconducting limit.

Intuitively, one can consider the following two heuristic arguments from the different limits, as presented in the article by Rossnagel, which was cited in the previous post:

1. Semiconducting limit: If one can somehow reduce the band gap energy, $E_G$, then at some point, the binding energy to form an exciton, $E_B$, will exceed $E_G$, and the system will unstable to the spontaneous formation excitons.
2. Semimetallic limit: In this case, one considers screening effects. If one decreases the band overlap, a characteristic energy, $E_1$, will be reached such that particle-hole pairs will be insufficiently screened, leading to a localization of the charge carriers.

Therefore, in the regime of $E_1$$E_G$ <$E_B$, the excitonic insulator state is expected. Properties of the excitonic insulator state are presented pedagogically in a Les Houches lecture by Kohn in this book, which is very difficult to find!

In a solid state context, it has been difficult to establish whether the excitonic insulator state has been realized because a lattice distortion is expected to accompany the transition to the excitonic insulator ground state. Therefore, it is difficult to isolate the driving mechanism behind the transition (this difficulty will be familiar to those who study high T-c superconductivity!).

There are a few materials suspected to possess excitonic insulator ground states in a solid state setting: 1T-TiSe$_2$, Ta$_2$NiSe$_5$ and TmSe$_{0.45}$Te$_{0.55}$. In my personal opinion, the case for 1T-TiSe$_2$ is probably the strongest purely because there have been far more experiments on this material than the other candidate materials.

Though this state of matter was considered almost 50 years ago, it still remains relevant today. As Landau once said,

Unfortunately, everything that is new is not interesting, and everything which is interesting, is not new.

## Transition Metal Dichalcogenide CDWs

There is an excellent review paper by K. Rossnagel on the origin of charge density waves (CDWs) in the transition metal dichalcogenide compounds (such as 2H-NbSe$_2$, 1T-TiSe$_2$, 2H-TaSe$_2$, etc.) . A lot of the work on these materials was undertaken in the 70s and 80s, but there has been a recent revival of interest because of the nature of superconductivity in a few of these compounds.

By “nature”, I mean that  the phase diagrams in these materials bear a striking resemblance to the phase diagram in the cuprates, except that the anti-ferromagnetism is replaced by a CDW phase. Shown below is the phase diagram for 1T-TiSe$_2$ under pressure and with copper intercalation (taken from this paper).

Strangely, with copper intercalation, the Hall resistance is negative, while  it is positive under pressure. This is interesting because like the cuprates, superconductivity can be brought about with either electrons or holes as majority carriers. A similar phase diagram is also observed for another TMD 1T-TaS$_2$ (see here for instance). 1T-TaS$_2$ has also been shown to exhibit Mott physics at low temperature in the parent compound.

It is suspected that the origin of the CDWs in 1T-TiSe$_2$ and 1T-TaS$_2$ are at least in part electronically driven (see Rossnagel’s review article and references therein). This makes the observation of the superconductivity in these compounds all the more interesting — as the superconductivity may also be primarily electronically driven. I have also blogged previously about another set of CDW materials (the rare earth tritellurides) that exhibit cuprate-like phase diagrams including an antiferromagnetic phase, and also about the interplay between CDWs and superconductivity in NbSe$2$.

It seems to me that there are some really quite fundamental open questions in the study of these compounds, which is in part why I keep re-visiting this topic myself.