Saturday, May 14, 2022

Emergence matters (in a nutshell)

Emergence is one of the most important concepts in the sciences: from physics to biology to sociology. Most of the big questions in science involve emergence. Yet there is no consensus about what emergence is, how to define it, or why it matters. This is my own attempt to clarify what some of the important issues and questions are. For reasons of brevity, I give no references and only a few examples. They can come later. Here I am trying to take a path that is intermediate between the precision of philosophers and the looseness of condensed matter physicists' discussion of emergence. My goals are clarity and brevity.

Characteristics of emergent phenomena

Consider a system that is composed of many interacting parts. If the properties of the system are compared with the properties of the individual parts, a property of the whole system is an emergent property if it has the following characteristics.

1. Novelty 

An emergent property of the system is a property that is not present in the individual parts of the system.

2. Modification of parts 

An emergent property of the system is associated with a modification of the properties of and the relationships between the parts of the system. 

3. Universality

An emergent property is universal in the sense that it is independent of many of the details of the parts. As a consequence, there are many systems that can have the emergent property.

4. Irreducibility

An emergent property can be reduced to properties of the parts.

5. Predictability

An emergent property is difficult to predict solely from knowledge of the properties of the parts and how they interact with one another.

Here are a few issues to consider about the five characteristics above. 

First, “emergent property” could possibly be replaced with emergent phenomenon, object, or state.

Second, for each of the five characteristics is it necessary and/or sufficient for the system property to be emergent?

Third, one of the most contested characteristics concerns predictability. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity, which provided a posteriori, rather than a priori, understanding. A key word in the statement above is “solely”.

Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties. The property of the system is simply the sum of the properties of the parts.

Scales and hierarchies

Central to emergence is the idea of different scales. Emergent properties only occur when scales become larger. Scales that are simply defined, and might be called extrinsic, are the number of parts, length scale, and time scale. A more subtle scale, which might be called intrinsic, are the scales associated with the emergent property. This emergent scale is intermediate between that of the parts and that of the whole system.

Emergent scales lead naturally to hierarchies, such those associated with different scientific disciplines, as shown below. Hierarchies also occur within individual disciplines.

At each level there are distinct phenomena, concepts, theories, and scientific methods.

Another important scale is that of complexity. Generally, as one goes up the hierarchy one says that the level of complexity increases. Giving a precise version of such statements is not simple.

Complexity

Simple rules can lead to complex behaviour. This is nicely illustrated by cellular automata. It is also seen in other systems with emergent properties. For example, the laws describing the properties of electrons and ions in a crystal or a large molecule are quite simple (Schrodinger’s equation plus Coulomb’s law). Yet from these simple rules, complex phenomena emerge: all of chemistry and condensed matter physics!

There is no agreed universal measure for the complexity of a system or with many components. One possibility is the Kolmogorov measure. Using such measures to elucidate emergence, such as how complexity changes with other scales, is an important challenge.

Other issues

There are a host of other issues and topics that enter discussions about emergence. Some of these are of a more philosophical nature. Here I just list them: robustness, quality vs. quantity, objective vs. subjective, universality vs. particularity, ontology vs. epistemology, discontinuities, incommensurability, theory reduction, asymptotic singularities, top-down causation, supervenience, differentiation and integration (not calculus) of system parts, reductionism, foundationalism, fundamentalism, strong versus weak emergence, and criteria for theory acceptance.

Discussion of some of these issues can be quite abstract but to make the discussion above more precise they may need to be considered. 

Emergence is relevant to practical matters such as scientific strategy, priorities, allocation of resources, and our dispositions as scientists. Too often views on these issues are implicit and not reflected upon. 

The practical matter of scientific strategy

When studying a system, the first choice that must be made is what scale or scales to focus on. For example, in materials science, the options range from the atomic scale to the macroscopic. This choice determines the tools and methods, both experimental and theoretical, that can be used to study the system. In different words, the scientist is making a choice of ontology: the object they choose to study. This then determines epistemology: the concepts, theories, and organising principles may use or hope to discover. Effective theories and toy models enter here. 

When systems have been studied by a range of methods and at a range of scales, a challenge is the synthesis of the results of these studies. Value-laden judgements are made about the priority, importance, and validity of such attempts at synthesis. Often synthesis is relegated to a few sentences in the introductions and conclusions of papers.

For known systems and emergent properties, there is the possibility of creating new methods and probes to investigate them at appropriate scales.

New systems can be created and investigated in the hope of discovering new emergent properties (e.g., new states of matter) or more modestly, that manifest an emergent property that is more amenable to scientific study or technological application.

As emergent properties involve multiple scales they are often of interest to and amenable to study by more than one scientific discipline. This creates opportunities and challenges for inter-disciplinary collaboration.

Individual scientists must and do make decisions about the relative priority of the different strategies outlined above. Research groups, departments, institutions, professional societies, and funding agencies must and do also make decisions about such priorities. The decision outcomes are also emergent properties of a system with multiple scales from the individual scientist to global politics. I claim that too often these weighty decisions are made implicitly, rather than explicitly following debate and deliberation.

The disposition of the scientist

All scientists are human. In our professional life, we have hopes, aspirations, values, fears, attitudes, expectations, and prejudices. These are shaped by multiple influences from the personal to the cultural to the institutional. We should reflect on the past century of our study of emergent systems from physics to biology to sociology. If we honestly evaluate our successes and failures I think this may lead us to have certain dispositions that are interrelated.

Humility. There is so much we do not understand. Furthermore, we fail abjectly at predicting emergent properties. This is not surprising. Unpredictability is one of the characteristics of emergent properties. There is a hubris associated with grand initiatives such as “the theory of everything”, the Human Genome Project, “materials by design”, and macroeconomic modelling. 

Expect surprises. There are many exciting discoveries waiting. They will be found by curiosity and serendipity.

Wonder. Emergent phenomena are incredibly rich and beautiful to behold, from physics to biology to sociology. Furthermore, the past century has seen amazing levels of understanding. But this is a “big picture” and “coarse-grained” understanding, not the description that the reductionists lust for and claim possible. 

Realistic expectations. Given the considerations above I think we should have modest expectations of the levels of understanding possible, and what research programs, from that of individual scientists to billion-dollar initiatives, can achieve. We need to stop the hype. Modest expectations are particularly appropriate with respect to our ability to control emergent properties.

The holy grail

“The philosophers have only interpreted the world, in various ways. The point, however, is to change it.”

Karl Marx

Understanding complex systems with emergent properties is an ambitious scientific challenge. This enterprise has intrinsic intellectual merits. But a whole other dimension and challenge is to use this understanding to modify, manipulate, and control the properties of systems with emergent properties. This enticing prospect appeals to technologists, activists, and governments. Such promises feature prominently in grant applications, press releases, and reports from funding agencies. Diverse examples of this control goal include chemical modification of known superconductors to produce room-temperature superconductivity, drug design, social activism, the leadership of business corporations, and governments attempting to manage the economy. 

However, we should honestly reflect on decades of “scientifically informed” and “evidence-based” initiatives in materials science, medicine, poverty alleviation, government economic policy, business management, and political activism. Unfortunately, the fruit from these initiatives is disappointing, particularly compared to what has often been promised.

My goal is not to promote despair but rather to prevent it.  With more realistic expectations, based on reality rather than fantasy, we are more likely to make significant progress in finding ways to make some progress (albeit modest but worthwhile) in learning how to manipulate these complex systems.

This post contains many claims that require discussion, refinement or abandonment. I welcome suggestions on how to improve these ideas.

Tuesday, April 26, 2022

The Story of Science is a nice video series

 I am on the lookout for good video resources about science that I can recommend to others, particularly non-scientists. By chance, I recently came across the BBC production, The Story of Science: Power, Proof, and Passion, hosted by Michael Mosley.

There is also a beautiful book that goes with the series, containing more detail, including colour illustrations. I was able to get the DVDs and the book from my local public library.

I particularly appreciate that science is presented as a human endeavour and progress is influenced by local contexts (economic, political, religious, ...). That can be acknowledged and enjoyed without descending into a social constructivist view of scientific knowledge. In a similar vein, the series does not have an ideological edge, or embrace some common tropes that too often popular video treatments may promote such as science the saviour, science the moneymaker, science the spoiler, science the monster-maker, ... or that science is uncontrollable, is inscrutable, or is the domain of evil/eccentric geniuses,....

The series introduced me to several colourful characters who played key roles in the history of science, including Hennig Brand, Hans Sloan, Georges Cuvier, Horace-Benedict de Saussure, Simon Sevin, Richard Trevithick, ...

Thursday, April 14, 2022

Elite imitation and flailing universities

The mission of universities is thinking: teaching students to think and enabling scholars to think about the world we live in. Yet, it is debatable whether most universities in the world achieve these goals. Arguably, things are getting worse. Universities are flailing. Why?

Most universities desperately want to be elite. They want to be like Harvard, Caltech, Oxford, Princeton, Berkeley, Stanford, ...
But non-elite universities do not have the necessary resources to be elite. Yet they are controlled by elites (management on high salaries, faculty educated at elite universities) who want to be elite and so settle for elite imitation.

"A flailing university is what happens when the principal cannot control its agents. The flailing university cannot implement its own plans and may have its plans actively subverted when its agents work at cross-purposes. The non-elite university flails because it is simultaneously too large and too small: too large because the non-elite university attempts to legislate and regulate every aspect of the work of faculty and students and too small because it lacks the resources and personnel to achieve its ambitions. 

To explain the mismatch between the non-elite universities' ambitions and their abilities, consider the premature demands by elites in non-elite universities for goals, policies, curricula, infrastructure, and outcomes more appropriate to an elite university. 

In order to satisfy external actors (government, business, parents, ...) non-elite universities often take on tasks that overwhelm institutional capacity, leading to premature load bearing. As these authors put it, “By starting off with unrealistic expectations of the range, complexity, scale, and speed with which organizational capability can be built, external actors set both themselves and (more importantly) the students and researchers that they are attempting to assist to fail”. 

The expectations of external actors are only one source of imitation, however. Who people read, listen to, admire, learn from, and wish to emulate is also key. Another factor driving inappropriate imitation is that the elites in non-elite universities—senior management and high-profile faculty—are closely connected with business elites and elite universities, usually more closely than they are to the students and faculty at their own university. As a result, this elite initiates and supports policies that appear to it to be normal even though such policies may have little relevance to the student and faculty as a whole and may be wildly at odds with the university capacity. This kind of mimicry of what appear to be the best elite university policies and practices is not necessarily ill intentioned. It is simply one by-product of the background within which the elites operates. University managers engage with business elites and managers at other non-elite universities."

I actually did not write most of the text above, I just took the text from the first two pages of the article below and replaced some words (e.g. Indian state with non-elite university, Indian citizens with students and faculty). 

Premature Imitation and India’s Flailing State 
Shruti Rajagopalan, Alexander T. Tabarrok

I came across the article after listening to a podcast episode that interviews the two authors, recommended by my son.

I also recommend Shutri's own podcast, Ideas of India, including a recent episode, Where did development economics go wrong?


What do you think? Are universities like a flailing state? Is the problem elite imitation?

Friday, April 8, 2022

Why is there so much symmetry in biological systems?

 One of the biggest questions in biology is, What is the relationship between genotypes and phenotypes? In different words, how does a specific gene (DNA sequence) encode information that allows a very specific biological structure with a unique function to emerge?

Like big questions in many fields, this is a question about emergence.

In biology, this mapping from genotype to phenotype occurs at many levels from protein structure to human personality. An example is how the RNA encodes the structure of a SARS-CoV2 virion.

A fascinating thing about biological structures is that many have a certain amount of symmetry. The human body has reflection symmetry and many virions have icosahedral symmetry. What is the origin of this tendency to symmetry? Could evolution produce it?

Scientists will sometimes make statements such as the following about evolution.

Symmetric structures preferentially arise not just due to natural selection but also because they require less specific information to encode and are therefore much more likely to appear as phenotypic variation through random mutations.

How do we know this is true? Can such a statement be falsified? Or at least, can we produce concrete models or biological systems that are consistent with this statement?

There is a fascinating paper in PNAS that addresses the questions above.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution 
Iain G. Johnston, Kamaludin Dingle, Sam F. Greenbury, Chico Q. Camargo, Jonathan P. K. Doye, Sebastian E. Ahnert, and Ard A. Louis 

Here are a few highlights from the article. First, how one gets specific about information content and algorithms.
Genetic mutations are random in the sense that they occur independently of the phenotypic variation they produce. This does not, however, mean that the probability P(p) that a Genotype-Phenotype [GP] map produces a phenotype p upon random sampling of genotypes will be anything like a uniformly random distribution. 
Instead, ... arguments based on the coding theorem of algorithmic information theory (AIT) (7) predict that the P(p) of many GP maps should be highly biased toward phenotypes with low Kolmogorov complexity K(p) (8). 
High symmetry can, in turn, be linked to low K(p) (6911). An intuitive explanation for this algorithmic bias toward symmetry proceeds in two steps: 
1) Symmetric phenotypes typically need less information to encode algorithmically, due to repetition of subunits. This higher compressibility reduces constraints on genotypes, implying that more genotypes will map to simpler, more symmetric phenotypes than to more complex asymmetric ones (23). 
2) Upon random mutations these symmetric phenotypes are much more likely to arise as potential variation (1213), so that a strong bias toward symmetry may emerge even without natural selection for symmetry.
The authors consider several concrete models and biological systems that illustrate this bias toward symmetry. The first involves the structure of protein complexes, as given in the Protein Data Base (PDB).


A) Protein complexes self-assemble from individual units. 

(B) Frequency of 6-mer protein complex topologies found in the PDB versus the number of interface types, a measure of complexity 
K˜(p). 
Symmetry groups are in standard Schoenflies notation: C6D3C3C2, and C1. There is a strong preference for low-complexity/high-symmetry structures. 

(C) Histograms of scaled frequencies of symmetries for 6-mer topologies found in the PDB (dark red) versus the frequencies by symmetry of the morphospace of all possible 6-mers illustrate that symmetric structures are hugely overrepresented in the PDB database. 

Note the logarithmic scales for the probabilities (frequencies), meaning that the probabilities span four orders of magnitude. The authors claim that "many genotype–phenotype maps are exponentially biased toward phenotypes with low descriptional complexity. "
This intuition that simpler outputs are more likely to appear upon random inputs into a computer programming language can be precisely quantified in the field of AIT (7), where the Kolmogorov complexity K(p) of a string p is formally defined as a shortest program that generates p on a suitably chosen universal Turing machine (UTM). 

From AIT the authors produce a bound (equation 1, and below), that exhibits the exponential decay of probability with complexity, similar to that seen in their graphs, such as the one shown below, for a model gene regulatory network that is modeled by 60 ordinary differential equations (ODEs). The red dashed line is the bound below.

𝑃(𝑝)2𝑎𝐾˜(𝑝)𝑏,  [1


Scaled frequency vs. complexity for the budding yeast ODE cell cycle model (30). Phenotypes are grouped by complexity of the time output of the key CLB2/SIC1 complex concentration. Higher frequency means a larger fraction of parameters generate this time curve. The red circle denotes the wild-type phenotype, which is one of the simplest and most likely phenotypes to appear. The dashed line shows a possible upper bound from Eq. 1. There is a clear bias toward low-complexity outputs.

One minor comment is that I was surprised that the authors did not reference the classic 1956 paper by Crick and Watson. They introduced the concept of "genetic economy". Prior to any knowledge of the actual structure of virions, they predicted that virions would have icosahedral symmetry because that reduced the cost of the genome coding for the structure of the virion.

Hence, it would be interesting to explore the relationship between the PNAS paper and this one.
There is a nice New York Times article about the PNAS paper. I thank Sophie van Houtryve for bringing that to my attention leading me to the PNAS paper.

Friday, March 25, 2022

Anthony Jacko (1985-2022): condensed matter theorist

I was very sad when last week I learned of the death of Anthony Jacko, a former member of the Condensed Matter Theory group at UQ. He was only 36 years old, having been diagnosed with stage 4 cancer at the end of last year.

Jacko's funeral was this week. Family and friends spoke warmly of his intelligence, humour, faithfulness, passion for life, and endearing quirkiness. There were both tears and laughs.

I will say something here about his scientific contributions, though at times like this what we achieve professionally does not really seem that important.

I first met Jacko as an undergraduate at UQ when he took an advanced undergraduate condensed physics course with me in 2006. That year he did an undergraduate honours (fourth year) project with Ben Powell and John Fjaerestad, on the Kadowaki-Woods ratio. This work eventually led to a Nature Physics paper, that I discussed in this blog post.

In 2007 I was quite happy when Jacko decided to do a Ph.D. with me and Ben Powell. We tried to come up with simple effective Hamiltonians for organometallic complexes that are used in organic LEDs and solar cells. Although we made some progress, I think the questions we tried to address have still not been answered definitively. The most progress has subsequently been made by Ben Powell.

For a postdoc, Jacko moved to Frankfurt to work with Roser Valenti and Harald Jeschke (now at Okayama University). I was really impressed how Jacko learned how to do reliable DFT-based electronic structure calculations and to use Wannier orbitals to extract tight-binding model parameters. Jacko brought this expertise back to Ben Powell's group at UQ, where he worked from 2013 to 2018.

During that time Jacko co-authored a string of really nice papers that inspired me to write multiple blog posts, such as those below. Looking back over that work I see how careful, solid, and systematic it is. Basically, good science, that we do not see enough of these days.

The broad issue is as follows. Understanding strong electron correlations in complex molecular materials requires effective Hamiltonians that are a realistic representation of the essential physics and chemistry. Sometimes next-nearest-neighbour interactions and subtleties in crystal structure really do matter. Other times they do not. The methods used by Jacko provided a robust way of doing this.





Faculty hope that former students will come to their funeral. We also hope that we won't have to attend the funeral of any of our students. It is very sad.

An endowment is being created at The University of Queensland, to fund an undergraduate physics prize that will be awarded each year in honour of Jacko.

My condolences to Jacko's partner, Alana, and to family and friends.

Thursday, March 17, 2022

Predicting new states of quantum matter is highly unlikely

Last year New Scientist published a nice article by Jon Cartwright

States of matter: The unthinkable forms beyond solid, liquid and gas

From time crystals to supersolids, we keep discovering extraordinary new kinds of matter – now the true challenge is being able to predict what we'll find next

Unlike the typical New Scientist article, this one is a measured and reasonable discussion about reality, rather than the latest wild and breathless speculations that the magazine is rife with. Unfortunately, it is behind a paywall.

I was interviewed for the article, which ends (see below) by contrasting my pessimism with the optimism of Andrei Bernevig. His optimism is based on this recent paper that reports a systematic identification of stoichiometric compounds that have topological bands and so can support topological states of matter. That is important and wonderful work. But, it is looking at what can be considered a "one-electron" problem, and so does not shake my pessimism. I do hope I am wrong.



Wednesday, March 2, 2022

Unusual metal-insulator transitions arising from interplay of frustration, flat bands, and strong correlations

My colleagues and I recently posted a preprint

C3 symmetry breaking metal-insulator transitions near a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

H. L. Nourse, Ross H. McKenzie, B. J. Powell

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the non-interacting theory at half-filling, the Fermi energy lies within a flat band where strong correlations are enhanced and the lattice exhibits frustration. We find a correlation driven first-order metal-insulator transition to two different insulating ground states - a dimer valence bond solid Mott insulator when inter-triangle correlations dominate, and a broken C3 symmetry antiferromagnet that arises from frustration when intra-triangle correlations dominate.

The metal-insulator transitions into these two phases have very different characters. 

The metal-broken C3 antiferromagnetic transition is driven by spontaneous C3 symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. 

The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. 

Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.

We welcome comments.

Friday, February 25, 2022

Quotes to entice and entertain the reader

Some authors make use of epigraphs in their books. An epigraph is a short quotation at the beginning of a chapter that aims to set the stage for what follows. My general observation is that many of the epigraphs are rather obscure and the connection to the content of the chapter is not clear. Perhaps, I am just too ignorant about classical literature, or perhaps some authors are just trying to be too clever. But, sometimes I think they are creative, enticing, and even humorous.

I tried having a go at using epigraphs for Condensed Matter Physics: A Very Short Introduction. Unfortunately, after doing this I discovered that epigraphs are no longer allowed in the VSI series.

Anyway, I had fun doing it and so here I present the epigraphs I came up with.

1 What is condensed matter physics?

… thin flakes like frost on the ground appeared on the desert floor. When the Israelites saw it, they said to each other, “What is it?” … [they] called the bread manna. [Manna sounds like the Hebrew for What is it?]  It was white like coriander seed and tasted like wafers made with honey.

Exodus 16 

2 A multitude of states of matter

“There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.” 

Hamlet

3 Symmetry matters

The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree...

Aristotle, Metaphysics

4 The order of things

John Milton, Paradise Lost

5 Adventures in Flatland

Points, Lines, Squares, Cubes, Extra-Cubes — we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices

Edwin Abbott, Flatland

6 The critical point

Aristotle answers: "Because only particulars can be perceived, and science is of  universals." ...out of numerous particulars the universal becomes evident.

George Henry Lewes 

7 Quantum matter

"I think I can safely say that nobody understands quantum mechanics." 

Richard Feynman

8 Topology matters

A mathematician who does not know the difference between a doughnut and a coffee mug is a topologist.

9 Emergence

F. Scott Fitzgerald: “The rich are different from you and me.” 

Ernest Hemingway: “Yes, they have more money.” 

10 The endless frontier

"New frontiers of the mind are before us, and if they are pioneered with the same vision, boldness, and drive with which we have waged this war we can create a fuller and more fruitful employment and a fuller and more fruitful life."

Franklin D. Roosevelt

I believe the times demand new invention, innovation, imagination, decision. I am asking each of you to be pioneers on that New Frontier.

John F. Kennedy

What do you think about epigraphs? 

Can you give a book in which you thought they were particularly good?

What do you think of those above?

I welcome alternative suggestions.

Monday, January 31, 2022

The joys and frustrations of making video recordings in powerpoint

 I have recently been doing something that many of you are probably already doing thanks to online teaching in the pandemic: using PowerPoint to make a video recording of a slide presentation. Particularly for online courses that are not live this can make a lecture more engaging.

First, I will share a few helpful things I learned. To get the best quality video it is best not to use regular room lighting and the camera on your laptop or desktop monitor. It turns out, for reasons I still do not fully understand, that generally, the quality of the video from your phone is much better than from your laptop camera. So I am using my phone with free Irium software to do the recording. I have the phone mounted on a tripod that includes a ten-inch LED ring light. The picture quality really is a lot better.

Now, I come to the weird, frustrating, and random problems that I am having. At first, ppt would not do video recording on my regular MacBook, but it would on my old MacBook, even though they are basically running the same software. Then a few days later it did start to work on the regular laptop, but only for a few days. For the first few days, the recordings went fine, then I experienced the following random and unpredictable outcomes, even though I had not (knowingly) changed anything.

a. Video and sound recording is fine.

b. There is no recording.

c. Video records fine but there is no sound.

d. Video records fine but the sound only starts working at some random point in the video. Usually, it is out of sync with the video.

I have asked Dr. Google for solutions but found little that is relevant or effective. I have tried changing cameras and microphones but this never provides a lasting solution.

I welcome ideas and suggestions.

Here are two things that I have wondered about.

a. the ppt files are very large (half a gigabyte). Are the different components a bit slow talking to each other?

b. IT services at UQ now has remote control of our laptops and can force updates and restarts. Sometimes when I am not using my laptop it has shut down and rebooted.

Has anyone had similar experiences?

Monday, January 24, 2022

Angle-Dependent Magnetoresistance as a probe of Fermi surface properties in cuprates

About twenty-five years ago I became interested in how the Fermi surface of the metallic state of organic charge-transfer salts could be mapped out by measuring the interlayer resistance as a function of the direction of a large applied magnetic field. [A nice review from 2004 is by Mark Kartsovnik]. Later this technique was used for a range of other metals including strontium ruthenate, iron pnictides, semiconductor heterostructures, and finally cuprates, mostly in the overdoped region.

For the cuprates, it was discovered that one could not only map out the shape of the intralayer Fermi surface, but also anisotropies in the scattering rate and the interlayer hopping integral. Of particular interest was the finding that the overdoped cuprates were not simple Fermi liquids, as usually claimed, but more like anisotropic marginal Fermi liquids.

It should be stressed that the Fermi surface information is extracted indirectly by comparing experimental curves of angle-dependence to calculations based on different models for the shape of the Fermi surface, anisotropies in the scattering rate, and interlayer hopping. Thus, there is a fair bit of curve fitting to determine the parameters of the model. However, when one has observations at several magnetic fields, temperatures, and curves for the angle dependence in all directions, there are a lot of constraints, and specific anisotropies tend to produce some specific qualitative features in the shapes of the curves. Examples are shown below, taken from the Nature paper referenced below.

Recently, measurements have been reported on samples of the cuprate Nd-LSCO 

[La1.6xNd0.4SrxCuO4] at dopings of p=0.21 and p=0.24, lying on both sides of the putative quantum critical point at p=0.23. 

The differences between the ADMR at these two dopings are analysed quantitatively in a preprint, which claims to show that at p=0.21 the Fermi surface is reconstructed due to (pi,pi) ordering. This is important as it relates to the fundamental question as to the origin of the pseudogap state.

Fermi surface transformation at the pseudogap critical point of a cuprate superconductor

Yawen Fang, Gael Grissonnanche, Anaelle Legros, Simon Verret, Francis Laliberte, Clement Collignon, Amirreza Ataei, Maxime Dion, Jianshi Zhou, David Graf, M. J. Lawler, Paul Goddard, Louis Taillefer, B. J. Ramshaw

Submitted on 3 Apr 2020 (v1), last revised 26 Nov 2020 (v2)

Aside: There is also a Nature paper, Linear-in temperature resistivity from an isotropic Planckian scattering rate, by the same group that compares the p=0.24 observations to those on the overdoped cuprate Tl2201 [p=0..29]. The arxiv notes "substantial text overlap" between the preprint above and the preprint for the Nature paper. [Figure 2 in v1 of the preprint above is in the Nature paper].

Here I focus on the first preprint as it stimulated a nice theory preprint

Interpreting Angle Dependent Magnetoresistance in Layered Materials: Application to Cuprates

Seth Musser, Debanjan Chowdhury, Patrick A. Lee, T. Senthil

They present a strong case against the main claim of Fang et al. that their ADMR data supports a reconstructed Fermi surface for the p=0.21 system.

There are several nice things about this preprint.

1. It shows how one should be careful about interpreting ADMR

2. It highlights the possible role of an anisotropic quasi-particle weight, Z(phi), where phi denotes the position on the intralayer Fermi surface, not the direction of the field. Anisotropy can arise from correlation effects and or "coherence factors" associated with Fermi surface reconstruction due to an ordered state. 

2. In their modeling, Fang et al. did not include the effects of Z(phi) and Musser et al. show that when it is included the qualitative differences in the ADMR that they claim arise due to the ordered state do not appear.

3. The authors consider a "toy" model for which some analytical results can be obtained. 

4. This provides some physical insight into the origins of the different features in the data, such as the peak around theta=40 degrees [It is just the magic angle associated with the average radius of the Fermi surface] and how the behaviour near theta=90 degrees depends on the relative size of different parameters [see especially equation (16)].

5. What is happening in this material may not be generic to the cuprates. "The van Hove filling in Nd-LSCO is located between the two dopings, p = 0.21 and p = 0.24, respectively. Thus what was a large Fermi surface centered at the Γ-point on the overdoped side will become a Fermi surface centered at (π, π) on the underdoped side, assuming no reconstruction occurs"

6. The most important insight is at the beginning of Section V. When the value of of the interlayer hopping integral t_perp(phi) averaged over the Fermi surface, changes from non-zero to zero an upturn in the ADMR at low angles (i.e. fields almost parallel to the layers) to a downturn. This suggests an alternative explanation for the transition seen in the preprint.

7. It highlights the often overlooked fact that observation of ADMR is not conclusive evidence of a three-dimensional Fermi surface. Using the parameters from the experimental preprint gives typical values of t_perp * tau ~ 0.1, and so the materials are far from the regime of a coherent three-dimensional Fermi surface.

I have a few minor comments

a. Like many others, the authors incorrectly credit with Yamaji explaining the magic angles associated with ADMR. However, Yamaji's explanation is not the correct one because it involves quantised orbits, whereas the effect is semi-classical, as explained by Kartsovnik, Laukhin, Pesotskii, Schegolev, and Yakovenko. 

b. Investigation of the role of small closed orbits when the magnetic field is almost parallel to the layers is credited to Schofield and Cooper. However, there was earlier and more detailed work by Hanasaki et al. Albeit, both of these papers consider the clean high field limit and so are of debatable relevance.

c. It would be nice to know the status of Fang et al., preprint on which this paper is based, particularly as the first authors of both are in the same department.

Tuesday, January 18, 2022

Graduate students are people

Every scientist is a person. They have a unique personality and a unique life story. Their family, friends, education, hopes, romances, cultural background, past disappointments have shaped who they are today. This past has had a significant influence on their current motivation, fears, ability to work with others, confidence, sense of identity, and manner of communication. It is important that we grapple with all this complexity if we are to appreciate and respect others, and to help them be successful. Graduate students are not slaves, robots, or all the same. Graduate students are people.

These complexities are too often overlooked. But we must engage them if we are to personally care for students and colleagues, and relate to them in a manner that helps them be successful. These issues were brought home to me recently reading the novel, Transcendent Kingdom by Yaa Gyasi. I thank my daughter for the gift, particularly as it was not the kind of book that I might normally have sought out.

The main character in the novel is Gifty, a graduate student in neuroscience at Stanford. Her parents immigrated to the U.S.A from Ghana and she grew up in Alabama, just like the author. Gifty's choice of research topic is motivated by her life experience including her brother's struggle with drug addiction. The research  described in the novel is actually based on a real scientific paper written by a friend of the author.

Molecular and Circuit-Dynamical Identification of Top-Down Neural Mechanisms for Restraint of Reward Seeking

Christina K. Kim, Li Ye, Joshua H. Jennings, Nandini Pichamoorthy, Daniel D. Tang, Ai-Chi W.Yoo, Charu Ramakrishnan, Karl Deisseroth

The novel gives an inside view of the life of a graduate student, describes experiments on mice, including the use of fluorescent proteins to image brain activity. Although science and graduate education is not the main point the novel, it may be good to give or recommend to non-scientists that you would like to understand a little of your world. The novel is easy to read and written in beautiful language.  The main character (author) is an astute observer of herself, others, and social dynamics. The novel captures some of the intensity, independence, stubbornness, and introversion of a brilliant student.


The narrative naturally engages with a wide range of issues, including the immigrant experience and the associated prejudice, racism, poverty, dislocation, and alienation that are too often encountered. It considers family relationships, particularly the bond and tensions between a mother and an adult child. It gives a picture of what it may be like to be a young woman of colour in an elite institution. Then there is sexuality, white Pentecostal churches in the USA, science and religion, mental illness, drug addiction, a personal face on the opioid crisis, the philosophy of neuroscience, including the mind-brain problem,... This does seem like a long list of issues but the author manages to engage with them in a natural and meaningful way as part of a coherent narrative.

Perhaps the only criticism I might have is that I felt that the ending was a little too quick, neat, and may betray the complexity that the rest of the novel so beautifully captured.

Here are some other reviews and articles about the novel that I found most interesting. A review in the Washington post, A review in The New York TimesThe back story of how a visit to a friends lab at Stanford led Gyasi to write the book.