Phil Anderson biography is now available

The biography, A Mind Over Matter: Philip Anderson and the Physics of the Very Many by

Andrew Zangwill is now out. I just ordered my copy.

I am looking forward to reading it and will eventually post a review. I look forward to hearing comments from others. 

Update. I received my copy and have already read two-thirds of it. Loving it!

Lessons from the discovery of liquid crystals

I recently learned a little about the history of the discovery of liquid crystals, stimulated by Soft Matter: A Very Short Introduction by Tom McLeish. Besides being a fascinating story there are lessons about the importance of curiosity-driven research, interdisciplinarity, serendipity, and the long road to technology.

Friedrich Reinitzer (1857 - 1927) was a botanist and chemist who worked at the Institute of Plant Physiology in Prague. He was studying cholesterol with the aim of determining its molecular weight. He produced crystals of cholesteryl benzoate and measured their heat capacity as a function of temperature. Aside: For chemists today this measurement is known as differential scanning calorimetry (a constant source of heat is added and the temperature measured as a function of time). 

In 1888, Reinitzer observed that the crystal melted at 145.5 degrees Celsius (signified by absorption of heat), forming a milky liquid. However, at 178.5 degrees Celsius, there was a second absorption of heat, and the liquid became transparent. This suggested that there were two melting transitions. Puzzled by this Reinitzer consulted the physicist and crystallographer, Otto Lehmann, who promoted the idea that this was a new state of matter, which he dubbed a "liquid crystal" (or flowing crystal).

Today, cholesteryl benzoate is classified as a chiral nematic liquid crystal, which is also sometimes known as a cholesteric liquid crystal, in honour of the first one. A schematic of the ordering is shown below.

The milkiness was not explained until the 1960s by Pierre-Gilles de Gennes, who exploited an analogue with a superconductor in a magnetic field.

More detail is in the paper

Liquid‐Crystal Science from 1888 to 1922: Building a Revolution 

Michel Mitov 

This discovery of liquid crystals was the first of many cases where a new state of matter was discovered by a thermodynamic measurement. Others include superfluid 4He (the lambda transition) and superfluid 3He, as I have recently highlighted.

Emergence and a heap of sand

A piece of gold metal is shiny but a single gold atom is not.

Tin is a superconductor but a single tin atom is not.

Water is wet but a single water molecule is not.

A brain thinks but a single neuron does not.

Shininess, wetness, and thinking are all emergent phenomena. The whole is greater than the sum of the parts. More is different. Although these ideas come from twentieth-century science I recently learn that there are ancient antecedents. According to Wikipedia

The sorites paradox (/soʊˈraɪtiːz/; sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

What is the minimum number of gold atoms needed to produce shininess?

How large must a grain of tin be for it to superconduct?

When spontaneous symmetry breaking is involved there are subtleties. Strictly, speaking it only occurs in the thermodynamic limit, i.e. for an infinite system. However, for a finite system, one can observe some properties associated with symmetry breaking such as rigidity. These issues can be addressed in the laboratory with ultracold atoms and with metallic grains of superconductors, both of which can be produced with controlled numbers of particles, ranging from a few hundred to billions. There also are some resonances with the problem of trying to identify the quantum-classical boundary. 

Finally, piles of sand were central to the discovery of self-organised criticality.

The most essential critical thinking skill for citizens?

 I believe that there is one verb that describes the mission of universities (think) and that teaching a discipline means teachings students how to think in accord with that discipline.

But, what about high school? What are the key critical thinking skills that all students should learn? In particular, what is needed they can become engaged citizens who play a constructive role in a democracy.

I wonder if the most essential skill is to be able to consider an issue and critically evaluate different perspectives on the issue. Consider issues that are often topics of public debate (and acrimony): taxation, immigration, government regulation, freedom of speech, funding health care, covid lockdowns, capitalism, socialism, ... 

These are all complex issues and there is a wide range of perspectives on each of them. First, a student (citizen) should be able to acknowledge the existence of different perspectives. Second, objectively identify (or at least understand) the essential content of the different perspectives. Third, identify (or at least understand) the strengths and weaknesses of each of the perspectives, including acknowledging the level of evidence including its uncertainty. Fourth, compare and contrast these strengths and weaknesses. Fifth, be able to make the case for the perspective they may prefer. This may be too ambitious. But, it is a desirable goal.

I should point out that I am not at all proposing something postmodern/relativist along the lines of "all views are equally valid" or that "all views should get equal air time." Rather, such exercises and skills should lead to the ability to see why extremist and crackpot views should not get the attention or credibility that too often they do.

How does one achieve this? A concrete example is provided by an Indian newspaper presents opinion columns with Left, Right, and Centre views on specific issues.

There is a related but distinct skill that all citizens should desirably have, empathy, i.e. the ability to put oneself in the shoes of another (their context, background, and life experience) and see why they hold the views they do. This is more of an emotional skill, rather than an intellectual one. This skill enables one to understand and communicate better with those who have wildly different views than our own.

What do you think? What critical thinking skills do think should be promoted? What is realistic?

Signatures of soft matter

What is soft matter? 

Soft Matter: A Very Short Introduction by Tom McLeish has just been published.

McLeish identifies six characteristics of soft matter.

1. Thermal motion 

They exhibit large local spatial rearrangements of their microscopic constituents under thermal agitation. In contrast,  "hard" materials experience only small distortions due to thermal motion.

2. Structure on intermediate length scales

There are basic units ("fundamental" structures), typically involving a very large number (hundreds to thousands) of atoms, that are key to understand soft matter behaviour. These basic units are neither macroscopic nor microscopic (in the atomic sense), but rather mesoscopic (meso from the Greek word for middle). The relevant scales range from several nanometres up to a micrometer. An example of these length scales is those associated with (topological) defects in liquid crystals, such as those shown below.

Image is from here.

3. Slow dynamics

The mesoscopic length scales and complex structures lead to phenomena occurring on time scales of the order of seconds or minutes.

4. Universality

The same physical properties can arise from materials with quite different underlying chemistries.
This characteristic is of significant practical relevance. Solving a problem for one specific material can also solve it for whole families of materials. This universality is also of deep conceptual significance as understanding a general phenomenon is usually more powerful than just a specific example. 

5. Common experimental techniques

The dominant tools are microscopy, scattering (light, x-rays, neutrons), and rheometers which measure mechanical properties such as viscosity (rheology).

6. Multi-disciplinarity

Soft matter is studied by physicists, chemists, engineers, and biologists. 

The chapter titles in the book are 

Milkiness, muddiness, and inkiness [Colloids]

Sliminess and stickiness [Polymers]

Gelification and soapiness [Foams and Self-assembly]

Pearliness [Liquid crystals]

Liveliness [Active matter]

I highly recommend the book. Hopefully, later I will write a review.

Magnetic field induced (thermodynamic) phase transitions in graphite

One of the most common and reliable indicators of a phase transition into a new state of matter is anomalies (e.g. discontinuities or singularities) in thermodynamic properties such as specific heat capacity. This is how the superfluid phases of helium 4 and helium 3 were both discovered. Further transport experiments were required to show that the new states of matter were actually superfluids. This point was highlighted at the end of my last post.

In 2014, I wrote about the puzzling magnetoresistance of graphite and some experiments that were interpreted as evidence of a metal-insulator transition when the electrons are in the lowest Landau level of the graphene layers. This interpretation was partly motivated by theoretical predictions of charge density wave (CDW) transitions in this regime. I expressed some caution and skepticism about this interpretation, highlighting problems in other systems where magnetoresistance anomalies were given such interpretations.  I suggested that thermodynamic measurements should be performed.

In 2015, I highlighted similar issues, suggesting there is no metal-insulator transition in extremely large magnetoresistance materials, contrary to claims in luxury journals. Within two months my claim was shown to be correct.

I was delighted to recently learn from Benoit Fauque that he and his collaborators have now performed measurements of the specific heat of graphite in high magnetic fields.

Wide critical fluctuations of the field-induced phase transition in graphite 

Christophe Marcenat, Thierry Klein, David LeBoeuf, Alexandre Jaoui, Gabriel Seyfarth, Jozef Kačmarčík, Yoshimitsu Kohama, Hervé Cercellier, Hervé Aubin, Kamran Behnia, Benoît Fauqué

The figure below shows the ratio of the specific heat to temperature versus temperature for different values of the magnetic field. In an elemental metal, this would be the temperature and field-independent and equal to the specific heat coefficient gamma. The temperature dependence and peak at a particular temperature are reminiscent of the behaviour for a BCS superconductor or quasi-one-dimensional CDW transition.

I want to highlight a couple of nice things about this data and the analysis in the paper. First, the value of the specific heat coefficient at small fields is several orders of magnitude smaller than in an elemental metal (due to the low density and effective mass of charge carriers) and has a value consistent with band structure calculations. I presume that measuring such small values is a significant experimental achievement. 

Secondly, the linear increase in gamma with the magnetic field and the rate of increase are also consistent with band structure. These agreements increase confidence in the reliability of the measurements and their identification with electronic contributions to the specific heat. For context, the field of strongly correlated electron materials is littered with dubious identifications. An example concerns claims of spinons in an organic charge-transfer salt.

Most importantly the data above suggests that there is a thermodynamic phase transition and that the transition temperature increases with the magnetic field. The corresponding phase diagram can be compared to that suggested by the magnetoresistance measurements from 2014. This is done in the figure below.

The fact that the transition temperature deduced from the specific heat is tracking the anomalies in the earlier magnetoresistance measurements suggests the identification of the latter with a metal-insulator transition back in 2014 was correct. I am happy to be have been proven wrong! That's good science!

Kapitsa, Landau, and quasi-particles

Earlier I suggested that the founders of condensed matter physics were Onnes, Landau, Bardeen, Anderson, and Wilson. I might also add Brian Josephson. But, as pointed out by Ben Powell, this list is theory-centric and so I am thinking more about experimentalists. I think my first addition would be Pyotr Kapitsa. He received a Nobel Prize for "his basic inventions and discoveries in the areas of low-temperature physics" and he managed to save Landau from the Soviet gulag. However, there is a lot more to Kapitsa. Two particular experimental achievements were finding ways to produce large quantities of liquid helium and the production of high magnetic fields. Both of these were key for revealing the details of the Fermi surface of metals through quantum magnetic oscillations and ultimately for finding new states of matter (such as superfluidity) and mapping out phase diagrams.

I was wondering how influential Kapitsa was in influencing Landau's scientific thinking. Biographical Memoirs of Fellows of the Royal Society has obituaries of Landau written by Kapitsa and by Evgeny Lifshitz. Kapitsa's is fairly boring, almost reading like something written by a Soviet bureaucrat, noting "The only interruption in his work at the Institute occurred between 1938 and 1939". No mention is made is that this was because he was in prison for mocking Stalin! Although the following is worth noting: 

 To what extent Landau valued ... connexion with experiment is revealed by the following. His theoretical department at the Institute was small (there were no more than ten research workers and aspirants). Although I suggested that the Academy might set up a special Institute of Theoretical Physics on as large a scale as he wished, Landau not only declined, but even refused to discuss the matter. He said that size was not important and he was extremely happy to be classed as a staff member of the experi mental institute.

It is also interesting that Landau never read any scientific literature himself, and never wrote anything!

Lifshitz's obituary is more detailed and focuses on Landau's science, rather than just reciting his CV. The following shows just how important Kapitsa was for Landau scientifically. Lifshitz states

But Landau’s greatest contribution to physics was the theory of quantum liquids. Its significance continues to increase and undoubtedly during recent decades it has also had a revolutionary effect on other fields of physics— solid state and even nuclear physics. 

The theory of superfluidity was stated by Landau in 1940-41 soon after the discovery in 1937 by P. L. Kapitza of this basic property of helium-II....

The discovery and explanation of superfluidity is also remarkable for its truly constructive interaction between experiment and theory. The research of Kapitza and Landau was carried out in close scientific co-operation and there is no doubt that results of the wide experimental research into processes of heat transfer in liquid helium carried out by Kapitza in 1939-41, had a stimulating effect on theoretical constructions. For his part, Landau formulated his theories while these experiments were still in progress, which made it possible to interpret the results of new experiments immediately. 

The basis of Landau’s theory is the notion of ‘quasi-particles’ (elementary excitations) which compose the energy spectrum of liquid helium. Landau was the first to put the question of the energy spectrum of a macroscopic body in this most general form, and he also found the character of the spectrum for a quantum liquid of the type to which liquid helium (the 4He isotope) belongs;

The concept of quasi-particles is arguably one of the most important in quantum many-body theory and condensed matter.

Aside: I had forgotten this and tended to think quasi-particles were introduced by Landau in his Fermi liquid theory paper fifteen years later.

The comments above follow the common narrative of the discovery of superfluidity, which as Sebastien Balibar argues is debatable. This narrative exclusively focuses on Kapitsa and Landau. The new state of matter, Helium-II, associated with a singularity in the specific heat of liquid 4He at the lambda temperature, was discovered in 1927 by Willem Keesom in Leiden. Superfluidity was independently discovered in 1937 by Allen and Misener. Theories of superfluidity, including the two-fluid model, by Laszlo Tisza and Fritz London, were developed before Landau's.

Nevertheless, the main point remains clear. It is highly likely that Landau and Kapitsa had a significant influence on one another. Such synergy between experiment and theory is at the heart of condensed matter physics. Kapitsa was definitely following the integrated approach of Kammerlingh Onnes: development of experimental techniques, careful measurements, addressing fundamental questions, and interaction with theorists.