## Saturday, May 18, 2019

### Phonons in organic molecular crystals.

In any crystal the elementary excitations of the lattice are phonons. The dispersion relation for these quasi-particles relates their energy and momentum. This dispersion relation determines thermodynamic properties such as the temperature dependence of the specific heat and plays a significant role in electron-phonon scattering and superconductivity in elemental superconductors. A nice introduction is in chapter 13 of Marder's excellent text. [The first two figures below are taken from there].

The dispersion relation is usually determined in at least one of three different ways.

1. The classical mechanics of balls and harmonic springs, representing atoms and chemical bonds, respectively. One introduces empirical parameters for the strengths of the bonds (spring constants).

2. First-principles electronic structure calculations, often based on density functional theory (DFT). This actually just determines the spring constants in the classical model.

3. Inelastic neutron scattering.

The figure below shows the dispersion relations for a diamond lattice using parameters relevant to silicon, using method 1. I find it impressive that this complexity is produced with only two parameters.

Furthermore, it produces most of the details seen in the dispersion determined by method 3. (Squares in the figure below.) which compare nicely with method 2. (solid lines below).

The following paper may be a benchmark.

Phonon dispersion in d8-naphthalene crystal at 6K
I Natkaniec, E L Bokhenkov, B Dorner, J Kalus, G A Mackenzie, G S Pawley, U Schmelzer and E F Sheka

The authors note that method 3. is particulary challenging for three reasons.
• The difficulties in growing suitable single-crystal samples.
• The high energy resolution necessary to observe the large number of dispersion curves (in principle there are 3NM modes, where N is the number of atoms per molecule and M is the number of molecules per unit cell).
• The high momentum resolution necessary to investigate the small Brillouin zone (due to the large dimensions of the unit cell).
The figure below shows their experimental data for the dispersions. The solid lines are just guides to the eye.

The authors also compare their results to method 1. However, the results are not that impressive, partly because it is much harder to parameterise the intermolecular forces, which are a mixture of van der Waals and pi-pi stacking interactions. Hence, crystal structure prediction is a major challenge.

A recent paper uses method 2. and compares the results of three different DFT exchange-correlation functionals to the neutron scattering data above.
Ab initio phonon dispersion in crystalline naphthalene using van der Waals density functionals
Florian Brown-Altvater, Tonatiuh Rangel, and Jeffrey B. Neaton

What I would really like to see is calculations and data for spin-crossover compounds.

## Thursday, May 16, 2019

### Introducing phase transitions to a layperson

I have written a first draft of a chapter introducing phase diagrams and phase transitions to a layperson. I welcome any comments and suggestions. Feel free to try it out on your aunt or uncle!

## Tuesday, May 7, 2019

Today we just take it for granted that crystals are composed of periodic arrays of interacting atoms. However, that was only established definitively one hundred years ago.
I have been brushing up on phonons with Marder's nice textbook, Condensed Matter Physics.
There are two historical perspectives that I found particularly fascinating. Both involve Max Born.

In a solid the elastic constants completely define the speeds of sound (and the associated linear dispersion relationship). In a solid of cubic symmetry, there are only three independent elastic constants, C_11, C_44, and C_12.
Cauchy and Saint Venant showed that if all the atoms in a crystal interact through pair-wise central forces then C_44=C_12. However, in a wide range of elemental crystals, one finds that C_12 is 1-3 times larger than C_44. This discrepancy caused significant debate in the 19th century but was resolved in 1914 by Born who showed that angular forces between atoms could explain the violation of this identity. From a quantum chemical perspective, these angular forces arise because it costs energy to bend chemical bonds.

The first paper on the dynamics of a crystal lattice was by Born and von Karman in 1912. This preceded the famous x-ray diffraction experiment of von Laue that established the underlying crystal lattice. In 1965, Born reflected
The first paper by Karman and myself was published before Laue's discovery. We regarded the existence of lattices as evident not only because we knew the group theory of lattices as given by Schoenflies and Fedorov which explained the geometrical features of crystals, but also because a short time before Erwin Madelung in Göttingen had derived the first dynamical inference from lattice theory, a relation between the infra-red vibration frequency of a crystal and its elastic properties....
Von Laue's paper on X-ray diffraction which gave direct evidence of the lattice structure appeared between our first and second paper. Now it is remarkable that in our second paper there is also no reference to von Laue. I can explain this only by assuming that the concept of the lattice seemed to us so well established that we regarded von Laue's work as a welcome confirmation but not as a new and exciting discovery which it really was.
This raises interesting questions in the philosophy of science. How much direct evidence do you need before you believe something? I can think of two similar examples from more recent history: the observation of the Higgs boson and gravitational waves. Both were exciting, and rightly earned Nobel Prizes.
However, many of us were not particularly surprised.
The existence of the Higgs boson made sense because it was a necessary feature of the standard model, which can explain so much.
Gravitational waves were a logical consequence of Einstein's theory of general relativity, which had been confirmed in many different ways. Furthermore, gravitational waves were observed indirectly through the decay of the orbital period of binary pulsars.

## Wednesday, May 1, 2019

### Emergence: from physics to international relations

Today I am giving a seminar for the School of Political Science and International Studies at UQ.
Here are the slides.

## Thursday, April 25, 2019

### Modelling the emergence of political revolutions

When do revolutions happen? What are the necessary conditions?
Here are the claims of two influential political theorists.

a single spark can cause a prairie fire’’
Mao Tse Tung

“it is not always when things are going from bad to worse that revolutions break out,... On the contrary, it often happens that when a people that have put up with an oppressive rule over a long period without protest suddenly finds the government relaxing its pressure, it takes up arms against it. … liberalization is the most difficult of political arts”
Alexis de Tocqueville (1856)

Is it possible to test such claims? What is the relative importance of levels of perceived hardship and government illegitimacy, oppression, penalties for rebellion, police surveillance, ...?

An important paper in 2002 addressed these issues.
Modeling civil violence: An agent-based computational approach
Joshua M. Epstein

The associated simulation is available in NetLogo.
It exhibits a number of phenomena that can be argued to be emergent: they are a collective and are not necessarily unanticipated from the model.

Tipping points
There are parameter regimes at which there are no outbursts of rebellion.

Free assembly catalyzes rebellious outbursts
Epstein argues that this is only understood ex post facto.

Punctuated equilibrium
Periods of civil peace interspersed with outbursts of rebellion.

Probability distribution of waiting times between outbursts.
This distribution is not build explicitly into the model which involves only uniform probability distributions.
[Terminology here is analogous to biological evolution].

Salami corruption
Legitimacy can fall much further incrementally than it can in one jump, without stimulating large-scale rebellion.
[I presume the origin of Epstein's terminology is that salami is sliced something thinly... Maybe a clearer analogy would be the proverbial frog in a pot of slowly heated water].

de Tocqueville effect
Incremental reductions in repression can lead to large-scale rebellion. This is in contrast to incremental decreases in legitimacy.

## Monday, April 22, 2019

### Ten years of blogging!

I just realised that last month I had been blogging for ten years.
On the five year anniversary, I reflected on the influence that the blog has had on me.
I don't have much to add to those reflections. The second five years has not been as prolific but has been just as enriching and I am grateful for all the positive feedback and encouragement I have received from readers.

## Wednesday, April 17, 2019

### The emergence of social segregation

Individuals have many preferences. One is that we tend to like to associate with people who have some commonality with us. The commonality could involve hobbies, political views, language, age, wealth, ethnicity, religion, values, ... But some of us also enjoy a certain amount of diversity, at least in certain areas of life. We also have varying amounts of tolerance for difference.
A common social phenomenon is segregation: groups of people clump together in spatial regions (or internet connectivity) with those similar to them. Examples range from ethnic ghettos and teenage cliques to "echo chambers" on the internet.

The figure below shows ethnic/racist segregation in New York City. It is taken from here.

In 1971 Thomas Schelling published a landmark paper in the social sciences. It surprised many because it showed how small individual preferences for similarity can lead to large scale segregation. The context of his work was how in cities in the USA racially segregated neighbourhoods emerge.

One version of Schelling's model is the following. Take a square lattice and each lattice point can be black, white or vacant. Fix the relative densities of the three quantities and begin with a random initial distribution. A person is "unhappy" if only 2 or less of their 8 neighbours (nearest and next-nearest neighbours) on the lattice are like them. [They have a 25% threshold for moving]. They then move to a nearby vacancy. After many iterations/moves to an equilibrium is reached where everyone is "happy" but there is significant segregation.

The figure is taken from here.

There are several variants of the model that Schellman presented in later papers and an influential book Micromotives and Macrobehavior, published in 1978. He received the Nobel Prize in Economics in 2005 for work in game theory.

There is a nice simulation of the model in NetLogo. For example, you can see how if you set the individual preference for similarity at 30% one ends up with a local similarity of 70%.
In the Coursera, Model Thinking, Scott Page has a helpful lecture about the model.

This can be considered to be the first agent-based model. It is fascinating that Schellman did not use a computer but rather did his simulation'' manually on a checkerboard!

Physicists have considered variants of Schelling's model that can be connected to more familiar lattice models from statistical mechanics, particularly the Ising model. Examples include

Ising, Schelling and self-organising segregation
D. Stauffer and S. Solomon

Phase diagram of a Schelling segregation model
This connects to classical spin-1 models such as the Blume-Capel model.

A unified framework for Schelling's model of segregation
Tim Rogers and Alan J McKane

Competition between collective and individual dynamics
Sébastian Grauwin, Eric Bertin, Rémi Lemoy, and Pablo Jensen

Shelling's model is a nice example of emergence in a social system. A new entity [highly segregated neighbourhoods] emerges in the whole system thatwase not anticipated based on a knowledge of the properties of the components of the system.

## Friday, April 12, 2019

### Should graduate students pick their own research field?

Paul Romer won the Nobel Prize in Economics in 2018. There is an interesting podcast where he is in conversation with Tyler Cowan. In it, there is the following quote that readers may love!
We subsidize graduate education through money that goes to professors, but we let the professors make the decisions about the problems they work on, and then, therefore, the things the students are trained in. I’d rather let the students be the ones who decide, “Yeah, I don’t really want to work in high-energy physics. It’s kind of dead end. I think there’s something much more exciting in condensed-matter physics.”
I mostly post this for amusement.
[I thank my economist son, for bringing it to my attention].

However, Romer does raise an interesting issue. There is a distinct contrast between the systems in the USA and Australia. In the USA faculty get grants and use them to hire graduate students. In Australia, most Ph.D. students get their own scholarship (fellowship) which pays their tuition and a living allowance (salary). They are then free to pick an advisor (supervisor) and topic, which is then approved (usually routinely) by various committees.
I am not sure this is a better system. Too often, students still tend to flock to advisors who are "famous" (but give them little time or exploit them) or those working on the latest fashionable (hyped up) topic ... On the other hand, if a student wants to work on a particular topic that is currently not "hot" there is more opportunity for that, for better or worse.

What do you think?

## Tuesday, April 9, 2019

### Coupling of the lattice to spin-crossover transitions

There is a very nice paper
Complete Set of Elastic Moduli of a Spin-Crossover Solid: Spin-State Dependence and Mechanical Actuation
Mirko Mikolasek, Maria D. Manrique-Juarez, Helena J. Shepherd, Karl Ridier, Sylvain Rat, Victoria Shalabaeva, Alin-Ciprian Bas, Ines E. Collings, Fabrice Mathieu, Jean Cacheux, Thierry Leichle, Liviu Nicu, William Nicolazzi, Lionel Salmon, Gábor Molnár, and Azzedine Bousseksou

It investigates the spin-crossover in a specific compound with a suite of techniques, including x-ray diffraction, inelastic neutron scattering, and micro-electromechanical systems (MEMS).

The nice results reflect significant advances over the past few decades in neutron scattering and microfabrication.

The graph below shows the vibrational density of states of the Fe nuclei and the low-spin (LS) and high-spin (HS) states. Note how the LS modes around 50 meV (400 cm-1) soften significantly in the HS state. These modes are the Fe-N stretches in the octahedron. This softening is associated with a significant increase in entropy which helps drive the spin-crossover transition.
Note that there is a small parabolic part at low energies of a few meV.

The figure below is a "blow up" of the low energy data.
The energy resolution is amazing!
The graph shows the density of states divided by E^2.
Why?
In an isotropic solid (or a powder such as used here) in the Debye model for phonons, the density of states is proportional to E^2 and the proportionality is determined by the speed of sound, v_D.

One clearly sees several things.
1. For E less than about 3 meV, the DOS is quadratic in E, as predicted by Debye.
2. The lattice softens with the spin-crossover.
3. The deviation from quadratic occurs at a smaller E for HS than LS.

The values of the speed of sound can be combined with the lattice constant to estimate the Debye frequency, which is roughly where the deviation from quadratic dependence should occur.
I have done this (since the authors don't appear to have) and one gets values of the order of a few meV, consistent with experiment.

From the speed of sound, one can also determine the Young's modulus. This can then be compared to the bulk modulus, which can be determined from MEMS. The values obtained by these different methods are consistent with one another.
Overall, the values of the bulk modulus for different spin-crossover complexes, of order 5-10 GPa, are comparable to those for organic molecular crystals.

## Friday, April 5, 2019

### What is condensed matter physics?

How would you answer this question if you were asked by a non-expert who likes to learn and understand new things?
For example, a smart high school student, your uncle who reads a lot of popular science, an academic colleague in sociology, an economics graduate, ...
A draft of my answer is here.
I welcome suggestions for improvements.
Feel free to try it out on people you know who might be interested.

## Tuesday, April 2, 2019

### Chemistry finally joins the arxiv era

The physics arXiv started way back in 1991. Yet chemists strongly resisted following suit. Indeed if you posted a preprint on the arXiv American Chemical Society (ACS) journals would not publish it.
Eight years ago, Derek Lowe, asked Why Isn't There an arXiv for chemistry?

Well, finally ACS has succumbed and set up their own chemrxiv and announced that they will consider manuscripts that have been posted on the arXiv.

I thank Ben Powell for letting me know about the promising development.

## Thursday, March 28, 2019

There is no doubt that the level of hype in science is increasing. You see it in grant applications, university press releases, introductions and conclusion in papers (especially in luxury journals), talks, ... Hype is also a broader problem in society, including in the business world and politics.

Why is hype bad for science?
Some will say something like, I agree that it is not good, but we have to do it to survive. Anyway, we all know what is really true and so it does not matter..."

However, I think there are many problems, particularly for the long term flourishing of science.

Waste of time
Figuring out that a hyped'' result or research field is actually just hype can take significant time. This is particularly true if one actually tries to reproduce a result and discover all the problems.

Mis-allocation of resources
Researchers, students, and funding agencies flock to hyped fields. However, it can take quite a while and a lot of money for the community to come to the consensus that things are not going to live up to the hype. This is compounded by the fact that people whose careers are enhanced by a hyped result or field are not going to back down too easily and are going to want to keep things going, at least until the next big thing comes along.

Obscuring or hiding problems that need to be solved to make real progress
Making real and significant progress in science is very hard. Every technique has its limitations. Every result involves some uncertainty. Turning science in the lab into a commercially viable technology may arguably be even harder. The obstacles are many. The best way to progress in science and technology is to clearly and honestly state the problems and challenges. This is one of my many concerns about functional electronic materials.

Intellectual integrity
Science is all about intellectual integrity. Losing our credibility with broader society won't be good for science or for society, particularly when it comes to developing well-informed public policy.

## Tuesday, March 26, 2019

### Noel Hush (1924- 2019): pioneering theoretical chemist

I was sad to hear last week that Professor Noel Hush died at age 94. Noel [also known as Prof.] was a pioneer in theoretical chemistry and chemical physics. He had a profound influence on both fields, particularly in their development in Australia.

Arguably his greatest scientific contribution was in the theory of electron transfer. Depending on where you are from this is called Hush-Marcus theory, Marcus-Hush theory, or Marcus theory. In particular, in 1958 Hush derived one of the most important equations in chemical physics, which can be used for design principles for functional electronic materials. A key concept here is the notion of diabatic states.

I had the privilege of knowing and working with Prof. Hush on and off over the past decade. As I made an adiabatic transition from condensed matter into chemical physics Prof. Hush provided a lot of encouragement, wisdom, perspective, and ideas. He strongly believed that theoretical chemists and condensed matter theorists could have mutually beneficial interactions. Together with Jeff Reimers and Laura McKemmish, we co-authored seven papers together. The last papers were published when Noel was 90 years old!

Besides his significant legacy of scientific knowledge, there is an incredible legacy of people that he taught, supervised, mentored, encouraged, and collaborated with.

There is an interesting interview of Prof. Hush about his life by Robyn Williams from 2011.

## Saturday, March 23, 2019

### Emergence and complexity in social systems

Emergent phenomena occur in social systems. For example, self-organisation, power laws, networks, aggregation/segregation, political polarisation, political revolutions...
Can lessons from condensed matter physics help at all in understanding and modeling of social systems? Can analogies from social systems help non-scientists understand some of the basic ideas in condensed matter?

In two months I am giving a  seminar in a new UQ multi-disciplinary seminar series, Futures of International Order. In preparation, I am slowly engaging with relevant literature, particularly the work of Scott Page, including his course on Model Thinking at Coursera. The NetLogo software is helpful for exploring a range of simple models.
However, before plunging in here are a few tentative thoughts of ideas that might connect with condensed matter, in the vein of reviews such as

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models
Didier Sornette

Statistical physics of social dynamics
Claudio Castellano, Santo Fortunato, and Vittorio Loreto

Emergence occurs in systems with many interacting components. In social systems, the components are human agents. They can aggregate into emergent entities such as neighbourhoods, institutions, and communities. Associated with these new entities are new scales of size (number of agents), length, time, and connectivity. New effective interactions between entities can also emerge. Even knowing all the details of the system components and the interactions it can be very difficult to predict the properties of the whole system. Surprises are common. Humility is needed.

Qualitative changes can occur due to small quantitative changes in a system parameter.
In condensed matter examples are phase transitions between different states of matter.  Furthermore, these changes can be directly seen as discontinuities or singularities in observables. Order parameters can quantify the changes. In social systems, similar phenomena are sometimes called tipping points.

Universality versus particularity
Close to a critical point for a phase transition most of the details of the system components and their interactions do not matter. Properties such as critical exponents are independent of most details. This is wonderful for theory because one can describe large classes of diverse systems with the same model/theory and one does not have to know all the details of the system.
Similar issues of universality are also relevant when one considers phenomena at different length scales. For example, one does not need to know anything about the atoms (even their existence!) in a crystal to develop a theory of elasticity or the propagation of sound waves.
When it comes to social systems there are a wide range of phenomena that can be potentially described by the same model. For example, Miller and Page point out that the essence of the standing ovation problem is how a binary choice (sit or stand) is influenced by the behaviour of one's neighbours. This is similar to choices as to whether to join a riot, take illegal drugs, or whether to vote of political party A or B.

## Thursday, March 21, 2019

Even though I have not posted about it for a while, mental health continues to be on my radar. I monitor my own mental health carefully and generally things are going well. Tragically, I still meet many in academia struggling with the issue. It is also in the news because of the recent death by suicide of Princeton economist, Alan Krueger. A few months ago, Stanford theoretical physicist, Shoucheng Zhang, also died by suicide.

The Chronicle of Higher Education has an article about how Krueger's death is prompting conversations about how the culture of academia can be unconducive to mental health.

Last week there was an excellent New York Times Opinion piece by Lisa Pryor
A “formulation” gathers the biological, psychological and social factors that lead to a mental illness — and offers clues to the way out of suffering.

## Tuesday, March 19, 2019

Alejandro Mezio and I just posted a preprint
Orbital-selective bad metals due to Hund’s rule and orbital anisotropy: a finite-temperature slave-spin treatment of the two-band Hubbard model

The central result is shown in the Figure below. It shows the phase diagram of the metallic phase as a function of temperature and the Hund's rule interaction J in a system with two bands of differing bandwidth. Uc1 ~ W1 is the critical interaction for a Mott insulator in a one band system with bandwidth W1.
The system is a Hund's metal in that the strong correlations arise from J and not from proximity to a Mott insulating phase (note that U=0.5Uc1).
In the orbital-selective bad metal, one of the bands is a coherent Fermi liquid (with well-defined Fermi surface) and the second (narrower) band is a bad metal.

Two things that I find particularly interesting are the following.

Stability of the bad metal and the orbital-selective bad metal are enhanced by increasing J and/or by increasing band anisotropy.

The temperatures at which the bad metals occur is orders of magnitude smaller than the Fermi temperature for the corresponding non-interacting system (being of the order of W1~ Uc1).

## Thursday, March 14, 2019

### Imaging orbital-selective quasi-particles in a Hund's metal

Over the past two decades, a powerful new technique has been developed to determine quasi-particle properties in strongly correlated electron systems, based on STM (scanning tunneling microscope) measurements. Quasi-particle interference (QPI) has proved to be particularly useful for studying cuprates (e.g. in revealing the d-wave pairing) and now for iron-based superconductors. The basic physics is as follows. One measures the changes in the local tunneling density of states N(r,E), associated with a single impurity that scatters quasi-particles with a change in momentum q. Then the Fourier transform of this change is

The text above is taken from a nice paper
Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe
A. Kostin, P.O. Sprau, A. Kreisel, Yi Xue Chong, A.E. Böhmer, P.C. Canfield, P.J. Hirschfeld, B.M. Andersen and J.C. Séamus Davis

They show theoretically that the intensity of the interference pattern is quite sensitive to the quasi-particle weights of the different d-orbital bands. The experiments are consistent with
The key figure is below. It shows shaded intensity plots of the change in DOS as a function of wavevector. The central column is experimental data with E increasing from -20 meV to +15 meV as one goes down the column. The left and right columns show theoretical values for the same quantities, calculated with all the quasi-particle weights Z=1 (left) and the Z values above (right).

The large variation between the Z values for different orbitals shows how the effect of the correlations are orbital selective.

The same Z values were used by the same cast of characters in a study of the superconducting state that showed orbital selectivity played a key role in the Cooper pairing, including the significant variation of the energy gaps over the different Fermi surfaces. The quantitative agreement between experiment and the associated theory is quite impressive.

I thank Alejandro Mezio for bringing the papers to my attention.

## Thursday, March 7, 2019

### Why is quantum matter so interesting?

Last year Ben Powell wrote a Perspective for Science, The Expanding Materials Multiverse. It begins with a nice statement about why quantum condensed matter is so interesting, exciting, and challenging.
High-energy physicists are limited to studying a single vacuum and its excitations, the particles of the standard model. For condensed-matter physicists, every new phase of matter brings a new “‘vacuum.” Remarkably, the low-energy excitations of these new vacua can be very different from the individual electrons, protons, and neutrons that constitute the material. The materials multiverse contains universes where the particle-like excitations carry only a fraction of the elementary electronic charge, are magnetic monopoles, or are their own antiparticles. None of these properties have ever been observed in the particles found in free space. Often, emergent gauge fields accompany these “fractionalized” particles, just as electromagnetic gauge fields accompany charged particles. On page 1101 of this issue, Hassan et al. provide a glimpse of the emergent behaviors of a putative new phase of matter, the dipole liquid. What particles live in this universe, and what new physics is found in this and neighboring parts of the multiverse?
There is also a nice figure which makes an everyday analogy to illustrate different states of matter.

## Monday, March 4, 2019

### Ten key ideas about condensed matter physics?

I am slowly working towards writing a Condensed Matter Physics: Very Short Introduction.
But first I am trying to clarify my audience and goals. Some earlier posts have helped me clarify this.

My intended audience is probably not you! Rather it is a person who wants to get the flavour of what CMP is actually about.  Examples might include a smart final year high school who wants to study science at university, or a first-year chemistry undergraduate, or an economics graduate, or a sociology professor, ...

My goal is to show that CMP is intellectually exciting, intellectually challenging, and intellectually important.

The VSI format is 8-10 chapters and 30-35 thousand words. It is meant to be written in the style of an engaging essay not a technical paper.

My plan is to basically have one clear and specific idea that I want to communicate in each chapter. I am thinking that in order to increase interest and comprehension that for each chapter I will aim to include.

An easily understandable analogy to illustrate the main idea.
A few relevant and illuminating figures.
An interesting historical anecdote.
An example of a technological application.
An example of cross-fertilisation to another field of science.

So here is the current version of my chapter headings and the main idea(s) I want each chapter to communicate.

1.     What is condensed matter physics?

CMP is concerned with studying and understanding material systems composed of large numbers of atoms. How do the properties of the system emerge from the properties of the constituent atoms and the interactions between them? It is a multi-faceted approach to studying materials and involves a unifying set of concepts. Quite abstract ideas and concepts can be quite powerful for understanding quite practical systems.

2.     A plethora of states of matter

Even for the simplest materials, there is a multitude of different phases, i.e. qualitatively different states of matter. Transitions between distinct phases are defined by discontinuities in properties. Phase diagrams encode what phase is stable under specific external conditions such as temperature, pressure, and magnetic field.

3.     Symmetry matters

Distinct phases are associated with distinct ordering of the system. A unifying concept to distinguish and classify different phases and their associated ordering is how they differ in the type of symmetry that they have. What different classes of symmetry are mathematically possible significantly constrains what is physically possible.

4.     The order of things

The type and quantity of order and the broken symmetry in a distinct state of matter can be described by a small set of numbers represented by the “order parameter’’.

Confining a material to one or two dimensions can lead to new states of matter. Furthermore, imagining a world of variable dimension can actually lead to a better understanding of materials in our three-dimensional world.

6.     The critical point: details do not matter

Under a very special set of external conditions, a phase transition is not associated with discontinuous properties. These conditions are represented by the critical point in the phase diagram.  Very different material systems can have the same properties close to the critical point. Understanding this universality requires looking at the system at many different length scales.

7.     Quantum matter

The weirdness of quantum theory is most commonly manifest at the level of single atoms and molecules. Surprisingly, quantum effects can also be seen “with the naked eye” in states of matter such as superconductors and superfluids.

8.     Topology matters

Abstract ideas about shapes help us understand spatially non-uniform broken symmetry states. They also lead to new states of quantum matter, that do not involve broken symmetry.

9.     Emergence matters

Condensed matter physics is all about emergence: the sum is greater than the parts. From a system composed of many interacting components new (often unanticipated) properties, concepts, and organising principles emerge. Reality is stratified.

10.  Future challenges

Almost all new states of matter are discovered by experiment and often by accident rather than being predicted theoretical. An open question and challenge is to what extent one can predict new states or to design materials with specific properties. There are significant open challenges in all facets of CMP: synthesis, characterisation, measurement, computation, and theory. Finally, given the great success of CMP at understanding emergence in complex systems a challenge is to adapt the approach and concepts to other complex systems, ranging from biology to sociology.

I welcome feedback.
But keep in mind the audience.
I do not want to add material, but perhaps even cut material (e.g. chapter 8).

What do you wish non-CMP people understood about CMP?

## Friday, March 1, 2019

### Generalised rigidity is a key concept

What are some of the most important concepts in condensed matter physics?
In a recent comment on this blog Gautam Menon suggested that one of them is that of generalised rigidity, i.e. the elasticity of order parameters associated with broken symmetry phases.

A while ago I wrote a post trying to introduce Phil Anderson's discussion of the concept.

Basically, generalised rigidity quantifies how the free energy of a system varies when introduces spatial variations in the order parameter. These variations can result from boundary conditions, fluctuations, or topological defects.

Depending on the type of broken symmetry there are just a few parameters, maybe only one, involved in defining the rigidity. One is looking at "linear" response and so symmetry determines how many different terms one can write down that are second order in a gradient operator.

A concrete example is the Frank free energy density associated with non-chiral nematic crystals.
Here n is a unit vector (the order parameter) and there are just three parameters and K1, K2, and K3. The three terms represent pure splay, bend, and twist, respectively. Spatial uniformities are at the heart of liquid crystal displays.

Historical aside. It is impressive that Frank wrote this down in 1958, without any reference to Landau.

For s-wave superconductivity and superfluids such as 4He, there is just one parameter, known as the superfluid stiffness or superfluid density. This is the coefficient of the gradient term in the Ginzburg-Landau theory and determines the superconducting "coherence length".

The generalised rigidity is also important because it is central to the renormalisation group theory of critical phenomena, which start with Ginzburg-Landau-Wilson functionals (effective actions). For most cases, one discovers that higher order gradient terms are "irrelevant'' to long wavelength properties and the rigidities are renormalised by fluctuations.

The spin stiffness is the only parameter (energy scale) that appears in a non-linear sigma model treatment of ferromagnetism and antiferromagnetism. The model is sufficient to describe all of the long-wavelength and low-energy properties.

The XY model also involves just one parameter, the rigidity.  From this model one gets the Kosterlitz-Thouless transition.

Note that for both the non-linear sigma model and XY model in one and two dimensions there is no long-range order (symmetry breaking) [Mermin-Wagner theorem] yet the rigidity still has meaning.

The rigidity also determines the emergent length scales in these systems, including the size of topological defects such as vortices, skyrmions, disinclinations,....

A nice detailed discussion of much of the above is in Chaikin and Lubensky, particularly chapter 6.

## Monday, February 25, 2019

### Management lessons not learned from the discovery of graphene

I just read the Random Walk to Graphene, by Andre Geim. It is the lecture he gave when receiving the 2010 Nobel Prize in Physics. I should have read it long ago but was motivated to read it now because the following sentence features in Joseph Martin's "purloined letter'' argument about why condensed matter physics lacks status.
Graphene has literally been before our eyes and under our noses for many centuries but was never recognized for what it really is.
I learned some nice science from the lecture. Foremost, it is a great story of scientific creativity, perseverance, and serendipity. However, I want to mention a few things that highlight how the story strongly conflicts with most views about how science is currently "managed" and people operate.

Geim starts by recounting his Ph.D. and early postdoc years. His Ph.D papers were cited twice, by co-authors.
The subject was dead a decade before I even started my Ph.D. However, every cloud has its silver lining and what I uniquely learned from that experience was that I should never torture research students by offering them “zombie” projects.
Several years later he worked on a new topic as a staff scientist in Russia.
This experience taught me an important lesson that introducing a new experimental system is generally more rewarding than trying to find new phenomena within crowded areas.
He notes that when after a six-month visiting postdoc in Nottingham he entered the Western postdoc market with an h-index of 1!

When he was in the Netherlands as a young faculty member in a high magnetic field lab he began to experiment in creative directions leading to investigations of "magnetic water" and the iconic experiment of the levitating frog for which he received an Ig Nobel Prize.
we saw balls of levitating water (Fig. 1). This was awesome. It took little time to realize that the physics behind this phenomenon was good old diamagnetism. It took much longer to adjust my intuition to the fact that the feeble magnetic response of water (105), that is billions of times weaker than that of iron, was sufficient to compensate the Earth’s gravity. Many colleagues, including those who worked with high magnetic fields all their lives, were flabbergasted, and some of them even argued that this was a hoax....

The levitation experience was both interesting and addictive. It taught me the important lesson that poking in directions far away from my immediate area of expertise could lead to interesting results, even if the initial ideas were extremely basic. This in turn influenced my research style, as I started making similar exploratory detours that somehow acquired the name “Friday night experiments.” The term is of course inaccurate. No serious work can be accomplished in just one night. It usually requires many months of lateral thinking and digging through irrelevant literature without any clear idea in sight.
The story of the discovery of graphene using cellotape [Scotch tape, sticky tape] was more complicated, circuitous, and involved a lot more hard work than I realised.
There were two dozen or so [friday night] experiments over a period of approximately 15 years and, as expected, most of them failed miserably. But there were three hits, the levitation, gecko tape, and graphene.
The story of the first publication is interesting. It took nine months to get the paper into Science.
First, we submitted the manuscript to Nature. It was rejected and, when further information requested by referees was added, rejected again. According to one referee, our report did “not constitute a sufficient scientific advance.” Science referees were more generous (or more knowledgeable?), and the presentation was better polished by that time. In hindsight, I should have saved the time and nerves by submitting to a second-tier journal, even though we all felt that the results were groundbreaking.
This is consistent with my belief that there is not a lot of correlation between great discoveries and publication in luxury journals.

So what should we learn from this story?
First, we should all be a little more adventurous and take some risks and explore new areas. Previously, I have argued successful researchers should move onto new hard problems.
A lot of this relates to diminishing returns and opportunity costs.
Yet, unfortunately, there are now significant institutional and cultural pressures against this. However, I think senior faculty have a responsibility to buck these trends.

Second, funding agencies and university management really need to learn from this story of graphene. It really goes against metrics, KPIs, short term goals, making people "accountable" for extremely well-defined timetables and research outcomes, and forcing/hiring people to work on the latest hot topic.

Graphene is cool! And I am sure that there is a lot that remains to be discovered about graphene. However, I find it disturbing that so many people have flocked to the field. A few years ago I met a faculty member from Manchester and they said they were on the out because they were not working on graphene and there was a lot of pressure for people to be working on it.

There is another side to the story that I am not sure what to make of which has an Australian connection. When Alan Gilbert was vice-chancellor at the University of Melbourne he tried to build a parallel private for-profit institution, Melbourne University Private. This turned out to be a massive failure, wasting hundreds of millions of dollars. In 2004 Gilbert moved to Manchester as Vice Chancellor. Of course, his main goal was to lift Manchester in the global rankings.
According to the university's strategic plan[8] (largely a copy of his [Gilbert's] earlier and now abandoned Melbourne Agenda (2002)[9]) the university aims to have five Nobel Laureates on its staff by 2015, at least two of whom will have full-time appointments, and three of which it is intended to secure by 2007. During Gilbert's tenure as vice chancellor, a Nobel Prize winner in economics, Joseph Stiglitz, was appointed the head of the Brooks World Poverty Institute at Manchester, and Sir John Sulston was appointed to a chair in the Faculty of Life Sciences. After Gilbert's death Andre Geimand Konstantin Novoselov, both of whom were appointed before Gilbert moved to Manchester, were awarded the Nobel Prize for Physics in 2010.
From the little I know about Gilbert it is very hard for me to see how he would have supported Geim's approach to doing science, particularly given that there were not well-defined immediate benefits to the corporate sector.

## Tuesday, February 19, 2019

### Superconducting order in organic charge transfer salts

A long-standing question for superconductivity in organic charge transfer salts concerns the symmetry of the superconducting order parameter. Is it unconventional (i.e. not s-wave) and if so are there nodes in the energy gap? Over the years there have been a wide range of claims, both theoretical and experimental.

Most recently a combined theory-STM experiment claimed the symmetry was d + s and that there were 8 nodes on the Fermi surface.

Two of my UQ colleagues recently posted a nice preprint that comes to a different conclusion.
Microwave Conductivity Distinguishes Between Different d-wave States: Umklapp Scattering in Unconventional Superconductors
D. C. Cavanagh, B. J. Powell

Microwave conductivity experiments can directly measure the quasiparticle scattering rate in the superconducting state. We show that this, combined with knowledge of the Fermi surface geometry, allows one to distinguish between closely related superconducting order parameters, e.g., dx2y2 and dxy superconductivity. We benchmark this method on YBa2Cu3O7δ and, unsurprisingly, confirm that this is a dx2y2 superconductor. We then apply our method to κ-(BEDT-TTF)2Cu[N(CN)2]Br, which we discover is a dxy superconductor.
In 2005 Ben Powell  (and others) showed that the simplest RVB theory gives such an order parameter with nodes required by symmetry.
[Aside: in our paper, this is denoted d_x2-y2, but that is because of how the x-y axes are defined].