Thursday, March 21, 2019

Mental health in academia

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
Mental Illness Isn’t All in Your Head 
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

Orbital-selective bad metals

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).

We welcome comments.

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’’.

5.     Adventures in flatland

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.
Thinking about this made me appreciate just how important and useful the concept is.

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

Don't follow the pack!

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.
The Wikipedia page about Gilbert states,
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.