Friday, February 24, 2017

Excellent notes on the Quantum Hall Effect

In the condensed matter theory group at UQ we regularly run reading groups, where we work through a book, review article, or some lecture notes. This is particularly important as our PhD students don't take any courses.

Currently we are working through some nice lecture notes on the Quantum Hall effect, written by David Tong. They are very accessible and clear, particularly in putting the QHE in the context of topology, edge states, Berry's phase, Chern insulators, TKNN, ...

On his website he also has lectures on a wide range of topics from kinetic theory to string theory.

Wednesday, February 22, 2017

Desperately seeking Weyl semi-metals. 2.

Since my previous post about the search for a Weyl semimetal in pyrochlore iridates (such as R2Ir2O7, where R=rare earth) read two more interesting papers on the subject.

Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates 
Hongbin Zhang, Kristjan Haule, and David Vanderbilt

Using a careful DMFT+DFT study they are able to reproduce experimental trends across the series, R=Y, Eu, Sm, Nd, Pr, Bi.

They show that when the self energy due to interactions is included that the band structure is topologically trivial, contrary to the 2010 proposal based on DFT+U.

They also find that the quasi-particle weight is quite small (about 0.1 for R=Sm, Nd and 0.2 for Pr). This goes some way towards explaining the fact that the infrared conductivity gives an extremely small Drude weight (about 0.05 electrons per unit cell), a puzzle I highlighted in my first post.

Field-induced quantum metal–insulator transition in the pyrochlore iridate Nd2Ir2O7 
Zhaoming Tian, Yoshimitsu Kohama, Takahiro Tomita, Hiroaki Ishizuka, Timothy H. Hsieh, Jun J. Ishikawa, Koichi Kindo, Leon Balents, and Satoru Nakatsuji

The authors make much of two things.

First, the relatively low magnetic field (about 10 Tesla) required to induce the transition from the magnetic insulator to the metallic phase. Specifically, the relevant Zeeman energy is much smaller that the charge gap in the insulating phase.
However, one might argue that the energy scale one should be comparing to is the thermal energy associated with the magnetic transition temperature.

Second. the novelty of this transition.
However, in 2001 a somewhat similar transition was observed in the organic charge transfer salt, lambda-(BETS)2FeCl4. It is even more dramatic because it undergoes a field-induced transition from a Mott insulator to a superconductor. The physics is also quite similar in that it can also be described by Hubbard-Kondo model, where local moments are coupled to interacting delocalised electrons.

Monday, February 20, 2017

Senior faculty position in Experimental Condensed Matter available at UQ

My department has just advertised a faculty position. 

I will be interested to see how many applicants want to escape Trumpland for sunny Queensland [which BTW has excellent gun control and national health care...].

Friday, February 17, 2017

A new picture of unconventional superconductivity

Two key ideas concerning unconventional superconductors are the following.

1. s-wave and p-wave pairing (in momentum space) are associated with spin singlet and spin triplet pairing, respectively. This can be shown with minimal assumptions (no spin-orbit coupling and spatial inversion symmetry).

2. If superconductivity is seen in proximity to an ordered phase (e.g. ferromagnetism or antiferromagnetism) with a quantum critical point (QCP) then the pairing can be "mediated" by low energy fluctuations (e.g. magnons) associated with the ordering.

3. Non-fermi liquid behaviour may be seen in the quantum critical region about the QCP.

However, an interesting paper shows that neither of the above is necessarily true.

Superconductivity from Emerging Magnetic Moments 
Shintaro Hoshino and Philipp Werner

They find spin triplet superconductivity with s-wave symmetry. This arises because there is more than one orbital per site and due to the Hund's rule coupling spin triplets can form on a single site.

They also find the pairing is strongest near the "spin freezing crossover" which is associated with the "Hund's metal", i.e. the bad metal arising from the Hund's rule interaction, and has certain "non-Fermi liquid" properties.

The results are summarised in the phase diagrams below, which has a striking similarity to various experimental phase diagrams that are usually interpreted in terms of 2. above.
However, all the theory is DMFT and so there are no long wavelength fluctuations.

Tuesday, February 14, 2017

Four subcultures of the university

A while back I was in a discussion about "What is the culture of the university? What would a sociologist or anthropologist say?"

I thought about this quite a while and came to the conclusion that most universities (particularly research universities in the Western world) do not have a single culture, but rather four distinct subcultures.

First, let me make an observation about modern cosmopolitan cities: New York, Brisbane, Bangalore, Paris, London, ... Within each city, there can co-exist several distinct social groups and subcultures, e.g. African-American, Jewish, homeless, business elite, Muslim, WASPs, Hispanic, ...
Culture is not just about what kind of restaurants they eat at. It concerns values.
Although they may occupy the same physical space (and to a certain extent the same political and economic space), the values of these communities are often distinctly different. If you don't think this I suggest you talk to someone from one community who has married someone (or tried to) from a different community. Or someone who has changed their religion from that of one community to another. These cross-cultural actions can be traumatic and divisive. There are small groups of people who may bridge more than one subculture, but they are in a minority. In reality, the amount of meaningful engagement and communication between the communities can be extremely small. Previously, I posted about when the conflicting values of faculty and students collide.

So here are my four subcultures of the university.
I am deliberately being provocative and extreme to make the point that the university is more fractured than some realise or might acknowledge.

Scholars, monks, and nuns.
This consists of most faculty, graduate students, and a few "nerdy" undergraduates, such as those in special honours program. They love learning and understanding things. Money is not so important. Some will happily work long hours because they love what they are doing. Research should not have to be justified in pragmatic economic terms. They think students should come to university to "expand their minds" not to get a piece of paper or a job. The university has intrinsic value.

Undergrads and party animals.
This sub-culture is provocatively captured in the novel, I am Charlotte Simmons by Tom Wolfe
According to Wikipedia
“Despite Dupont’s [the university] elite status, in the minds of its students, sex, alcohol, and social status rule the day. The student culture is focused upon gaining material wealth, physical pleasure, and a well-placed social status; academics are only important insofar as they help achieve these goals.”
Many undergraduates may not be party animals. Many are not as privileged as Dupont students. But,  the majority (and their parents) still have a completely functional view of education: it is a means towards employment and social advancement.

The neoliberal management class.
This is not just the very highly paid senior managers but the massive support staffs that go with them. Keep in mind that at most universities more than half of the staff are not doing any teaching or research. The 4 key values are management, money, metrics, and marketing. Neoliberalism is like a religion: it defines rationality and morality. It is not to be questioned.

The invisible underclass.
This includes the cafeteria workers, janitors, "adjunct faculty" on short-term teaching contracts, and unpaid "visiting scholars" from the Majority world. They are poorly paid, have uncertain employment, and virtually no voice. Their main value is survival. Yet the university would grind to a halt without them. A testimony to their invisibility is that I did not originally include them in my original version of this post. However, I read a moving New York Times article by Rosa Ines Rivera, a Harvard cafeteria worker and an article about a Singapore student group that ran a special event to honor janitors at their university.

What do you think? Is this characterisation reasonable?

Friday, February 10, 2017

Instability of the Fermi liquid near the Mott transition

In the metallic state of many strongly correlated electron materials, Fermi liquid properties are only observed at relatively low temperatures, at a scale (the coherence temperature T_coh) that can be orders of magnitude less than the Fermi temperature that is estimated from the relevant electronic band structure. Above T_coh one observes a "bad metal" and the absence of quasi-particles.

These features are nicely captured by Dynamical Mean-Field Theory (DMFT).
An interesting question is whether this low-temperature scale can be captured in simpler theories.

Alejandro Mezio and I just finished a paper

The phase diagram at half filling is shown below. Note how near the Mott insulator T_coh is orders of magnitude smaller than W/2, the scale of the Fermi temperature for U=0. It is also much smaller than this scale multiplied by Z, the band renormalisation due to interactions.
We welcome comments.

Wednesday, February 8, 2017

Emergence of the Hubbard bands near the Mott transition

Dynamical Mean-Field Theory (DMFT) has given many insights into the Mott metal-insulator transition in strongly correlated electron materials. In the metallic phase, DMFT nicely describes the interplay between the quasi-particles associated with Fermi liquid behaviour and the Hubbard bands that also exist in the insulating phase. DMFT gives a first-order phase transition and captures the emergence of bad metallic behaviour and the associated transfer of spectral weight.

On the down side DMFT is computationally expensive, particularly close to the Mott transition, as it requires solution of a self-consistent Anderson impurity problem. [If Quantum Monte Carlo is used one also has to do a tricky imaginary time continuation]. When married with atomistic electronic structure calculations (such as based on (Density Functional Theory) DFT-based approaches) DMFT becomes even more expensive. Sometimes I also feel DMFT can be a bit of a "black box."

Slave boson mean-field theory (SBMT) (and equivalently the Gutzwiller approximation (GA) to the Gutzwiller variational wave function) is computationally cheaper and also gives some insight. However, these approaches only describe the quasi-particles, completely miss the Hubbard bands and the associated physics, and give a second-order phase transition. This is sometimes known as the Brinkman-Rice picture.

There is a nice preprint that solves these problems.

Emergent Bloch Excitations in Mott Matter 
Nicola Lanatà, Tsung-Han Lee, Yongxin Yao, Vladimir Dobrosavljević

In addition to the physical orbitals they introduce "ghost orbitals" that are dispersionless (i.e. a flat band) and non-interacting. However, one starts with a Gutzwiller variational wave function that includes the "ghost orbitals". This enables capturing the charge fluctuations in the physical orbitals.
One sees that the Hubbard bands emerge naturally (as a bonus they are dispersive) provided one includes at least two ghost orbitals in the metallic phase and on in the Mott insulating phase.
There is a simple "conservation" of numbers of bands at play here.
The authors state that the Mott transition is a topological transition because of the change in the number of bands.

The metallic (insulating) phase is characterised by three (two) variational parameters.

The results compare well, both qualitatively and quantitatively, with DMFT.

The figure below shows plots of the spectral function A(E,k) for different values of the Hubbard U. The Mott transition occurs at U=2.9.
The color scale plots are DMFT results.
The green curves are from the ghost orbital approach with the size of the points proportional to the spectral weight of the pole in the one-electron Greens function.

Monday, February 6, 2017

A changing dimension to public outreach about science

I think it is worth noting that there are many distinct goals for public outreach activities concerning science. These include the following:

Show that science is fun, cool, and beautiful.

Teach about science, both with regard to how it is done and what we know from it.

Recruit students to study science, possibly at a particular institution.

Lobby for increased funding for science.

Enhance the public visibility of a specific institution (lab, university).

Defend scientific knowledge as reliable. 
This is particularly true of areas which have become politicised (partisan) such as climate change, childhood vaccinations, and evolutionary biology, and for which there are significant enterprises promoting "denial", "skepticism", or "alternative" views.

First, given these distinct goals, I think one needs to design activities that are tailored to a specific goal. Previously, I have discussed the problem of doing demonstrations for school kids that actually teach something about science rather than being like a magic show.
Perhaps one can achieve more than one goal, but I think it is unlikely.

Second, what is interesting and of great concern is that the last goal is a relatively new one. There are now sizeable (and sometimes very vocal) sections of the community who think science cannot be trusted. This is well highlighted in a recent Op-Ed piece in the New York Times, A Scientist's March on Washington is a Bad Idea by Robert S. Young. I agree with his argument that given the nature of the problem a march may be counter-productive, particularly as it will be painted as just another "liberal" political lobby group. A better strategy is for scientists to engage with a diverse range of community groups at a more grass roots level. Sometimes this means using subtle and diplomatic strategies such as described in this NYT article and by Katharine Hayhoe.

Third, this problem is very challenging because it is part of a much larger political and social problem, particularly in the USA. There is now a significant fraction of the population who have become disenfranchised from and distrustful of a broad range of public institutions: government, multi-national companies, universities, mainstream media, Wall street, "elites", ..... and science gets lumped in with all that.

Friday, February 3, 2017

Should you put "theory" or "experiment" in the title of your paper?

A referee for a recent paper, entitled "Effect of hydrogen bonding on infrared absorption intensity", suggested that we should add "theory" to the title since the chosen title could equally be about an experimental paper. In the end, we declined but did make the abstract clearer that the paper was purely theoretical.

I thought this is an interesting issue, that I had not thought about explicitly before. If you look at titles of papers it is true that it is sometimes not clear whether the paper is theoretical, experimental, or joint theory and experiment. This is particularly true with theory papers with titles such as "Property X of material ABC" or experimental papers with titles such as "Strong electron correlations in materials class Y". To experts who working are on the same topic or who know the authors it may be obvious. But to others, it may not be so obvious.

Does it matter?
Surely if the abstract makes it clear then it is o.k.?
[Again it is amazing how for some abstracts in luxury journals you have to read to practically the last sentence to figure it out. This is because experimental papers can be clothed in theoretical hype].

The suggestion prompted me to do two things.
First, I looked through the titles of most of my papers and found that the only ones which contained "theory" were those which referred to a particular technique, e.g. "Dynamical mean-field theory" or "linear spin wave theory".

Second, I looked at the titles of some famous papers, such as BCS and by P.W. Anderson.
BCS is "Theory of superconductivity" and the abstract begins "A theory...".
PWA does have "theory" in some papers but not others.

The only conclusion I came to from all of this is that I think we should work hard on the titles (and abstracts) of our papers, since the title may determine whether or not they are read.

Maybe it is tangential, but it also reminded me that like Anderson, I am largely against combined theory and experiment papers.

What do you think? Does it matter?