The value of vacations

This is the first week of classes for the beginning of the academic year.

In preparation for a busy semester, I took last week off work (my last four posts were automated) and visited my son in Canberra (where I grew up) and spent some time hiking in one of my favourite places, Kosciusko National Park. One photo is below. This reminded me of the importance of vacations and down time, of the therapeutic value of the nature drug, and of turning off your email occasionally.

Above Lake Albina on the main range.

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.

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.

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...].

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.

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?

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

Low quasi-particle coherence temperature in the one band Hubbard model: a slave-boson approach

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.