The essence of the Hund's metal

I think one of the most interesting ideas to emerge in the theory of correlated electron materials over the past five years is that of a Hund's metal, particularly how bad metal behaviour is enhanced by the presence of the Hund's rule coupling associated with degenerate d-orbitals and multiple bands.  This is relevant to many transition metal compounds. I recently found the following paper quite helpful. It builds on important earlier work by Luca de Medici.

Electronic correlations in Hund metals
L. Fanfarillo and E. Bascones

A couple of key ideas.

In a single band Hubbard model as one approaches the Mott insulator the probability of double occupancy decreases and so does the local charge fluctuations. This reduces the quasi-particle weight Z, which is the overlap of the ground state with a non-interacting Fermi sea.
A Hund's metal is different.

Hund's coupling polarizes the spin locally. The small Z in a Hund metal is due to the small overlap between the noninteracting states and the spin polarized atomic states [5,7,36]. The suppression of Z is thus concomitant with an enhancement of the spin fluctuations CS; see Fig. 3(a) [below].

Here CS=⟨S2⟩−〈S〉2 with 〈S〉=0 and S=12∑a=1,...,N(na↑−na↓). Arrows in Fig. 3(a) mark J∗H(U) the interaction at which the system enters into the Hund metal defined empirically as the value of JH with the strongest suppression of Z, i.e., the most negative dZ/dJH value, after which Z stays finite; see Fig. S2(c) in SM [35]. Above J∗H, CS reaches a value close to that of the Mott insulator at this filling showing that in the Hund metal state each atom is highly spin polarized, Figs. 3(a) and S3(b) and S3(c) in SM [35].

The three curves (black, green, red) correspond to 5 electrons in 6 orbitals, 3 electrons in 4 orbitals, and 2 electrons in 3 orbitals, respectively.

Unlike in a single band, as the system becomes more correlated (with increasing Hund's coupling J_H) the charge fluctuations can increase, as shown below.

It would be interesting to see how much of this essential physics is captured in a two-site Hubbard-Kanomori model such as this one.

An important open question is whether the signatures of a bad metal (such as thermopower of order k_B/e, no Drude peak, .... are the same for a Hund's metal and a single band system.

Keeping things in perspective

Recently I had a discussion with a friend who just started a new faculty position. There are both positives and negatives with his new situation. We discussed how it is easy for a few negatives to weigh upon us and we lose perspective of the bigger picture. This is particularly true for those of us who are more introspective and melancholy, and possibly perfectionists. No job is perfect. There will always be frustrations and disappointments.
Some of these issues are addressed in my post, Should I change jobs?

I also think some people loose perspective about positives. They have a success [whether finishing a Ph.D., getting a grant, or a paper in a luxury journal] and they start thinking they are entitled to all sorts of things [whether, a permanent job, large amounts of funding, a promotion, ....].

How can we keep things in perspective?
Talk to others about your situation.
Write a list of both positives and negatives.
Factor in how your personality distorts your objectivity.

Should Hollywood make a Linus Pauling biopic?

The past few years has seen Hollywood make movies about famous scientists and mathematicians, including A Beautiful Mind (John Nash), The Theory of Everything (Stephen Hawking), The Imitation Game (Alan Turing), and now The Man Who Knew Infinity (Ramanujan).
The latter is to be released April 29 in the USA and May 5 in Australia.


Are there others?

This post is not about the important issue whether this is a good thing, particularly when you consider all the creative license taken, and whether the movies capture the science in an appropriate way.

First, what kind of scientist is an appropriate candidate for such a movie?
I think their life must have some significant components of romance, scandal, tragedy, and redemption. The list above does include substantial ingredients of most of these. Pure scientific heroism and brilliance just does not cut it.

Second, who might be some candidates from condensed matter physics or theoretical chemistry?

Feynman was one that came to mind, particularly because of the tragic death of his first wife and his involvement in the Challenger inquiry. However, I see that back in 1998 there was Infinity, starring Matthew Broderick and Patricia Arquette. It looks like it was box office flop. Has anyone seen it?
Interestingly, about 15 years ago, Alan Alda commissioned and was the lead actor in a play QED about Feynman. No signs of a movie.

So who might be other candidates? Greats like John Bardeen, Phil Anderson, Walter Kohn, are just too boring ....
But, what about Linus Pauling? There is the romance and partnership with his wife, amazing lecturing skills, the political activism and persecution, and the controversy of his views about vitamin C.

Perhaps William Shockley might make the cut, because of his role in starting Silicon Valley, conflict with everyone, and racist views, ...

Any other ideas?

Simple analytical models for crystal structure energetics

I am currently teaching my solid state class the basics of crystal structures.
For any simple material a basic question is:
can you construct a simple analytical model that can quantitatively predict (actually postdict) the following?

• the most stable crystal structure (e.g. FCC vs. BCC)
• the lattice constant 
• the binding energy of the crystal 
• the bulk modulus (i.e. compressibility) ?

Sometimes people make a big deal about the fact that computations based on Density Functional Theory approximations (with the "right" functional!) do reasonably well at post-dicting the above. However, it is important to acknowledge that

* there are very simple analytical models that do well too
* the relative energy differences between different structures are very small and may be quite sensitive to the choice of approximation.

Previously, I have posted about the challenge of crystal structure prediction for organic molecules.

In past years I gave a lecture about the predictions of simple analytical models, but lately I struggle to fit it into the course (a mistake?).
Here are my old slides, which closely follow Ashcroft and Mermin and Marder.

I find it quite striking how well these simple theories work and that they show how the energy difference between different crystal structures is quite small. For example, for inert gases modelled by a Lenard Jones potential the relative energy difference between FCC and hexagonal close packed is 0.1 per cent.
This subtle competition between different phases shows that this is not a unique feature of strongly correlated electron systems.

Factoring the advisor into evaluation of job candidates

When considering applicants for postdoc and junior faculty positions it is natural to focus on the track record of the applicant, particularly journal publications (number, quality, citations, ...). However, I think one really needs to take into account who are the advisor(s) of the candidate.

It is important to remember that you are hiring the student not their advisor.

Consider two extreme candidates and their advisors.

Joan's advisor Susan is at a "highly ranked" university and runs a large well oiled machine that graduates students on time and produces a steady stream of publications, some in luxury journals. Each student project makes extensive use of hardware and software from previous generations of students. Most of the papers have long author lists. Susan tends to work on somewhat interesting but safe problems that are guaranteed to produce papers in a timely manner. Joan met rarely one-to-one with Susan, but was actually mostly supervised by postdocs. Their discussion always focussed on the next step for getting results for a paper. There was little discussion of the big picture, background knowledge, career advice, or other issues. Susan travels extensively, promoting her group's work in highly polished talks, increasing citations. Susan writes beautiful letters of reference that really "sell" her group members.

John's advisor Steve is well known for just a few highly original papers. Steve is not particularly well organised and supervises few students. He assigns them difficult problems that may not bear fruition and few graduate on time, or have many papers at the end of their Ph.D. Each project is self- contained and the students have to write all their own code from scratch. Steve worked closely with John making sure he had a good foundation and learnt all the "tricks of the trade". Steve is adverse to self-promotion and does not like going to conferences, particularly big ones. Steve writes dry letters of reference that are cautious about the strengths of his group members.

Who would be the better hire? Joan or John?
Although his "track record" may not be as impressive, John actually may have the stronger scientific training and have more potential than Joan.

Having made the above point, students and postdocs are heavily influenced by their advisors, for better or worse. There are always exceptions, but most pick up good and bad habits from their advisor. This covers a wide range of issues from attitude to hype, carefully checking results, quality of talks, breadth of interests, focus, .....  True, some students do learn little from their advisor, either because their advisor has no interest in teaching them or the student is too stubborn or proud to learn anything. In the end, hiring someone whose advisor trains their students well and models scientific integrity, is a good move.

What do you think?