Condensed matter on the public stage, and not in a good way

This week, condensed matter physics has been getting far more broad public attention than usual, and while in the abstract I like our discipline getting noticed, this is definitely not how I’d have preferred it to happen.

First, more fun re Ranga Dias.  Fresh off renewed controversy about claims of room temperature superconductivity in Lu-N-H at high pressures (claims of reproduction of the effect seem unreliable to me), it’s come out that this paper, already under an “expression of concern”, is being retracted.  This has been widely reported - see here (hurray for student journalism) and here and here for example.  It is abundantly clear that data fabrication/copying has taken place here.  Between this, the other retraction, and the clear evidence of thesis content plagiarism, it’s hard to see any signs of credibility remaining.  

Then there is the claim via preprints (here, here) of room temperature superconductivity at ambient pressure in a lead oxide compound from investigators in Korea.  Cutting to the chase:  it is very unlikely, in my view, that this pans out, for multiple reasons.  Extraordinary claims hardly ever hold up.  There are multiple weird issues with the data in the figures (e.g., magnetic susceptibility data that shows up in both papers with the same units but axes that differ in magnitude by a factor of 7000 - which numbers are reliable, if either?  Resistivity that seem bizarrely large (0.01 Ohm-cm is bigger than the Mott-Ioffe-Regel limit - again, are the units right?).  A specific heat that doesn’t reach 3R at high temperatures.  Not clear of the resistance is really zero in the nominally superconducting part of the V-I curves.).  That said, if the video and the not-crazy-scale susceptibility data are trustworthy, this stuff is very diamagnetic, more so than graphite, which is quite unusual.  At least the authors do provide a comparatively straightforward synthesis recipe, so replication attempts should clear this up in a week or two.  

None of this is thaaaaaaat unusual, by the way.  There are claims of weird superconductivity at some rate.  It’s easy to screw up measurements, especially in inhomogeneous materials.  Unfortunately, social media (esp the site formerly known as twitter) drastically amplifies this stuff.  I assume Michio Kaku is going to be on tv any second now talking about how this will change the world.  Hopefully responsible journalists will be effective at pointing out that a non-reviewed preprint on the arxiv is not conclusive.  

I’m traveling, so updates will be sparse, but I will try to keep an eye on the comments.

Disorganized thoughts on "Oppenheimer"

I saw "Oppenheimer" today.  Spoiler warning, I suppose, though I think we all know how this story ends.  Just in case you were wondering, there is no post-credit scene to set up the sequel.  (For the humor-impaired: that was a joke.)

The movie was an excellent piece of film-making, and I hope it's an opportunity for a large viewing audience to learn about a reasonable approximation of incredibly consequential history.  Sure, I can nitpick about historical details (why did Nolan leave out "Now we are all sons of bitches", transfer a bet to a different person,  and omit Fermi dropping bits of paper to estimate the yield of the Trinity test?  Why did he show Vannevar Bush seemingly hanging out at Los Alamos?  Update: rereading The Making of the Atomic Bomb, I was surprised to learn that Bush apparently was, in fact, present at the Trinity test!  Also, I do now see on an updated cast list that Kistiakowsky was portrayed in the movie, so I may have been wrong about the bet as well.  Mea culpa.).  Still, the main points come through - the atmosphere of war-time Los Alamos, and the moral complexity and ambiguity of Oppenheimer and the bomb.  

The definitive work about the Manhattan Project is The Making of the Atomic Bomb by Richard Rhodes.  That book truly captures the feeling of the era and the project.  Rereading it now, it still amazes how physicists and chemists of the time were able to make astonishing progress.  Reading about how Fermi & co. discovered moderation of neutrons (that is, slowing of neutrons through inelastic scattering off of hydrogen-containing materials like paraffin) is just mind-blowing as an experimentalist.  (They stumbled upon this by realizing that they got different experimental results if they ran their measurements on wood tables rather than marble tables within the same lab.)  

I saw someone lamenting on twitter that this movie was unlikely to inspire a generation of young people to go into physics.  Clearly that was not the intent of the film at all.  I think it's a net positive if people come away from the movie with a sense of the history and the fact that individual personalities have enormous sway even in the face of huge historical events.  Many people in the story are physicists, but the point is that they're complicated people dealing with the morality of enormously consequential decisions (on top of the usual human frailties).  (One thing the movie gets right is Teller's relentless interest in "the super" and his challenges in working with others on the Manhattan Project.  If Teller had been a less challenging personality, the course of nuclear weapons development may have been very different.  It reminds me superficially of William Shockley, whose managerial skills or lack thereof directly led to the creation of Silicon Valley.) 

For those interested in reading more about the context of the Manhattan Project, I recommend a couple of items.  The Los Alamos Primer are the notes that were given to incoming Project members and make for fascinating reading, accessible at the advanced undergrad level.  The Farm Hall transcripts are the transcribed recordings of interned German scientists held by the British in August, 1945.  They go from denial (the Americans couldn't possibly have developed a bomb) to damage control (clearly we slow-walked everything because we didn't really want the Nazis to get nuclear weapons) in the space of a couple of days.  

What are "quantum oscillations"?

For the first time in a couple of decades, I was visiting the Aspen Center for Physics, which is always a fun, intellectually stimulating experience.  (Side note: I sure hope that the rapidly escalating costs of everything in the Aspen area don't make this venue untenable in the future, and that there are growing generous financial structures that can allow this to be accessible for those of limited funding.)  One of the topics of discussion this week was "quantum oscillations" in insulators, and I thought it might be fun to try to explain, on some accessible level, just how weird those observations are.  

Historically, quantum oscillations are observed in metals and (doped) semiconductors, and they have been a great tool for understanding electronic structure in conductive materials, a topic sometimes called "fermiology".   First, I need to talk about Fermi surfaces.

Annoyingly, it's easiest to describe the electronic states in a crystal in terms of "reciprocal space" or \(\mathbf{k}\)-space, where the wave-like electronic states are labeled by some wavevector \(\mathbf{k}\), and have some (crystal) momentum given by \(\hbar \mathbf{k}\).  ( Near the bottom of an energy band, the energy of such a state is typically something like \(E_{0} + (\hbar^2 k^2)/2m^{*}\), where \(m^{*}\) is an effective mass.)

At low temperatures, the electrons settle into their lowest energy states (toward low values of \(\mathbf{k}\)), but they stack up in energy because of the Pauli principle, so that there is some blob (possibly more than one) of filled states in \(\mathbf{k}\)-space, with a boundary called the Fermi surface, surrounded by empty states.  Because the relationship between energy and momentum, \(E(\mathbf{k})\), depends on the atoms in the material and the crystal structure, the Fermi surface can be complicated and have funny shapes, like the one shown in the link.  "Fermiology" is the term for trying to figure out, experimentally, what Fermi surfaces look like.  This matters because knowing which electronic states are the highest occupied affects many properties that you might care about.  The electrons in states right "at" the Fermi surface are the ones that have energetically nearby empty states and thus are the ones that respond to perturbations like electric fields, temperature gradients, etc.

Now turn on a magnetic field.  Classically, free electrons in a magnetic field \(B\) with some velocity perpendicular to the field will tend to move in circles (in the plane perpendicular to the field) called cyclotron orbits, and that orbital motion has a characteristic cyclotron frequency, \(\omega_{c} = eB/m\).  In the quantum problem, free electrons in a magnetic field have allowed energies given by \((n+1/2)\hbar \omega_{c}\).  Since there are zillions of conduction electrons in a typical chunk of conductor, that means that each of these Landau levels holds many electrons.  

An electron with wavevector
\(\mathbf{k}\) in a magnetic 
field \(\mathbf{B}\) will trace
out an orbit (yellow) in
\(\mathbf{k}\)-space.

For electrons in a conducting crystal, the idea of cyclotron motion still works, though the energy of an electronic state involves both the magnetic field and the zero-field band structure.  For an electron with wavevector \(\mathbf{k}\), one can define a velocity \(\mathbf{v}= (1/\hbar) \nabla_{\mathbf{k}}E(\mathbf{k})\) and use that in the Lorentz force law to figure out how \(\mathbf{k}\) varies in time.  It turns out that an electron at the Fermi surface will trace out an orbit in both real space and \(\mathbf{k}\)-space.  (Of course, for this physics to matter, the system has to be sufficiently free of disorder and at sufficiently low temperatures that the electrons are unlikely to scatter as they trace out orbits.)

Now imagine sweeping the magnetic field.  As \(B\) is ramped up, discrete cyclotron energy levels will sweep past the energy of the highest occupied electronic states, the Fermi surface.  That coincidence, when there are a lot of electronic states at the Fermi energy coinciding with a cyclotron level, leads to a change in the number of electronic states available to undergo transitions, like scattering to modify the electrical resistance, or shifting to different spin states because of an external magnetic field.  The result is, quantities like the resistance and the magnetization start to oscillate, periodic in \(1/B\).    (It's a bit more  complicated than that for messy looking Fermi surfaces - oscillations in measured quantities happen when "extremal orbits" like the ones shown in the second figure are just bracketed by contours of cyclotron energy levels.  The period in \(1/B\) is inversely proportional to the area in \(\mathbf{k}\)-space enclosed by the orbit.).  

Fermi surface of Cu.  If a magnetic field
is directed as shown, there are two orbits
(purple) that will contribute oscillations
in resistivity and magnetization.

Bottom line:  in clean conductors at low temperatures and large magnetic fields, it is possible to see oscillations in certain measured quantities that are periodic in \(1/B\), and that period allows us to infer the cross-sectional area of the Fermi surface in \(\mathbf{k}\)-space.  Oscillations of the resistivity are called Shubnikov-De Haas oscillations, and oscillations of magnetization are called De Haas-van Alphen oscillations. 

These quantum oscillations, measured as a function of field at many different field orientations, have allowed us to learn a lot about the Fermi surfaces in many conducting systems.   

Imagine the surprise when De Haas-van Alphen oscillations were found in a material whose bulk is expected to be electrically insulating!  More on this soon.

Molecular electronics in 2023

This past week I was fortunate to attend this meeting, the most recent in an every-few-years series that brings together a group of researchers interested in electronic transport in molecular systems.  This brings together physicists and chemists, and this was the first one I've attended since this one in 2015.

The evolution of the field over the years has been very interesting.  Generally gone are the discussions of using actual chemically synthesized molecules as electronic devices in eventual ultrascaled computing applications.  Rather, there is a broad recognition that these systems are important testbeds for our understanding of physics that can have broad ramifications for understanding chemical processes (e.g. quantum interference in molecules leading to sharply energy dependent electronic transmission and therefore enhanced thermoelectric effects - more here), light emission (e.g. the role of local vibrations, Franck-Condon effects, and quantum interference in determining the lineshape of light from a single molecule), and the right ways to think about dissipation and the flow of energy at the extreme nanoscale in open, driven quantum systems.  In terms of the underlying physics, the processes at work in molecular devices are the same ones relevant in eventual single-nm CMOS electronic devices.

There were two particular lingering problems/mysteries discussed at the workshop that might be of particular broad interest.

• Current-induced spin selectivity (CISS) remains an intriguing and confusing set of phenomena.  The broad observation, advanced initially by the group of Prof. Ron Naaman, is that in several different experimental implementations, is that chiral molecules seem to couple nontrivially to electron spin - e.g., photoemission through chiral molecules can generate spin-polarized electrons, with the handedness of the chiral molecule and the direction of electron motion picking out a preferred spin orientation.  This has led to a diverse array of experiments (reviewed here) and proposed theoretical explanations (reviewed here).  CISS has been used, e.g., to get LEDs to emit circularly polarized light by spin-polarizing injected carriers.  The situation is very complicated, though, and while some kind of spin-orbit coupling must be at work, getting good agreement from theory calculations has proven challenging.  Recent measurements in chiral solids (not molecules) look comparatively clean to me (see here and here), bringing device design and spin Hall-based detection into play.
• Charge transport over through thick films of biomolecules remains surprising and mysterious.  In single-molecule experiments, when there are no molecular levels resonant with the electrons of the source and drain electrodes, conduction of electrons is through off-resonant tunneling.  As tunneling is exponentially suppressed with distance, this implies that the conductance \(G \sim \exp(-\beta L)\), where \(L\) is the length of the molecule, and \(\beta\) is a parameter that describes how quickly conduction falls off, and is typically on the order of 0.5 inverse Angstroms.   For longer molecules or thick films of molecules, conduction typically takes place through some flavor of thermally-activated hopping and is steeply suppressed as temperature is lowered.  In surprising contrast to this, thick (30-50 nm) films of some biomolecules show almost temperature-independent conduction from room temperature down to cryogenic temperatures.  This is really surprising!  

It's heartening to see how much is now understood about electronic transport and related phenomena down to molecular scales, and how there is still more left to learn.