Items of interest

 A couple of interesting papers that I came across this week:

• There is long been an interest in purely electronic cooling techniques (no moving parts!) that would work at cryogenic temperatures.  You're familiar with ordinary evaporative cooling - that's what helps cool down your tea or coffee when you blow across the top if your steaming mug, and it's what makes you feel cold when you step out of the shower.  In evaporative cooling, the most energetic molecules can escape from the liquid into the gas phase, and the remaining molecules left behind reestablish thermal equilibrium at a lower temperature.  One can make a tunnel junction between a normal metal and a superconductor, and under the right circumstances, the hottest (thermally excited) electrons in the normal metal can be driven into the superconductor, leading to net cooling of the remaining electrons in the normal metal.  This is pretty neat, but it's had somewhat limited utility due to relatively small cooling power - here is a non-paywalled review that includes discussion of these approaches.  This week, the updated version of this paper went on the arXiv, demonstrating in Al/AlOx/Nb junctions, it is possible to cool from about 2.4 K to about 1.6 K, purely via electronic means.  This seems like a nice advance, especially as the quantum info trends have pushed hard on improving wafer-level Nb electronics.
• I've written before about chirality-induced spin selectivity (see the first bullet here).  This is a still poorly understood phenomenon in which electrons passing through a chiral material acquire a net spin polarization, depending on the handedness of the chirality and the direction of the current.  This new paper in Nature is a great demonstration.  Add a layer of chiral perovskite to the charge injection path of a typical III-V multiple quantum well semiconductor LED, and the outcoming light acquires a net circular polarization, the sign of which depends on the sign of the chirality.  This works at room temperature, by the way.  

The physics of squeaky shoes

In these unsettling and trying times, I wanted to write about the physics of a challenge I'm facing in my professional life: super squeaky shoes.  When I wear a particularly comfortable pair of shoes at work, when I walk in some hallways in my building (but not all), my shoes squeak very loudly with every step. How and why does this happen, physically?  

The shoes in question.

To understand this, we need to talk a bit about a friction, the sideways interfacial force between two surfaces when one surface is sheared (or attempted to be sheared) with respect to the other.  (Tribology is the study of friction, btw.)  In introductory physics we teach some (empirical) "laws" of friction, described in detail on the wikipedia page linked above as well as here:

1.  For static friction (no actual sliding of the surfaces relative to each other), the frictional force \(F_{f} \le \mu_{s}N\), where \(\mu_{s}\) is the "coefficient of static friction" and \(N\) is the normal force (pushing the two surfaces together).  The force is directed in the plane and takes on the magnitude needed so that no sliding happens, up to its maximum value, at which point the surfaces start slipping relative to each other.
2. For sliding or kinetic friction, \(F_{f} = \mu_{k}N\), where \(\mu_{k}\) is the coefficient of kinetic or sliding friction, and the force is directed in the plane to oppose the relative sliding motion.  The friction coefficients depend on the particular materials and their surface conditions.
3. The friction forces are independent of the apparent contact area between the surfaces.  
4. The kinetic friction force is independent of the relative sliding speed between the surfaces.

These "laws", especially (3) and (4), are truly weird once we know a bit more about physics, and I discuss this a little in my textbook.  The macroscopic friction force is emergent, meaning that it is a consequence of the materials being made up of many constituent particles interacting.  It's not a conservative force, in that energy dissipated through the sliding friction force doing work is "lost" from the macroscopic movement of the sliding objects and ends up in the microscopic vibrational motion (and electronic distributions, if the objects are metals).  See here for more discussion of friction laws.

Shoe squeaking happens because of what is called "stick-slip" motion.  When I put my weight on my right shoe, the rubber sole of the shoe deforms and elastic forces (like a compressed spring) push the rubber to spread out, favoring sliding rubber at the rubber-floor interface.  At some point, the local static friction maximum force is exceeded and the rubber begins to slide relative to the floor.  That lets the rubber "uncompress" some, so that the spring-like elastic forces are reduced, and if they fall back below \(\mu_{s}N\), that bit of sole will stick on the surface again.  A similar situation is shown in this model from Wolfram, looking at a mass (attached to an anchored spring) interacting with a conveyer belt.   If this start/stop cyclic motion happens at acoustic sorts of frequencies in the kHz, it sounds like a squeak, because the start-stop motion excites sound waves in the air (and the solid surfaces).  This stick-slip phenomenon is also why brakes on cars and bikes squeal, why hinges on doors in spooky houses creak, and why that one board in your floor makes that weird noise.  It's also used in various piezoelectric actuators. 

Macroscopic friction emerges from a zillion microscopic interactions and is affected by the chemical makeup of the surfaces, their morphology and roughness, any adsorbed layers of moisture or contaminants (remember: every surface around you right now is coated in a few molecular layers of water and hydrocarbon contamination), and van der Waals forces, among other things.  The reason my shoes squeak in some hallways but not others has to do with how the floors have been cleaned.  I could stop the squeaking by altering the bottom surface of my soles, though I wouldn't want to use a lubricant that is so effective that it seriously lowers \(\mu_{s}N\) and makes me slip.  

Friction is another example of an emergent phenomenon that is everywhere around us, of enormous technological and practical importance, and has some remarkable universality of response.  This kind of emergence is at the heart of the physics of materials, and trying to predict friction and squeaky shoes starting from elementary particle physics is just not do-able. 

Brief items - light-driven diamagnetism, nuclear recoil, spin transport in VO2

Real life continues to make itself felt in various ways this summer (and that's not even an allusion to political madness), but here are three papers (two from others and a self-indulgent plug for our work) you might find interesting.

• There has been a lot of work in recent years particularly by the group of Andrea Cavalleri, in which they use infrared light to pump particular vibrational modes in copper oxide superconductors (and other materials) (e.g. here).  There are long-standing correlations between the critical temperature for superconductivity, \(T_{c}\), and certain bond angles in the cuprates.  Broadly speaking, using time-resolved spectroscopy, measurements of the optical conductivity in these pumped systems show superconductor-like forms as a function of energy even well above the equilibrium \(T_{c}\), making it tempting to argue that the driven systems are showing nonequilibrium superconductivity.  At the same time, there has been a lot of interest in looking for other signatures, such as signs of the ways uperconductors expel magnetic flux through the famous Meissner effect.  In this recent result (arXiv here, Nature here), magneto-optic measurements in this same driven regime show signs of field build-up around the perimeter of the driven cuprate material in a magnetic field, as would be expected from Meissner-like flux expulsion.  I haven't had time to read this in detail, but it looks quite exciting.  
• Optical trapping of nanoparticles is a very useful tool, and with modern techniques it is possible to measure the position and response of individual trapped particles to high precision (see here and here).  In this recent paper, the group of David Moore at Yale has been able to observe the recoil of such a particle due to the decay of a single atomic nucleus (which spits out an energetic alpha particle).  As an experimentalist, I find this extremely impressive, in that they are measuring the kick given to a nanoparticle a trillion times more massive than the ejected helium nucleus.  
• From our group, we have published a lengthy study (arXiv here, Phys Rev B here) of local/longitudinal spin Seebeck response in VO2, a material with an insulating state that is thought to be magnetically inert.  This corroborates our earlier work, discussed here.  In brief, in ideal low-T VO2, the vanadium atoms are paired up into dimers, and the expectation is that the unpaired 3d electrons on those atoms form singlets with zero net angular momentum.  The resulting material would then not be magnetically interesting (though it could support triplet excitations called triplons).  Surprisingly, at low temperatures we find a robust spin Seebeck response, comparable to what is observed in ordered insulating magnets like yttrium iron garnet.  It seems to have the wrong sign to be from triplons, and it doesn't seem possible to explain the details using a purely interfacial model.  I think this is intriguing, and I hope other people take notice.

Hoping for more time to write as the summer progresses.  Suggestions for topics are always welcome, though I may not be able to get to everything.

What is a Wigner crystal?

Last week I was at the every-2-years Gordon Research Conference on Correlated Electron Systems at lovely Mt. Holyoke.  It was very fun, but one key aspect of the culture of the GRCs is that attendees are not supposed to post about them on social media, thus encouraging presenters to show results that have not yet been published.  So, no round up from me, except to say that I think I learned a lot.

The topic of Wigner crystals came up, and I realized that (at least according to google) I have not really written about these, and now seems to be a good time.

First, let's talk about crystals in general.  If you bring together an ensemble of objects (let's assume they're identical for now) and throw in either some long-range attraction or an overall confining constraint, plus a repulsive interaction that is effective at short range, you tend to get formation of a crystal, if an object's kinetic energy is sufficiently small compared to the interactions.  A couple of my favorite examples of this are crystals from drought balls and bubble rafts.  As the kinetic energy (usually parametrized by a temperature when we're talking about atoms and molecules as the objects) is reduced, the system crystallizes, spontaneously breaking continuous translational and rotational symmetry, leading to configurations with discrete translational and rotational symmetry.  Using charged colloidal particles as buiding blocks, the attractive interaction is electrostatic, because the particles have different charges, and they have the usual "hard core repulsion".  The result can be all kinds of cool colloidal crystal structures.

In 1934, Eugene Wigner considered whether electrons themselves could form a crystal, if the electron-electron repulsion is sufficiently large compared to their kinetic energy.  For a cold quantum mechanical electron gas, where the kinetic energy is related to the Fermi energy of the electrons, the essential dimensionless parameter here is \(r_{s}\), the Wigner-Seitz radius.  Serious calculations have shown that you should get a Wigner crystal for electrons in 2D if \(r_{s} > \sim 31\).  (You can also have a "classical" Wigner crystal, when the electron kinetic energy is set by the temperature rather than quantum degeneracy; an example of this situation is electrons floating on the surface of liquid helium.)

Observing Wigner crystals in experiments is very challenging, historically.  When working in ultraclean 2D electron gases in GaAs/AlGaAs structures, signatures include looking for "pinning" of the insulating 2D electronic crystal on residual disorder, leading to nonlinear conduction at the onset of "sliding"; features in microwave absorption corresponding to melting of the crystal; changes in capacitance/screening, etc.  Large magnetic fields can be helpful in bringing about Wigner crystallization (tending to confine electronic wavefunctions, and quenching kinetic energy by having Landau Levels).  

In recent years, 2D materials and advances in scanning tunneling microscopy (STM) have led to a lot of progress in imaging Wigner crystals.  One representative paper is this, in which the moiré potential in a bilayer system helps by flattening the bands and therefore reducing the kinetic energy.  Another example is this paper from April, looking at Wigner crystals at high magnetic field in Bernal-stacked bilayer graphene.   One aspect of these experiments that I find amazing is that the STM doesn't melt the crystals, since it's either injecting or removing charge throughout the imaging process.  The crystals are somehow stable enough that any removed electron gets rapidly replaced without screwing up the spatial order.  Very cool.

Two additional notes:

• Spoof journals can be pretty funny, and this week I happened upon the Journal of Immaterial Science.  I thought that this paper was pretty great.
• I also ran into this video of N. David Mermin talking with Hans Bethe about the early days of solid state physics.  Good stuff.