What is the spin Seebeck effect?

Thermoelectricity is an old story, and I've also discussed it here.  Take a length of some conductor, and hold one end of that conductor at temperature \(T_{\mathrm{hot}}\), and hold the other end of that conductor at temperature \(T_{\mathrm{cold}}\).  The charge carriers in the conductor will tend to diffuse from the hot end toward the cold end.  However, if the conductor is electrically isolated, that can't continue, and a voltage will build up between the ends of the conductor, so that in the steady state there is no net flow of charge.  The ratio of the voltage to the temperature difference is given by \(S\), the Seebeck coefficient.  

It turns out that spin, the angular momentum carried by electrons, can also lead to the generation of voltages in the presence of temperature differences, even when the material is an insulator and the electrons don't move.  

Let me describe an experiment for you.  Two parallel platinum wires are patterned next to each other on the surface of an insulator.  An oscillating current at angular frequency \(\omega\) is run through wire A,  while wire B is attached to a voltage amplifier feeding into a lock-in amplifier.  From everything we teach in first-year undergrad physics, you might expect some signal on the lock-in at frequency \(\omega\) because the two wires are capacitively coupled to each other - the oscillating voltage on wire A leads to the electrons on wire B moving back and forth because they are influenced by the electric field from wire A.  You would not expect any kind of signal on wire B at frequency \(2 \omega\), though, at least not if the insulator is ideal.

However, if that insulator is magnetically interesting (e.g., a ferrimagnet, an antiferromagnet, some kinds of paramagnet), it is possible to see a \(2 \omega\) signal on wire B.  

In the spin Seebeck effect, a temperature gradient leads to a build-up of a net spin density across the magnetic insulator.  This is analogous to the conventional Seebeck effect - in a magnetically ordered system, there is a flow of magnons from the hot side to the cold side, transporting angular momentum along.  This builds up a net spin polarization of the electrons in the magnetic insulator.  Those electrons can undergo exchange processes with the electrons in the platinum wire B, and if the spins are properly oriented, this causes a voltage to build up across wire B due to the inverse spin Hall effect.  

So, in the would-be experiment, the ac current in wire A generates a temperature gradient between wire A and wire B that oscillates at frequency \(2 \omega\).  An external magnetic field is used to orient the spins in the magnetic insulator, and if the transported angular momentum points the right direction, there is a \(2 \omega \) voltage signal on wire B.   

I think this is pretty neat - an effect that is purely due to the quantum properties of electrons and would just not exist in the classical electricity and magnetism that we teach in intro undergrad courses.

(On writing this, I realized that I've never written a post defining the spin Hall and related effects. I'll have to work on that....  Sorry for the long delay between postings.  The beginning of the semester has been unusually demanding of my time.)

More amazingly good harmonic oscillators

 Harmonic oscillators are key elements of the physicist's toolkit for modeling the world.  Back at the end of March I wrote about some recent results using silicon nitride membranes to make incredibly high quality (which is to say, low damping) harmonic oscillators.  (Remember, the ideal harmonic oscillator that gets introduced in undergrad intro physics is a mass on a spring, with no friction or dissipation at all.  An ideal oscillator would have a \(Q\) factor that is infinite, and it would keep ringing forever once started.) This past week, two papers appeared on the arxiv showing that it's possible to design networks of (again) silicon nitride beams that have resonances at room temperature (in vacuum) with \(Q > 10^{9}\).  

(a) A perimeter mode of oscillation. (b) a false-
color electron micrograph of such a device.

One of these papers takes a specific motif, a suspended polygon made from beams, supported by anchoring beams coming from its vertices, as shown in the figure.  The resonant modes with the really high \(Q\) factors are modes of the perimeter, with nodes at the vertices.  This minimizes "clamping losses", damping that occurs at anchoring points (where the strain tends to be large, and where phonons can leak vibrational energy out of the resonator and into whatever is holding it).  

The other paper gets to a very similar design, through a process that combines biological inspiration (spiderwebs), physics insight, and machine learning/optimization to really maximize \(Q\).  

With tools like this, it's possible to do quantum mechanics experiments  (that is, mechanics experiments where quantum effects are dominant) at or near room temperature with these.  Amazing.

Brief items

 It's been a busy week, so my apologies for the brevity, but here are a couple of interesting papers and sites that I stumbled upon:

• Back when I first started teaching about nanoscience, I said that you'd really know that semiconductor quantum dots had hit the big time when you occasionally saw tanker trucks full of them going down the highway.  I think we're basically there.  Here is a great review article that summarizes the present state of the art.
• Reaching back a month, I thought that this is an impressive piece of work.  They combine scanning tunneling microscopy, photoluminescence with a tunable optical source, and having the molecule sitting on a layer of NaCl to isolate it from the electronic continuum of the substrate.  The result is amazingly (to me) sharp spectral features in the emission, spatially resolved to the atomic scale.
• The emergence of python and the ability to embed it in web pages through notebooks has transformative educational potential, but it definitely requires a serious investment of time and effort.  Here is a fluid dynamics course from eight years ago that I found the other day - hey, it was new to me.
• For a more up-to-the-minute example, here is a new course about topology and condensed matter.  Now if I only had time to go through this.  The impending start of the new semester. 
• This preprint is also an important one.  There have been some major reports in the literature about quantum oscillations (e.g., resistivity or magnetization vs. magnetic field ) being observed in insulators.  This paper shows that one must be very careful, since the use of graphite gates can lead to a confounding effect that comes from those gates rather than the material under examination.
• This PNAS paper is a neat one.  It can be hard to grow epitaxial films of some "stubborn" materials, ones involving refractory metals (high melting points, very low vapor pressures, often vulnerable to oxidation).  This paper shows that instead one can use solid forms of precursor compounds containing those metals.  The compounds sublime with reasonably high vapor pressures, and if one can work out their decomposition properly, it's possible to grow nice films and multilayers of otherwise tough materials.  (I'd need to be convinced that the purity achieved from this comparatively low temperature approach is really good.)

Metallic water!

What does it take to have a material behave as a metal, from the physicist's perspective?  I've written about this before (wow, I've been blogging for a long time).  Fundamentally, there have to be "gapless" charge-carrying excitations, so that the application of even a tiny electric field allows those charge carriers to transition into states with (barely) higher kinetic energies and momenta.  

Top: a droplet of NaK 
alloy.  Bottom: That 
droplet coated with 
adsorbed water that 
has become a metal. 
From here.

In conventional band insulators, the electronic states are filled right up to the brim in an energy band.  Apply an electric field, and an electron has no states available into which it can go without somehow grabbing enough energy to make it all the way to the bottom of the next (conduction) band.  Since that band gap can be large (5.5 eV for diamond, 8.5 eV for NaCl), no current flows, and you have an insulator.

This is, broadly speaking, the situation in liquid water. (Even though it's a liquid, the basic concept of bands of energy levels is still helpful, though of course there are no Bloch waves as in crystalline solids.)  According to calculations and experiments, the band gap in ordinary water is about 7 eV.  You can dissolve ions in water and have those carry a current - that's the whole deal with electrolytes - but ordinarily water is not a conductor based on electrons.  It is possible to inject some electrons into water, and these end up "hydrated" or "solvated" thanks to interactions with the surrounding polar water molecules and the hydronium and hydroxyl ions floating around, but historically this does not result in a metal.  To achieve metallicity, you'd have to inject or borrow so many electrons that they could get up into that next band.

This paper from late last week seems to have done just that.  A few molecular layers of water adsorbed on the outside of a droplet of liquid sodium-potassium metal apparently ends up taking in enough electrons (\( \sim 5 \times 10^{21}\) per cc) to become metallic, as detected through optical measurements of its conductivity (including a plasmon resonance).   It's rather transient, since chemistry continues and the whole thing oxidizes, but the result is quite neat!

Workshop highlights: Spins, 1D topo materials from carbon, and more

 While virtual meetings can be draining (no breaks to go hiking; no grabbing a beer and catching up, especially when attendees are spread out across a 7 timezones), this workshop was a great way for me to catch up on some science that I'd been missing.  I can't write up everything (mea culpa), but here are a few experimental highlights:

• Richard Berndt's group has again shown that shot noise integrated with STM is powerful, and they have used tunneling noise measurements to probe where and how spin-polarized transport happens through single radical-containing molecules on gold surfaces.
• Katharina Franke's group has looked at what happens when you have a localized spin on the surface of a superconductor.  Exchange coupling can rip apart Cooper pairs and bind a quasiparticle in what are called Yu-Shiba-Rusinov states.  With STM, it is possible to map these and related phenomena spatially, and the states can also be tuned via tip height, leading to very pretty data.

• 

  Amazing polymers from here.

  Pavel Jelinek gave a talk with some really eye-popping images as well as cool science.  I had not realized before that in 1D conjugated systems (think polyacetylene) it is possible to see a topological transition as a function of length, between a conjugated state (with valence-band-like orbitals filled, and conduction-band-like orbitals empty) and another conjugated state that has an unpaired electron localized at each end (equivalent to surface states) with effectively band inversion (empty valence-band-like states above filled conduction-band-like states) in the middle.  You can actually make polymers (shown here) that show these properties and image the end states via STM.  
  
• Latha Venkataraman spoke about intellectually related work.  Ordinarily, even with a conjugated oligomer, conductance falls exponentially with increasing molecular length.   However, under the right circumstances, you can get the equivalent topological transition, creating resonant states localized at the molecular ends, and over some range of lengths, you can get electronic conduction increasing with increasing molecular length.  As the molecule gets longer the resonances become better defined and stronger, though at even larger lengths the two end states decouple from each other and conductance falls again.
• Jascha Repp did a really nice job laying out their technique that is AFM with single-charge-tunneling to give STM-like information for molecules on insulating substrates.  Voltage pulses are applied in sync with the oscillating tip moving into close proximity with the molecule, such that single charges can be added or removed each cycle.  This is detected through shifts in the mechanical resonance of the AFM cantilever due to the electrostatic interactions between the tip and the molecule.  This enables time-resolved measurements as well, to look at things like excited state lifetimes in individual molecules.

The meeting is wrapping up today, and the discussions have been a lot of fun.  Hopefully we will get together in person soon!

2021 Telluride workshop on Quantum Transport in Nanoscale Systems

This week I'm (virtually) attending this workshop, which unfortunately is zoom-based because of the ongoing pandemic and travel restrictions.  As I've mentioned in previous years, it's rather like a Gordon Conference, in that it's supposed to be a smaller meeting with a decent amount of pre-publication work.   I'll write up some highlights later, but for now I wanted to feature this image.  At left is the molecular structure of [5]triangulene, which can be assembled by synthetic chemistry methods and surface catalysis (in this case on Au(111) surface).  At right is an AFM image taken using a tip functionalized by a carbon monoxide molecule.  In case you ever doubted, those cartoons from chemistry class are sometimes accurate!

Quantum computing + hype

 Last Friday, Victor Galitski published a thought-provoking editorial on linkedin, entitled "Quantum Computing Hype is Bad for Science".  I encourage people to read it.

As a person who has spent years working in the nano world (including on topics like "molecular electronics"), I'm intimately familiar with the problem of hype.  Not every advance is a "breakthrough" or "revolutionary" or "transformative" or "disruptive", and that is fine - scientists and engineers do themselves a disservice when overpromising or unjustifiably inflating claims of significance.  Incentives often point in an unfortunate direction in the world of glossy scientific publications, and the situation is even murkier when money is involved (whether to some higher order, as in trying to excite funding agencies, or to zeroth order, as in raising money for startup companies).   Nano-related research advances overwhelmingly do not lead toward single-crystal diamond nanofab or nanobots swimming through our capillaries.  Not every genomics advance will lead to a global cure for cancer or Alzheimers.  And not every quantum widget will usher in some quantum information age that will transform the world.  It's not healthy for anyone in the long term for unsupported, inflated claims to be the norm in any of these disciplines.

I am more of an optimist than Galitski.  

I agree that we are a good number of years away from practical general-purpose quantum computers that can handle problems large enough to be really interesting (e.g. breaking 4096-bit RSA encryption).  However, I think there is a ton of fascinating and productive research to be done along the way, including in areas farther removed from quantum computing, like quantum-enhanced sensing.  Major federal investments in the relevant science and engineering research will lead to real benefits in the long run, in terms of whatever technically demanding physics/electronics/optics/materials work force needs we will have.  There is very cool science to be done.  If handled correctly, increased investment will not come at the expense of non-quantum-computing science.  It is also likely not a zero-sum game in terms of human capital - there really might be more people, total, drawn into these fields if prospects for employment look more exciting and broader than they have in the past.  

Where I think Galitski is right on is the concern about what he calls "quantum Ponzi schemes".  Some people poured billions of dollars into anything with the word "blockchain" attached to it, even without knowing what blockchain means, or how it might be implemented by some particular product.  There is a real danger that investors will be unable to tell reality from science fiction and/or outright lying when it comes to quantum technologies.  Good grief, look how much money went into Theranos when lots of knowledgable people knew that single-drop-of-blood assays have all kinds of challenges and that the company's claims seemed unrealistic. 

I also think that it is totally reasonable to be concerned about the sustainability of this - anytime there is super-rapid growth in funding for an area, it's important to think about what comes later.  The space race is a good example.  There were very cool knock-on benefits overall from the post-Sputnik space race, but there was also a decades-long hangover in the actual aerospace industry when the spending fell back to earth.  

Like I said, I'm baseline pretty optimistic about all this, but it's important to listen to cautionary voices - it's the way to stay grounded and think more broadly about context.  

APS Division of Condensed Matter Physics Invited Symposium nominations

Hopefully the 2022 APS March Meeting in Chicago will be something closer to "normal", though (i) with covid variants it's good to be cautious about predictions, and (ii) I wouldn't be surprised if there is some hybrid content.  Anyway, I encourage submissions.  Having been a DCMP member-at-large and seen the process, it's to all of our benefit if there is a large pool of interesting contributions.

----

The Division of Condensed Matter Physics (DCMP) program committee requests your proposals for Invited Symposium sessions for the APS March Meeting 2022. DCMP hosts approximately 30 Invited symposia during the week of the March Meeting highlighting cutting-edge research in the broad field of condensed matter physics. These symposia consist of 5 invited talks centered on a research topic proposed by the nominator(s). Please submit only Symposium nominations. DCMP does not select individual speakers for invited talks.

Please use the APS nominations website for submission of your symposium nomination.

Submit your nomination

Nominations should be submitted as early as possible, and no later than August 13. Support your nomination with a justification, a list of five confirmed invited speakers with tentative titles, and a proposed session chair. Thank you for spending the time to help organize a strong DCMP participation at next year’s March Meeting.

Jim Sauls, Secretary/Treasurer for DCMP

Slow blogging + a couple of articles

Sorry - blogging has been slow in recent days because, despite it being summer, it's been a very busy time for various reasons.

Here are a couple of articles that I've come across that seem interesting.  On the news/popular writing front:

• The Hubble Space Telescope isn't dead yet!
• TSMC is going to crank up fab capacity for the older generation (e.g. 28 nm node) chips that do important things like run our cars.
• Intel might be trying to buy GlobalFoundries (the fab arm spun off by AMD a while ago).
• A great article by Natalie Wolchover about progress in pure math circles regarding relative sizes of infinities.

On the science front, there have been several cool things that I haven't had time to look at in depth.  A couple of quantum info papers:

• In this Nature paper, the google quantum AI team have used their 53 qubit chip to do proof-of-concept demonstrations of two different quantum error correction approaches.  Perhaps someone more knowledgable that me can chime in below in the comments about how the ratio of physical qubits to logical qubits depends on the fidelity and other properties of the physical qubits.  Basically, I'm wondering if, e.g., ion trap-based schemes would be able to make even better advantage out of the 1D error correction approach here.
• Meanwhile, in China a large group has demonstrated a 66 qubit system similar in design to the google/Martinis approach.  

Infrastructure and competitiveness

With the recent passage in the US Senate of an authorization that would potentially boost certain scientific investments by the US, and the House of Representatives version passing its versions for NSF and DOE, talk of "competitiveness" is in the air.  It took a while, but it seems to have dawned on parts of the US Congress that it would be broadly smart for the country to invest more in science and engineering research and education.  (Note that authorizations are not appropriations - declaring that they want to increase investment doesn't actually commit Congress to actually spending the money that way.  A former representative from my area routinely voted for authorizations to double the NSF budget, and then did not support the appropriations, so that he could claim to be both pro-science and anti-spending.) 

Looking through my old posts on related topics, I came across this one from 2014, about investment in shared research equipment at universities and DOE labs.  Since then, the NSF's former National Nanotechnology Infrastructure Network has been replaced by the National Nanotechnology Coordinated Infrastructure organization, but the overall federal support for this fantastic resource has actually gone down in real dollars, since its annual budget is unchanged since then at $16M/yr.  As I wrote back in 2014, in an era when one high end transmission electron microscope can cost $8M or more, that seems like underinvestment if the goal is to maximize innovation by making top-flight shared research instruments available to the broadest cross-section of universities and businesses.   

I reiterate my suggestion:  Companies (google? Intel? Microsoft? SpaceX? Tesla? 3M? Dupont? IBM?) and wealthy individuals who truly want to have a more competitive science and engineering workforce and innovation base should consider establishing an endowed entity to support research equipment and staffing at universities.   A comparatively modest investment ($300M) could support more than the entire NNCI every year, in perpetuity.  

Quantum coherence and classical yet quantum materials

Because I haven't seen this explicitly discussed anywhere, I think it's worth pointing out that everyday materials around us demonstrate some features of coherence and decoherence in quantum mechanics.

Quantum mechanics allows superposition states to exist - an electron can be in a state with a well-defined momentum, but that is a superposition of all possible position states along some wavefront.   As I mentioned here, empirically a strong measurement means coupling the system being measured to some large number of degrees of freedom, such that we don't keep track of the detailed evolution of quantum entanglement.  In my example, that electron hits a CCD detector and interacts locally with the silicon atoms in one particular pixel, depositing its charge and energy there and maybe creating additional excitations.  That "collapses" the state of the electron into a definite position.  This kind of measurement is a two-way street - a quantum system leaves its imprint on the state of the measuring apparatus, and the measurement changes the quantum system's state.

One fascinating aspect of the emergence of materials properties is that we can have systems that act both very classically (as I'll explain in a minute) and also very quantum mechanically at the same time, for different aspects of the material.  

If I have a piece of aluminum sitting in front of me (like the case of my laptop) that hunk of metal does not show up in a superposition of positions or orientations.  It surely seems to have a definite position and orientation, and if I looked closely at a given moment I would find the aluminum atoms arranged in crystal lattices, with clear atomic positions.  Somehow, the interactions of the aluminum with the broader environment have washed out the quantumness of the atomic positions.  (Volumes have been written about interpretations of quantum mechanics and "the measurement problem", as I touched on here.  In the many-worlds view, we live in a particular branch of reality, while there are other branches that correspond to other possible positions and orientations of the aluminum piece, one for each possible outcome of a positional or orientational measurement.  I'm not going to touch on the metaphysics behind how to think about this here, except to say that somehow the position of the aluminum empirically acts classically.)

What about the electrons in the piece of crystalline aluminum?  Well, we've learned about band structure.  The allowed quantum states of electrons in a periodic potential consists of bands of states.  Each of these states has an associated crystal momentum \(\hbar \mathbf{k}\), and there is some relationship between energy and crystal momentum, \(E(\mathbf{k})\).  There are values of energy between the bands that do not correspond to any allowed electronic quantum states in that periodic lattice.  In aluminum, the electronic states are filled up to states in the middle of a band.  (One can be more rigorous that this, but it's beside the point I'm trying to make.)  Interestingly, the electrons in those filled states energetically far away from the highest occupied states are coherent - they are wavelike and extended, and indeed the Bloch waves themselves are a direct consequence of quantum interference throughout the periodic lattice.  Why haven't these electrons somehow decohered into some classical situation?   If you imagine some dynamic interaction that would "measure" the location, say, of one of those electrons, you have to consider some final state in which the electron would end up.  Because all of the states at nearby energies are already occupied, and the electrons obey the Pauli Principle, there is no low-energy (on the scale of, say, the thermal energy available, \(k_{\mathrm{B}}T\)) path to decoherence.  You'd need much larger energy/higher momentum/shorter wavelength processes to reach those electrons and scatter them to empty final states (as in ARPES).

By that argument, though, the electrons that are energetically close to the Fermi level in metals should be vulnerable to decoherence - they have energetically nearby states into which they can be scattered, and a variety of comparatively low energy scattering processes (electron-electron scattering, electron-phonon scattering).   Is  that true?  Yes.  This is exactly why you can't see quantum interference effects in electrical conduction in metals at room temperature, but at low temperatures you can see interference effects like universal conductance fluctuations and understand the effects of decoherence on those effects quantitatively.

I find it remarkable that a piece of aluminum can show both the emergence of classical physics (the piece of aluminum is not spatially delocalized) while having quantum coherent degrees of within.  Understanding how to engineer robust quantum coherent systems despite the tendency toward environmental decoherence is key to future quantum information science and technology.

Nanoscale Views on the Scientific Sense podcast

I recently had the opportunity to be interviewed for the Scientific Sense podcast, available on a variety of platforms.  It was a fun discussion, and it's now available here (youtube link) or here (spotify link).  

Brief items

 

Some news items:

• Big news yesterday was the announcement at Condensed Matter Theory Center conference (I'll put up the link to the talk when it arrives on the CMTC youtube channel) by Andrea Young that ABC-stacked trilayer graphene superconducts at particular carrier densities and vertically directed electric field levels.  There are actually two superconducting states, with quite different in-plane critical fields (suggesting different pairing states).  Note that there is no twisting or moiré superlattice here, which suggests that superconductivity in stacked graphene may be more generic than has been thought.  Here is a relevant article in Quanta magazine.
• Here is a talk by Padmanabhan Balaram, about greed in the academic publishing industry.  Even open-access journals apparently have profit margins of 30-40% (!!).  Think about that when publishers claim that production costs and their amazing editorial experience really justify that authors pay $5K per open-access publication.  (Note to self:  get around to putting manuscripts up on the arxiv....)  The talk is also an indictment of fixation on publication metrics.
• On a lighter note, my very talented classmate, Yale chem professor Patrick Holland with a song about Reviewer 3.  It's more mellow than another famous response to Reviewer 3.
• I was going to write a blog post about the physics motivating the use of sticky substances on baseballs, only to discover that someone already wrote that piece.  The time is ripe for someone to try to go to the other extreme:  Some kind of miracle superomniphobic coating on the ball so that the no-slip condition for air at the surface is violated, and every pitch then travels more like a knuckleball.

The power of computational materials theory

With the growth of computational capabilities and the ability to handle large data volumes, it looks like we are entering a new era for the global understanding of material properties.  

As an example, let me highlight this paper, with the modest title, "All Topological Bands of All Stoichiometric Materials".  (Note that this is related to the efforts reported here two years ago.) These authors oversee the Topological Materials Database, and they have ground through the entire Inorganic Crystal Structure Database using electronic structure methods (density functional theory (see here, here, here) with VASP both with and without spin-orbit coupling) and an automated approach to checking for topologically nontrivial electronic bands.  This allows the authors to look at essentially all of the inorganic crystals that have reliable structural information and make a pass at characterizing whether there are topologically interesting features in their band structure.  The surprising conclusion is that almost 88% of all of these materials have at least one topologically nontrivial band somewhere (though it may be buried energetically far away from the electronic levels that affect charge transport, for example).  Considering that people didn't necessarily appreciate that there was such a thing as topological insulators until relatively recently, that's really interesting.  

This broad computational approach has also been applied by some of the same authors to look for materials with flat bands - these are systems where the electronic energy depends only very weakly on (crystal) momentum, so that interaction effects can be large compared to the kinetic energy.

The ability to do large-scale surveys of predicted material properties is an exciting development!

Ask me something.

 I realized today that I had not had an open "Ask me something" post since December, 2018.  Seems like it's time - please have at it.

What is disorder, to condensed matter physicists?

Condensed matter physicists throw around the term "disorder" quite a bit - what does this mean, and how is it quantified?  This is particularly important when worrying about comparatively delicate, exotic quantum states, as in the recent discussions of the challenge of experimentally observing emergent Majorana fermions at the interfaces between semiconductor nanowires and superconductors.  

Latent in the use of the word "disorder" is a contrast with "order".  One of the most powerful ideas in condensed matter is Bloch's theorem:  In (infinite) crystalline solids, the spatial periodicity of the arrangement of atoms in a lattice leads to the conservation of a quantity \(\hbar \mathbf{k}\), the crystal momentum, for the electrons.  The allowed energies of single-electron states in that lattice (neglecting electron-electron interaction effects) is then a function \(E(\mathbf{k})\), and it is possible to think about a wavepacket (blob) of electrons with some dominant \(\hbar \mathbf{k}\) propagating along, as discussed extensively here for example.   "Disorder" in this context is some break with perfect spatial periodicity, which breaks \(\mathbf{k}\) conservation - in the Drude picture, this is what causes electron trajectories to scatter and do a random, diffusive walk.  

Now, not all disorder is created equal.  In a metal like gold, there is a quantitative difference between having a dilute concentration of silver atoms substituted on gold sites, and alternately having the same concentration of vacancies on gold sites.  Surely the latter is somehow more disordered.  In quantum classes, we learn to think about scattering lengths, and in conductors one can ask the physically motivated question, how far would a wavepacket propagate between scattering events (a "mean free path", \(\ell\), compared to its dominant wavelength \(\lambda\)?  For a metal we can think of the product  \(k_{\mathrm{F}} \ell\), where \(k_{\mathrm{F}}\) is the Fermi wavevector, \(2 \pi/ \lambda_{\mathrm{F}}\).  A "good metal" has \( k_{\mathrm{F}} \ell >> 1 \).  When \(k_{\mathrm{F}} \ell\  < 1\), it doesn't make sense to think of propagating wavepackets anymore.  

In other contexts, it's more helpful to think of disorder explicitly as associated with an energy scale that I'll call \(\delta\).  Some sort of structural change in a material away from ordered perfection leads, on some length scale, to a shift in electronic energies by an amount of typical magnitude \(\delta\).  The question then becomes, how does \(\delta\) compare with other energy scales in the material?  The case above where \(k_{\mathrm{F}} \ell < 1\) roughly corresponds to \(\delta\) being comparable to the electronic bandwidth (the energetic extent of \(E(\mathbf{k})\).  When one wants to think about the effects of disorder on superconductors, an important ratio is \(\delta/\Delta\), where \(\Delta\) is the superconducting gap energy scale of the ordered case.   When one wants to think about the effects of disorder on some fragile emergent phase like a fractional quantum Hall state, then a relevant comparison is between \(\delta\) and the relevant energy scale associated with that state.  

TL/DR version:  "Disorder" is a catch-all term, and it is quantified by how strongly the system is perturbed away from some target ordered condition.  

It's worth remembering that some of the progenitors of modern physics thought that it would be impossible to learn much about the underlying physics of real materials because disorder would be too severe and too idiosyncratic (that is, that each kind of defect would have its own peculiar impacts).  That's why Pauli derisively said "Festkörperphysik ist eine Schmutzphysik" (solid-state physics is the physics of dirt).   Fortunately, we have been able to learn quite a bit, and disorder has its own beautiful results, even if it continues to be the bane of some problems.

Catching up

As may be obvious from my pace of posting, the last couple of weeks have been very busy and intense for multiple reasons.  I hope that once the academic year really ends I can get back into more of a routine.

Two notable stories this week:

• Two papers were published back-to-back in Science (here and here, with commentary here) that demonstrate (a) that comparatively macroscopic mechanical oscillators - drumheads - can be operated as true quantum objects (cooled down to the point where the thermal energy scale \(k_{\mathrm{B}}T\) is small compared to the quantum energy level spacing \(\hbar \omega\) (this has been done before); and that these resonators can be quantum mechanically entangled, so that the two have to be treated as a single quantum system when understanding measurements performed on each individually.   This can be used, in the case of the second paper, to allow clever measurement schemes that shift measurement back-action (see here for a nice tutorial) away from a target system, enabling precision measurements of the target better than standard quantum limits.  
• IBM has demonstrated 300 mm wafer fabrication of integrated circuits with features and techniques for the upcoming "2 nm node".  As I've mentioned before, we have fully transitioned to the point where labeling new semiconductor manufacturing targets with a length scale is basically a marketing ploy - the transistors on this wafer do not have 2 nm channel lengths, and the wiring does not have 2 nm lines and spaces.  However, this is a very impressive technical demonstration of wafer-scale success in a number of new approaches, including triple-stacked nanosheet gate-all-around transistors.

Brief items

 As we careen toward the end of the spring semester, here are a few interesting links for perusal:

• My colleagues at the Rice Center for Quantum Materials are running a mini-workshop this week about topology and correlations in condensed matter.
• More broadly, there is a new site for all things quantum at Rice.  More news in the coming weeks....
• Speaking of quantum, I thought that this paper was pretty impressive as a technical achievement.  The authors are able to cool a mechanical resonator (a suspended aluminum drumhead, essentially) down to 500 microKelvin (!), so cold that \(k_{\mathrm{B}}T\) is smaller than the harmonic oscillator energy levels - down to the quantum ground state for its center of mass motion.  As someone who built a nuclear demagnetization stage as part of my PhD, I have to respect achieving that temperature for a sample in vacuum.  Likewise, as someone who studied tunneling two-level systems in solids, it's impressive to see the logarithmic temperature dependence of sound speed in the aluminum extend smoothly down to below 1 mK.  
• On a more general thermodynamic topic, this paper really surprised me. It's a review article about the existence of a dynamical crossover (the "Frenkel line") that exists above the critical temperature and pressure for a number of fluids - basically a separation into different regimes of response (not true phases per se).  Embarrassingly, I'd never heard of this, and I need to find the time to read up on it.
• I'm late to the party on this, as it got quite a bit of press, but this paper is really interesting - special engineered light modes that are designed to propagate without distortion (though with attenuation) through scattering media.  There are many potential applications, such as medical imaging (with light or with ultrasound).
• Anyone want a dinner plate-sized chip with 2.4 trillion transistors? 

Lecturer position, Rice Physics & Astronomy

The Department of Physics and Astronomy at Rice University invites applications from recent Ph.D. graduates for a lecturer position in physics and astronomy, commencing July/August 2021.  Familiarity with and/or interest in physics education research, undergraduate teaching at the introductory level, pedagogy, and curricular issues is preferred. This is a non-tenure-track position for a two-year term with the possibility of reappointment for additional three-year terms.  This is a full-time, 9-month academic calendar position.  There would also be opportunities to develop innovative teaching methods and pursue independent research or collaborations with existing research programs (see web page https://physics.rice.edu/ ).  Evaluation of applications will begin May 15 and continue until the position is filled. Applications for this position must be submitted electronically at https://jobs.rice.edu/postings/26670.  Applicants should submit (1) a curriculum vitae, (2) a statement of teaching interests, (3) a statement on diversity and outreach, (4) a list of publications, and (5) the names, affiliations, and email addresses of three professional references.  Applicants must be eligible to work in the U.S. Rice University is committed to a culturally diverse intellectual community. In this spirit, we particularly welcome applications from all genders and members of historically underrepresented groups who exemplify diverse cultural experiences and who are especially qualified to mentor and advise all members of our diverse student population.

Rice University is an Equal Opportunity Employer with a commitment to diversity at all levels, and considers for employment qualified applicants without regard to race, color, religion, age, sex, sexual orientation, gender identity, national or ethnic origin, genetic information, disability, or protected veteran status. We encourage applicants from diverse backgrounds to apply.

NSF Workshop on Quantum Engineering Infrastructure

 I spent three afternoons this week attending a NSF workshop on Quantum Engineering Infrastructure.  This was based in part on the perceived critical need for shared infrastructure (materials growth, lithographic patterning, deposition, etching, characterization) across large swaths of experimental quantum information sciences, and the fact that the NSF already runs the NNCI, which was the successor of the NNIN.  There will end up being a report generated as a result of the workshop, hopefully steering future efforts.  (I was invited because of this post.)

The workshop was very informative, touching on platforms including superconducting qubits, trapped ions, photonic devices including color centers in diamond/SiC, topological materials, and spin qubits in semiconductors.  Some key themes emerged:

• There are many possible platforms out there for quantum information science, and all of them will require very serious materials development to be ready for prime time.  People forget that our command of silicon comes after thousands of person-years worth of research and process development.  Essentially every platform is in its infancy compared to that.  
• There is clearly a tension between the need for exploratory research, trying new processes at the onesy-twosy level, and the requirements for work at larger scale, which needs dedicated process expertise and control at a level not typically possible in a shared university facility.  Everyone also knows that progress is automatically slow if people have to travel off-site to some user facility to do part of their processing.  Some places are well situated - MIT, for example, has an exploratory fab facility here, and a dedicated 200 mm substrate superconducting circuit fab at Lincoln Labs.  Life is extra complicated when running an unusual process in some tool like a PECVD system or an etcher can "season" the gadget, leaving an imprint on subsequent process runs.
• Whoever really figures out how to do wafer-scale heteroepitaxy of single-crystal diamond will either become incredibly rich or will be assassinated by DeBeers.  
• Fostering a healthy relationship between industrial materials growers and academic researchers would be very important.  Industrial expertise can be fantastic, but there is not necessarily much economic incentive to work closely with academia compared with large-scale commercial pressures.  There may be a key role for government encouragement or subsidy.  
• It's going to be increasingly challenging for new faculty to get started in some research topics at universities - the detailed process knowhow and the need to buildup expertise can be expensive and slow to acquire compared to the timescale of, e.g., promotion to tenure.  An improved network that supports, curates, and communicates process development expertise might be extremely helpful.