Saturday, April 21, 2018

The Einstein-de Haas effect

Angular momentum in classical physics is a well-defined quantity tied to the motion of mass about some axis - its value (magnitude and direction) is tied to a particular choice of coordinates.  When we think about some extended object spinning around an axis with some angular velocity \(\mathbf{\omega}\), we can define the angular momentum associated with that rotation by \(\mathbf{I}\cdot \mathbf{\omega}\), where \(\mathbf{I}\) is the "inertia tensor" that keeps track of how mass is distributed in space around the axis.  In general, conservation of angular momentum in isolated systems is a consequence of the rotational symmetry of the laws of physics (Noether's theorem). 

The idea of quantum particles possessing some kind of intrinsic angular momentum is a pretty weird one, but it turns out to be necessary to understand a huge amount of physics.  That intrinsic angular momentum is called "spin", but it's *not* correct to think of it as resulting from the particle being an extended physical object actually spinning.  As I learned from reading The Story of Spin (cool book by Tomonaga, though I found it a bit impenetrable toward the end - more on that below), Kronig first suggested that electrons might have intrinsic angular momentum and used the intuitive idea of spinning to describe it; Pauli pushed back very hard on Kronig about the idea that there could be some physical rotational motion involved - the intrinsic angular momentum is some constant on the order of \(\hbar\).  If it were the usual mechanical motion, dimensionally this would have to go something like \(m r v\), where \(m\) is the mass, \(r\) is the size of the particle, and \(v\) is a speed; as \(r\) gets small, like even approaching a scale we know to be much larger than any intrinsic size of the electron, \(v\) would exceed \(c\), the speed of light.  Pauli pounded on Kronig hard enough that Kronig didn't publish his ideas, and two years later Goudsmit and Uhlenbeck established intrinsic angular momentum, calling it "spin".

Because of its weird intrinsic nature, when we teach undergrads about spin, we often don't emphasize that it is just as much angular momentum as the classical mechanical kind.  If you somehow do something to a system a bunch of spins, that can have mechanical consequences.  I've written about one example before, a thought experiment described by Feynman and approximately implemented in micromechanical devices.  A related concept is the Einstein-de Haas effect, where flipping spins again exerts some kind of mechanical torque.  A new preprint on the arxiv shows a cool implementation of this, using ultrafast laser pulses to demagnetize a ferromagnetic material.  The sudden change of the spin angular momentum of the electrons results, through coupling to the atoms, in the launching of a mechanical shear wave as the angular momentum is dumped into the lattice.   The wave is then detected by time-resolved x-ray measurements.  Pretty cool!

(The part of Tomonaga's book that was hard for me to appreciate deals with the spin-statistics theorem, the quantum field theory statement that fermions have spins that are half-integer multiples of \(\hbar\) while bosons have spins that are integer multiples.  There is a claim that even Feynman could not come up with a good undergrad-level explanation of the argument.  Have any of my readers every come across a clear, accessible hand-wave proof of the spin-statistics theorem?)

Tuesday, April 10, 2018

Chapman Lecture: Using Topology to Build a Better Qubit

Yesterday, we hosted Prof. Charlie Marcus of the Niels Bohr Institute and Microsoft for our annual Chapman Lecture on Nanotechnology.   He gave a very fun, engaging talk about the story of Majorana fermions as a possible platform for topological quantum computing. 

Charlie used quipu to introduce the idea of topology as a way to store information, and made a very nice heuristic argument about how topology encodes information in a global rather than a local sense.  That is, if you have a big, loose tangle of string on the ground, and you do local measurements of little bits of the string, you really can't tell whether it's actually tied in a knot (topologically nontrivial) or just lying in a heap.  This hints at the idea that local interactions (measurements, perturbations) can't necessarily disrupt the topological state of a quantum system.

The talk was given a bit of a historical narrative flow, pointing out that while there had been a lot of breathless prose written about the long search for Majoranas, etc., in fact the timeline was actually rather compressed.  In 2001, Alexei Kitaev proposed a possible way of creating effective Majorana fermions, particles that encode topological information,  using semiconductor nanowires coupled to a (non-existent) p-wave superconductor.   In this scheme, Majorana quasiparticles localize at the ends of the wire.  You can get some feel for the concept by imagining string leading off from the ends of the wire, say downward through the substrate and off into space.  If you could sweep the Majoranas around each other somehow, the history of that wrapping would be encoded in the braiding of the strings, and even if the quasiparticles end up back where they started, there is a difference in the braiding depending on the history of the motion of the quasiparticles.   Theorists got very excited a bout the braiding concept and published lots of ideas, including how one might do quantum computing operations by this kind of braiding.

In 2010, other theorists pointed out that it should be possible to implement the Majoranas in much more accessible materials - InAs semiconductor nanowires and conventional s-wave superconductors, for example.  One experimental feature that could be sought would be a peak in the conductance of a superconductor/nanowire/superconductor device, right at zero voltage, that should turn on above a threshold magnetic field (in the plane of the wire).  That's really what jumpstarted the experimental action.  Fast forward a couple of years, and you have a paper that got a ton of attention, reporting the appearance of such a peak.  I pointed out at the time that that peak alone is not proof, but it's suggestive.  You have to be very careful, though, because other physics can mimic some aspects of the expected Majorana signature in the data.

A big advance was the recent success in growing epitaxial Al on the InAs wires.  Having atomically precise lattice registry between the semiconductor and the aluminum appears to improve the contacts significantly.   Note that this can be done in 2d as well, opening up the possibility of many investigations into proximity-induced superconductivity in gate-able semiconductor devices.  This has enabled some borrowing of techniques from other quantum computing approaches (transmons).

The main take-aways from the talk:

  • Experimental progress has actually been quite rapid, once a realistic material system was identified.
  • While many things point to these platforms as really having Majorana quasiparticles, the true unambiguous proof in the form of some demonstration of non-Abelian statistics hasn't happened yet.  Getting close.
  • Like many solid-state endeavors before, the true enabling advances here have come from high quality materials growth.
  • If this does work, scale-up may actually be do-able, since this does rely on planar semiconductor fabrication for the most part, and topological qubits may have a better ratio of physical qubits to logical qubits than other approaches.
  • Charlie Marcus remains an energetic, engaging speaker, something I first learned when I worked as the TA for the class he was teaching 24 years ago. 

Thursday, March 29, 2018

E-beam evaporators - recommendations?

Condensed matter experimentalists often need to prepare nanoscale thickness films of a variety of materials.  One approach is to use "physical vapor deposition" - in a good vacuum, a material of interest is heated to the point where it has some nonzero vapor pressure, and that vapor collides with a substrate of interest and sticks, building up the film.  One way to heat source material is with a high voltage electron beam, the kind of thing that used to be used at lower intensities to excite the phosphors on old-style cathode ray tube displays.  

My Edwards Auto306 4-pocket e-beam system is really starting to show its age.  It's been a great workhorse for quick things that don't require the cleanroom.  Does anyone out there have recommendations for a system (as inexpensive as possible of course) with similar capabilities, or a vendor you like for such things?  

Wednesday, March 28, 2018

Discussions of quantum mechanics

In a sure sign that I'm getting old, I find myself tempted to read some of the many articles, books, and discussions about interpretations of quantum mechanics that seem to be flaring up in number these days.  (Older physicists seem to return to this topic, I think because there tends to be a lingering feeling of dissatisfaction with just about every way of thinking about the issue.)

To be clear, the reason people refer to interpretations of quantum mechanics is that, in general, there is no disagreement about the results of well-defined calculations, and no observed disagreement between such calculations and experiments.   

There are deep ontological questions here about what physicists mean by something (say the wavefunction) being "real".  There are also fascinating history-of-science stories that capture the imagination, with characters like Einstein criticizing Bohr about whether God plays dice, Schroedinger and his cat, Wigner and his friend, Hugh Everett and his many worlds, etc.  Three of the central physics questions are:
  • Quantum systems can be in superpositions.  We don't see macroscopic quantum superpositions, even though "measuring" devices should also be described using quantum mechanics.  Is there some kind physical process at work that collapses superpositions that is not described by the ordinary Schroedinger equation?   
  • What picks out the classical states that we see?  
  • Is the Born rule a consequence of some underlying principle, or is that just the way things are?
Unfortunately real-life is very busy right now, but I wanted to collect some recent links and some relevant papers in one place, if people are interested.

From Peter Woit's blog, I gleaned these links:
Going down the google scholar rabbit hole, I also found these:
  • This paper has a clean explication of the challenge in whether decoherence due to interactions with large numbers of degrees of freedom really solves the outstanding issues.
  • This is a great review by Zurek about decoherence.
  • This is a subsequent review looking at these issues.
  • And this is a review of "collapse theories", attempts to modify quantum mechanics beyond Schroedinger time evolution to kill superpositions.
No time to read all of these, unfortunately.

Wednesday, March 14, 2018

Stephen Hawking, science communicator

An enormous amount has already been written by both journalists and scientists (here too) on the passing of Stephen Hawking.  Clearly he was an incredibly influential physicist with powerful scientific ideas.  Perhaps more important in the broad scheme of things, he was a gifted communicator who spread a fascination with science to an enormous audience, through his books and through the careful, clever use of his celebrity (as here, here, here, and here).   

While his illness clearly cost him dearly in many ways, I don't think it's too speculative to argue that it was a contributor to his success as a popularizer of science.  Not only was he a clear, expository writer with a gift for conveying a sense of the beauty of some deep ideas, but he was in some ways a larger-than-life heroic character - struck down physically in the prime of life, but able to pursue exotic, foundational ideas through the sheer force of his intellect.   Despite taking on some almost mythic qualities in the eyes of the public, he also conveyed that science is a human endeavor, pursued by complicated, interesting people (willing to do things like place bets on science, or even reconsider their preconceived ideas).

Hawking showed that both science and scientists can be inspiring to a broad audience.  It is rare that top scientists are able to do that, though a combination of their skill as communicators and their personalities.  In physics, besides Hawking the ones that best spring to mind are Feynman (anyone who can win a Nobel and also have their anecdotes described as the Adventures of a Curious Character is worth reading!) and Einstein.   

Sometimes there's a bias that gifted science communicators who care about public outreach are self-aggrandizing publicity hounds and not necessarily serious intellects (not that the two have to be mutually exclusive).  The outpouring of public sympathy on the occasion of Hawking's passing shows how deep an impact he had on so many.  Informing and inspiring people is a great legacy, and hopefully more scientists will be successful on that path thanks to Hawking.   

Wednesday, March 07, 2018

APS March Meeting, day 3 and summary thoughts

Besides the graphene bilayer excitement, a three other highlights from today:

David Cobden of the University of Washington gave a very nice talk about 2d topological insulator response of 1T'-WTe2.  Many of the main results are in this paper (arxiv link).    This system in the single-layer limit has very clear edge conduction while the bulk of the 2d layer is insulating, as determined by a variety of transport measurements.  There are also new eye-popping scanning microwave impedance microscopy results from Yongtao Cui's group at UC Riverside that show fascinating edge channels, indicating tears and cracks in the monolayer material that are otherwise hard to see. 

Steve Forrest of the University of Michigan gave a great presentation about "How Organic Light Emitting Diodes Revolutionized Displays (and maybe lighting)".  The first electroluminescent organic LED was reported about thirty years ago, and it had an external quantum efficiency of about 1%.  First, when an electron and a hole come together in the device, they only have a 1-in-4 chance of producing a singlet exciton, the kind that can readily decay radiatively.  Second, it isn't trivial to get light out of such a device because of total internal reflection.  Adding in the right kind of strong spin-orbit-coupling molecule, it is possible to convert those triplets to singlets and thus get nearly 100% internal quantum efficiency.  In real devices, there can be losses due to light trapped in waveguided modes, but you can create special substrates to couple that light into the far field.  Similarly, you can create modified substrates to avoid losses due to unintentional plasmon modes.  The net result is that you can have OLEDs with about 70% external quantum efficiencies.   OLED displays are a big deal - the global market was about $20B/yr in 2017, and will likely displace LCD displays.  OLED-based lighting is also on the way.  It's an amazing technology, and the industrial scale-up is very impressive.

Barry Stipe from Western Digital also gave a neat talk about the history and present state of the hard disk drive.  Despite the growth of flash memory, 90% of all storage in cloud data centers remains in magnetic hard disks, for capacity and speed.  The numbers are really remarkable.  If you scale all the parts of a hard drive up by a factor of a million, the disk platter would be 95 km in diameter, a bit would be about the size of your finger, and the read head would be flying above the surface at an altitude of 4 mm, and to get the same data rate as a drive, the head would have to be flying at 0.1 c.  I hadn't realized that they now hermetically seal the drives and fill them with He gas.  The He is an excellent thermal conductor for cooling, and because it has a density 1/7 that of air, the Reynolds number is lower for a given speed, meaning less turbulence, meaning they can squeeze additional, thinner platters into the drive housing.  Again, an amazing amount of science and physics, plus incredible engineering.

Some final thoughts (as I can't stay for the rest of the meeting):

  • In the old days, some physicists seemed to generate an intellectual impression by cultivating resemblance to Einstein.  Now, some physicists try to generate an intellectual impression by cultivating resemblance to Paul McEuen.
  • After many years of trying, the APS WiFi finally works properly and well!  
  • This was the largest March Meeting ever (~ 12000 attendees).  This is a genuine problem, as the meeting is growing by several percent per year, and this isn't sustainable, especially in terms of finding convention centers and hotels that can host.  There are serious discussions about what to do about this in the long term - don't be surprised if a survey is sent to some part of the APS membership about this.

Superconductivity in graphene bilayers - why is this exciting and important

As I mentioned here, the big story of this year's March Meeting is the report, in back-to-back Nature papers this week (arxiv pdf links in this sentence), of both Mott insulator and superconductivity in graphene bilayers.  I will post more here later today after seeing the actual talk on this (See below for some updates), but for now, let me give the FAQ-style report.  Skip to the end for the two big questions:
Moire pattern from twisted bilayer
graphene, image from NIST.

  • What's the deal with graphene?  Graphene is the name for a single sheet of graphite - basically an atomically thin hexagonal chickenwire lattice of carbon atoms.  See here and here.  Graphene is the most popular example of an enormous class of 2d materials.  The 2010 Nobel Prize in physics was awarded for the work that really opened up that whole body of materials for study by the physics community.  Graphene has some special electronic properties:  It can easily support either electrons or holes (effective positively charged "lack of electrons") for conduction (unlike a semiconductor, it has no energy gap, but it's a semimetal rather than a metal), and the relationship between kinetic energy and momentum of the charge carriers looks like what you see for massless relativistic things in free space (like light).
  • What is a bilayer?  Take two sheets of graphene and place one on top of the other.  Voila, you've made a bilayer.  The two layers talk to each other electronically.  In ordinary graphite, the layers are stacked in a certain way (Bernal stacking), and a Bernal bilayer acts like a semiconductor.  If you twist the two layers relative to each other, you end up with a Moire pattern (see image) so that along the plane, the electrons feel some sort of periodic potential.
  • What is gating?  It is possible to add or remove charge from the graphene layers by using an underlying or overlying electrode - this is the same mechanism behind the field effect transistors that underpin all of modern electronics.
  • What is actually being reported? If you have really clean graphene and twist the layers relative to each other just right ("magic angle"), the system becomes very insulating when you have just the right number of charge carriers in there.  If you add or remove charge away from that insulating regime, the system apparently becomes superconducting at a temperature below 1.7 K.
  • Why is the insulating behavior interesting?  It is believed that the insulating response in the special twisted case is because of electron-electron interactions - a Mott insulator.  Think about one of those toys with sliding tiles.  You can't park two tiles in the same location, so if there is no open location, the whole set of tiles locks in place.  Mott insulators usually involve atoms that contain d electrons, like NiO or the parent compounds of the high temperature copper oxide superconductors.  Mott response in an all carbon system would be realllllly interesting.  
  • Why is the superconductivity interesting?  Isn't 1.7 K too cold to be useful?  The idea of superconductivity-near-Mott has been widespread since the discovery of high-Tc in 1987.  If that's what's going on here, it means we have a new, highly tunable system to try to understand how this works.  High-Tc remains one of the great unsolved problems in (condensed matter) physics, and insights gained here have the potential to guide us toward greater understanding and maybe higher temperatures in those systems.  
  • Why is this important?  This is a new, tunable, controllable system to study physics that may be directly relevant to one of the great open problems in condensed matter physics.  This may be generalizable to the whole zoo of other 2d materials as well. 
  • Why should you care?  It has the potential to give us deep understanding of high temperature superconductivity.  That could be a big deal.  It's also just pretty neat.  Take a conductive sheet of graphene, and another conducting sheet of graphene, and if you stack them juuuuuust right, you get an insulator or a superconductor depending on how many charge carriers you stick in there.  Come on, that's just wild.
Update:  A few notes from seeing the actual talk.
  • Pablo painted a picture:  In the cuprates, the temperature (energy) scale is hundreds of Kelvin, and the size scale associated with the Mott insulating lattice is fractions of a nm (the spacing between Cu ions in the CuO2 planes).  In ultracold atom optical lattice attempts to look at Mott physics, the temperature scale is nK (and cooling is a real problem), while the spatial scale between sites is more like a micron.  In the twisted graphene bilayers, the temperature scale is a few K, and the spatial scale is about 13.4 nm (for the particular magic angle they use).
  • The way to think about what the twist does:  In real space, it creates a triangular lattice of roughly Bernal-stacked regions (the lighter parts of the Moire pattern above).  In reciprocal space, the Dirac cones at the K and K' points of the two lattices become separated by an amount given by \(k_{\theta} \approx K \theta\), where \(\theta\) is the twist angle, and we've used the small angle approximation.  When you do that and turn on interlayer coupling, you hybridize the bands from the upper and lower layers.  This splits off the parts of the bands that are close in energy to the dirac point, and at the magic angles those bands can be very very flat (like bandwidths of ~ 10 meV, as opposed to multiple eV of the full untwisted bands).  Flat bands = tendency to localize.   The Mott phase then happens if you park exactly one carrier (one hole, for the superconducting states in the paper) per Bernal-patch-site.  
  • Most persuasive reasons they think it's really a Mott insulating state and not something else, besides the fact that it happens right at half-filling of the twist-created triangular lattice:  Changing the angle by a fraction of a degree gets rid of the insulating state, and applying a magnetic field (in plane or perpendicular) makes the system become metallic, which is the opposite of what tends to happen in other insulating situations.  (Generally magnetic fields tend to favor localization.)
  • They see spectroscopic evidence that the important number of effective carriers is determined not by the total density, but by how far away they gate the system from half-filling.
  • At the Mott/superconducting border, they see what looks like Josephson-junction response, as if the system breaks up into superconducting regions separated by weak links.  
  • The ratio of superconducting Tc to the Fermi temperature is about 0.5, which makes this about as strongly coupled (and therefore likely to be some weird unconventional superconductor) as you ever see.
  • Pablo makes the point that this could be very general - for any combo of van der Waals layered materials, there are likely to be magic angles.  Increasing the interlayer coupling increases the magic angle, and could then increase the transition temperature.
Comments by me:
  • This is very exciting, and has great potential.  Really nice work.
  • I wonder what would happen if they used graphite as a gate material rather than a metal layer, given what I wrote here.   It should knock the disorder effects down a lot, and given how flat the bands are, that could really improve things.
  • There are still plenty of unanswered questions.  Why does the superconducting state seem more robust on the hole side of charge neutrality as well as on the hole side of half-filling?  This system is effectively a triangular lattice - that's a very different beast than the square lattice of the cuprates or the pnictides.  That has to matter somehow.  Twisting other 2d materials (square lattice MXenes?) could be very interesting.
  • I predict there will be dozens of theory papers in the next two months trying to predict magic twist angles for a whole zoo of systems.

APS March Meeting 2018, day 2

Day 2 of the meeting was even more scattered than usual for me, because several of my students were giving talks, all in different sessions spread around.  That meant I didn't have a chance to stay too long on any one topic.   A few highlights:

Jeff Urban from LBL gave an interesting talk about different aspects of the connection between electronic transport and thermal transport.  The Wiedemann-Franz relationship is a remarkably general expression based on a simple idea - when charge carriers move, they transport some (thermal) energy as well as charge, so thermal conductivity and electrical conductivity should be proportional to each other.  There are a bunch of assumptions that go into the serious derivation, though, and you could imagine scenarios when you'd expect large deviations from W-F response, particularly if scattering rates of carriers have some complicated energy dependence.  Urban spoke about hybrid materials (e.g., mixtures of inorganic components and conducting polymers).  He then pointed out a paper I'd somehow missed last year about apparent W-F violation in the metallic state of vanadium dioxide.  VO2 is a "bad metal", with an anomalously low electrical conductivity.  Makes me wonder how W-F fairs in other badly metallic systems.

Ali Hussain of the Abbamonte group at Illinois gave a nice talk about (charge) density fluctuations in the strange metal phase (and through the superconducting transition) of the copper oxide superconductor BSSCO.  The paper is here.  They use a particular technique (momentum-resolved electron energy loss spectroscopy) and find that it is peculiarly easy to create particle-hole excitations over a certain low energy range in the material, almost regardless of the momentum of those excitations.  There are also systematics with how this works as a function of doping (carrier concentration in the material), with optimally doped material having particularly temperature-independent response. 

Albert Fert spoke about spin-Hall physics, and the conversion of spin currents in to charge currents and vice versa.  One approach is the inverse Edelstein effect (IEE).  You have a stack of materials, where a ferromagnetic layer is on the top.  Driving ferromagnetic layer into FMR, you can pump a spin current vertically downward (say) into the stack.  Then, because of Rashba spin-orbit coupling, that vertical spin current can drive a lateral charge current (leading to the buildup of a lateral voltage) in a two-dimensional electron gas living at an interface in the stack.  One can use the interface between Bi and Ag (see here).  One can get better results if there is some insulating spacer to keep free conduction electrons not at the interface from interfering, as in LAO/STO structures.  Neat stuff, and it helped clarify for me the differences between the inverse spin Hall effect (3d charge current from 3d spin current) and the IEE (2d charge current from 3d spin current). 

Alexander Govorov of Ohio also gave a nice presentation about the generation of "hot" electrons from excitation of plasmons.  Non-thermally distributed electrons and holes can be extremely useful for a variety of processes (energy harvesting, photocatalysis, etc.). At issue is, what does the electronic distribution really look like.  Relevant papers are here and here.  There was a nice short talk similar in spirit by Yonatan Dubi earlier in the day.