What is a crystal?

(I'm bringing this up because I want to write about "time crystals", and to do that....)

A crystal is a larger whole comprising a spatially periodic arrangement of identical building blocks.   The set of points that delineates the locations of those building blocks is called the lattice, and the minimal building block is called a basis.  In something like table salt, the lattice is cubic, and the basis is a sodium ion and a chloride ion.  This much you can find in a few seconds on wikipedia.  You can also have molecular crystals, where the building blocks are individual covalently bonded molecules, and the molecules are bound to each other via van der Waals forces.   Recently there has been a ton of excitement about graphene, transition metal dichalcogenides, and other van der Waals layered materials, where a 3d crystal is built up out of 2d covalently bonded crystals stacked periodically in the vertical direction.

The key physics points:   When placed together under the right conditions, the building blocks of a crystal spontaneously join together and assemble into the crystal structure.  While space has the same properties in every location ("invariance under continuous translation") and in every orientation ("invariance under continuous orientation"), the crystal environment doesn't.  Instead, the crystal has discrete translational symmetry (each lattice site is equivalent), and other discrete symmetries (e.g., mirror symmetry about some planes, or discrete rotational symmetries around some axes).   This kind of spontaneous symmetry breaking is so general that it happens in all kinds of systems, like plastic balls floating on reservoirs.  The spatial periodicity has all kinds of consequences, like band structure and phonon dispersion relations (how lattice vibration frequencies depend on vibration wavelengths and directions).

A book recommendation

I've been very busy lately, hence a slow down in posting, but in the meantime I wanted to recommend a book.  The Pope of Physics is the recent biography of Enrico Fermi from  Gino Segrè and Bettina Hoerlin.  The title is from Fermi's nickname as a young physicist in Italy - he and his colleagues (the "Via Panisperna boys", named for the address of the Institute of Physics in Rome) took to giving each other nicknames, and Fermi's was "the Pope" because of his apparent infallibility.  The book is compelling, gives insights into Fermi and his relationships, and includes stories about that wild era of physics that I didn't recall hearing before.   (For example, when trying to build the first critical nuclear pile at Stag Field in Chicago, there was a big contract dispute with Stone and Webster, the firm hired by the National Defense Research Council to do the job.  When it looked like the dispute was really going to slow things down, Fermi suggested that the physicists themselves just build the thing, and the put it together from something like 20000 graphite blocks in about two weeks.)

While it's not necessarily as page-turning as The Making of the Atomic Bomb, it's a very interesting biography that offers insights into this brilliant yet emotionally reserved person.  It's a great addition to the bookshelf.  For reference, other biographies that I suggest are True Genius:  The Life and Science of John Bardeen, and the more technical works No Time to be Brief:  A Scientific Biography of Wolfgang Pauli and Subtle is the Lord:  The Science and Life of Albert Einstein.

What is the difference between science and engineering?

In my colleague Rebecca Richards-Kortum's great talk at Rice's CUWiP meeting this past weekend, she spoke about her undergrad degree in physics at Nebraska, her doctorate in medical physics from MIT, and how she ended up doing bioengineering.  As a former undergrad engineer who went the other direction, I think her story did a good job of illustrating the distinctions between science and engineering, and the common thread of problem-solving that connects them.

In brief, science is about figuring out the ground rules about how the universe works.   Engineering is about taking those rules, and then figuring out how to accomplish some particular task.   Both of these involve puzzle-like problem-solving.  As a physics example on the experimental side, you might want to understand how electrons lose energy to vibrations in a material, but you only have a very limited set of tools at your disposal - say voltage sources, resistors, amplifiers, maybe a laser and a microscope and a spectrometer, etc.  Somehow you have to formulate a strategy using just those tools.  On the theory side, you might want to figure out whether some arrangement of atoms in a crystal results in a lowest-energy electronic state that is magnetic, but you only have some particular set of calculational tools - you can't actually solve the complete problem and instead have to figure out what approximations would be reasonable, keeping the essentials and neglecting the extraneous bits of physics that aren't germane to the question.

Engineering is the same sort of process, but goal-directed toward an application rather than specifically the acquisition of new knowledge.  You are trying to solve a problem, like constructing a machine that functions like a CPAP, but has to be cheap and incredibly reliable, and because of the price constraint you have to use largely off-the-shelf components.  (Here's how it's done.)

People act sometimes like there is a vast gulf between scientists and engineers - like the former don't have common sense or real-world perspective, or like the latter are somehow less mathematical or sophisticated.  Those stereotypes even comes through in pop culture, but the differences are much less stark than that.  Both science and engineering involve creativity and problem-solving under constraints.   Often which one is for you depends on what you find most interesting at a given time - there are plenty of scientists who go into engineering, and engineers can pursue and acquire basic knowledge along the way.  Particularly in the modern, interdisciplinary world, the distinction is less important than ever before.

Brief items

What with the start of the semester and the thick of graduate admissions season, it's been a busy week, so rather than an extensive post, here are some brief items of interest:

• We are hosting one of the APS Conferences for Undergraduate Women in Physics this weekend.  Welcome, attendees!  It's going to be a good time.
• This week our colloquium speaker was Jim Kakalios of the University of Minnesota, who gave a very fun talk related to his book The Physics of Superheroes (an updated version of this), as well as a condensed matter seminar regarding his work on charge transport and thermoelectricity in amorphous and nanocrystalline semiconductors.  His efforts at popularizing physics, including condensed matter, are great.  His other books are The Amazing Story of Quantum Mechanics, and the forthcoming The Physics of Everyday Things.  That last one shows how an enormous amount of interesting physics is embedded and subsumed in the routine tasks of modern life - a point I've mentioned before.   
• Another seminar speaker at Rice this week was John Biggins, who explained the chain fountain (original video here, explanatory video here, relevant paper here).
• Speaking of videos, here is the talk I gave last April back at the Pittsburgh Quantum Institute's 2016 symposium, and here is the link to all the talks.
• Speaking of quantum mechanics, here is an article in the NY Review of Books by Steven Weinberg on interpretations of quantum.  While I've seen it criticized online as offering nothing new, I found it to be clearly written and articulated, and that can't always be said for articles about interpretations of quantum mechanics.
• Speaking of both quantum mechanics interpretations and popular writings about physics, here is John Cramer's review of David Mermin's recent collection of essays, Why Quark Rhymes with Pork:  And other Scientific Diversions (spoiler:  I agree with Cramer that Mermin is wrong on the pronunciation of "quark".)  The review is rather harsh regarding quantum interpretation, though perhaps that isn't surprising given that Cramer has his own view on this.

Physics is not just high energy and astro/cosmology.

A belated happy new year to my readers.  Back in 2005, nearly every popularizer of physics on the web, television, and bookshelves was either a high energy physicist (mostly theorists) or someone involved in astrophysics/cosmology.  Often these people were presented, either deliberately or through brevity, as representing the whole discipline of physics.  Things have improved somewhat, but the overall situation in the media today is not that different, as exemplified by the headline of this article, and noticed by others (see the fourth paragraph here, at the excellent blog by Ross McKenzie).

For example, consider Edge.org, which has an annual question that they put to "the most complex and sophisticated minds".   This year the question was, what scientific term or concept should be more widely known?  It's a very interesting piece, and I encourage you to read it.  They got responses from 206 contributors (!).   By my estimate, about 31 of those would likely say that they are active practicing physicists, though definitions get tricky for people working on "complexity" and computation.  Again, by my rough count, from that list I see 12-14 high energy theorists (depending on whether you count Yuri Milner, who is really a financier, or Gino Segre, who is an excellent author but no longer an active researcher) including Sabine Hossenfelder, one high energy experimentalist, 10 people working on astrophysics/cosmology, four working on some flavor of quantum mechanics/quantum information (including the blogging Scott Aronson), one on biophysics/complexity, and at most two on condensed matter physics.   Seems to me like representation here is a bit skewed.  

Hopefully we will keep making progress on conveying that high energy/cosmology is not representative of the entire discipline of physics....

Some optimism at the end of 2016

When the news is filled with bleak items, like:

• The deaths of prominent scientists 
• The deaths of many notable figures (too many to link in entirety)
• Disturbing news about the environment, and news about news about the environment

it's easy to become pessimistic.   Bear in mind that modern communications plus the tendency for bad news to get attention plus the size of the population can really distort perception.  To put that another way, 56 million people die every year (!), but now you are able to hear about far more of them than ever before.  

Let me make a push for optimism, or at least try to put some things in perspective.  There are some reasons to be hopeful.  Specifically, look here, at a site called "Our World in Data", produced at Oxford University.  These folks use actual numbers to point out that this is actually, in many ways, the best time in human history to be alive:

• The percentage of the world's population living in extreme poverty is at an all-time low (9.6%).
• The percentage of the population that is literate is at an all-time high (85%), as is the overall global education level.
• Child mortality is at an all-time low.
• The percentage of people enjoying at least some political freedom is at an all-time high.

That may not be much comfort to, say, an unemployed coal miner in West Virginia, or an underemployed former factory worker in Missouri, but it's better than the alternative.   We face many challenges, and nothing is going to be easy or simple, but collectively we can do amazing things, like put more computing power in your hand than existed in all of human history before 1950, set up a world-spanning communications network, feed 7B people, detect colliding black holes billions of lightyears away by their ripples in spacetime, etc.  As long as we don't do really stupid things, like make nuclear threats over twitter based on idiots on the internet, we will get through this.   It may not seem like it all the time, but compared to the past we live in an age of wonders.

Mapping current at the nanoscale - part 2 - magnetic fields!

A few weeks ago I posted about one approach to mapping out where current flows at the nanoscale, scanning gate microscopy.   I had made an analogy between current flow in some system and traffic flow in a complicated city map.  Scanning gate microscopy would be analogous recording the flow of traffic in/out of a city as a function of where you chose to put construction barrels and lane closures.  If sampled finely enough, this would give you a sense of where in the city most of the traffic tends to flow.

Of course, that's not how utilities like Google Maps figure out traffic flow maps or road closures.  Instead, applications like that track the GPS signals of cell phones carried in the vehicles.  Is there a current-mapping analogy here as well?  Yes.  There is some "signal" produced by the flow of current, if only you can have a sufficiently sensitive detector to find it.  That is the magnetic field.  Flowing current density \(\mathbf{J}\) produces a local magnetic field \(\mathbf{B}\), thanks to Ampere's law, \(\nabla \times \mathbf{B} = \mu_{0} \mathbf{J}\).

Scanning SQUID microscope image of x-current density 

in a GaSb/InAs structure, showing that the current is 

carried by the edges.  Scale bar is 20 microns.  Image 

from Spanton et al., PRL 113, 026804 (2014).

Fortunately, there now exist several different technologies for performing very local mapping of magnetic fields, and therefore the underlying pattern of flowing current in some material or device.  One older, established approach is scanning Hall microscopy, where a small piece of semiconductor is placed on a scanning tip, and the Hall effect in that semiconductor is used to sense local \(B\) field.

Scanning NV center microscopy to see magnetic fields,

from Pelliccione et al., Nature Nano. 11, 700-705 (2016).

Scale bars are 400 nm.

Considerably more sensitive is the scanning SQUID microscope, where a tiny superconducting loop is placed on the end of a scanning tip, and used to detect incredibly small magnetic fields.  Shown in the figure, it is possible to see when current is carried by the edges of a structure rather than by the bulk of the material, for example.

A very recently developed method is to use the exquisite magnetic field sensitive optical properties of particular defects in diamond, NV centers.  The second figure (from here) shows examples of the kinds of images that are possible with this approach, looking at the magnetic pattern of data on a hard drive, or magnetic flux trapped in a superconductor.  While I have not seen this technique applied directly to current mapping at the nanoscale, it certainly has the needed magnetic field sensitivity.  Bottom line:  It is possible to "look" at the current distribution in small structures at very small scales by measuring magnetic fields.

Recurring themes in (condensed matter/nano) physics: Exponential decay laws

It's been a little while (ok, 1.6 years) since I made a few posts about recurring motifs that crop up in physics, particularly in condensed matter and at the nanoscale.  Often the reason certain mathematical relationships crop up repeatedly in physics is that they are, deep down, based on underlying assumptions that are very simple.  One example common in all of physics is the idea of exponential decay, that some physical property or parameter often ends up having a time dependence proportional to \(\exp(-t/\tau)\), where \(\tau\) is some characteristic timescale.

Buffalo Bayou cistern.  (photo by Katya Horner).

Why is this time dependence so common?  Let's take a particular example.  Suppose we are in the remarkable cistern, shown here, that used to store water for the city of Houston.   If you go on a tour there (I highly recommend it - it's very impressive.), you will observe that it has remarkable acoustic properties.  If you yell or clap, the echo gradually dies out by (approximately) exponential decay, fading to undetectable levels after about 18 seconds (!).  The cistern is about 100 m across, and the speed of sound is around 340 m/s, meaning that in 18 seconds the sound you made has bounced off the walls around 61 times.  Each time the sound bounces off a wall, it loses some percentage of its intensity (stored acoustic energy).

That idea, that the decrease in some quantity is a fixed fraction of the current size of that quantity, is the key to the exponential decay, in the limit that you consider the change in the quantity from instant to instant (rather than taking place via discrete events).    Note that this is also basically the same math that is behind compound interest, though that involves exponential growth.

Bismuth superconducts, and that's weird

Many elemental metals become superconductors at sufficiently low temperatures, but not all.  Ironically, some of the normal metal elements with the best electrical conductivity (gold, silver, copper) do not appear to do so.  Conventional superconductivity was explained by Bardeen, Cooper, and Schrieffer in 1957.  Oversimplifying, the idea is that electrons can interact with lattice vibrations (phonons), in such a way that there is a slight attractive interaction between the electrons.  Imagine a billiard ball rolling on a foam mattress - the ball leaves trailing behind it a deformation of the mattress that takes some finite time to rebound, and another nearby ball is "attracted" to the deformation left behind.  This slight attraction is enough to cause pairing between charge carriers in the metal, and those pairs can then "condense" into a macroscopic quantum state with the superconducting properties we know.  The coinage metals apparently have comparatively weak electron-phonon coupling, and can't quite get enough attractive interaction to go superconducting.

Another way you could fail to get conventional BCS superconductivity would be just to have too few charge carriers!  In my ball-on-mattress analogy, if the rolling balls are very dilute, then pair formation doesn't really happen, because by the time the next ball rolls by where a previous ball had passed, the deformation is long since healed.  This is one reason why superconductivity usually doesn't happen in doped semiconductors.

Superconductivity with really dilute carriers is weird, and that's why the result published recently here by researchers at the Tata Institute is exciting.  They were working bismuth, which is a semimetal in its usual crystal structure, meaning that it has both electrons and holes running around (see here for technical detail), and has a very low concentration of charge carriers, something like 10¹⁷/cm³, meaning that the typical distance between carriers is on the order of 30 nm.  That's very far, so conventional BCS superconductivity isn't likely to work here.  However, at about 500 microKelvin (!), the experimenters see (via magnetic susceptibility and the Meissner effect) that single crystals of Bi go superconducting.   Very neat.  

They achieve these temperatures through a combination of a dilution refrigerator (possible because of the physics discussed here) and nuclear demagnetization cooling of copper, which is attached to a silver heatlink that contains the Bi crystals.   This is old-school ultralow temperature physics, where they end up with several kg of copper getting as low as 100 microKelvin.    Sure, this particular result is very far from any practical application, but the point is that this work shows that there likely is some other pairing mechanism that can give superconductivity with very dilute carriers, and that could be important down the line.

Suggested textbooks for "Modern Physics"?

I'd be curious for opinions out there regarding available textbooks for "Modern Physics".  Typically this is a sophomore-level undergraduate course at places that offer such a class.  Often these tend to focus on special relativity and "baby quantum", making the bulk of "modern" end in approximately 1930.   Ideally it would be great to have a book that includes topics from the latter half of the 20th century, too, without having them be too simplistic.  Looking around on amazon, there are a number of choices, but I wonder if I'm missing some diamond in the rough out there by not necessarily using the right search terms, or perhaps there is a new book in development of which I am unaware.   The book by Rohlf looks interesting, but the price tag is shocking - a trait shared by many similarly titled works on amazon.  Any suggestions?

Quantum computing - lay of the land, + corporate sponsorship

Much has been written about quantum computers and their prospects for doing remarkable things (see here for one example of a great primer), and Scott Aronson's blog is an incredible resource if you want more technical discussions.   Recent high profile news this week about Microsoft investing heavily in one particular approach to quantum computation has been a good prompt to revisit parts of this subject, both to summarize the science and to think a bit about corporate funding of research.  It's good to see how far things have come since I wrote this almost ten years ago (!!).

Remember, to realize the benefits of general quantum computation, you need (without quibbling over the details) some good-sized set  (say 1000-10000) of quantum degrees of freedom, qubits, that you can initialize, entangle to create superpositions, and manipulate in deliberate ways to perform computational operations.  On the one hand, you need to be able to couple the qubits to the outside world, both to do operations and to read out their state.  On the other hand, you need the qubits to be isolated from the outside world, because when a quantum system becomes entangled with (many) environmental degrees of freedom whose quantum states you aren't tracking, you generally get decoherence - what is known colloquially as the collapse of the wavefunction.  

The rival candidates for general purpose quantum computing platforms make different tradeoffs in terms of robustness of qubit coherence and scalability.  There are error correction schemes, and implementations that combine several "physical" qubits into a single "logical" qubit that is supposed to be harder to screw up.  Trapped ions can have very long coherence times and be manipulated with great precision via optics, but scaling up to hundreds of qubits is very difficult (though see here for a claim of a breakthrough).  Photons can be used for quantum computing, but since they fundamentally don't interact with each other under ordinary conditions, some operations are difficult, and scaling is really hard - to quote from that link, "About 100 billion optical components would be needed to create a practical quantum computer that uses light to process information."   Electrons in semiconductor quantum dots might be more readily scaled, but coherence is fleeting.   Superconducting approaches are the choices of the Yale and UC Santa Barbara groups.

The Microsoft approach, since they started funding quantum computing research, has always been rooted in ideas about topology, perhaps unsurprising since their effort has been led by Michael Freedman.  If you can encode quantum information in something to do with topology, perhaps the qubits can be more robust to decoherence.  One way to get topology in the mix is to work with particular exotic quantum excitations in 2d that are non-Abelian.  That is, if you take two such excitations and move them around each other in real space, the quantum state somehow transforms itself to remember that braiding, including whether you moved particle 2 around particle 1, or vice versa.  Originally Microsoft was very interested in the \(\nu = 5/2\) fractional quantum Hall state as an example of a system supporting this kind of topological braiding.  Now, they've decided to bankroll the groups of Leo Kouwenhoven and Charlie Marcus, who are trying to implement topological quantum computing ideas using superconductor/semiconductor hybrid structures thought to exhibit Majorana fermions.

It's worth noting that Microsoft are not the only people investing serious money in quantum computing.   Google invested enormously in John Martinis' effort.  Intel has put a decent amount of money into a silicon quantum dot effort practically down the hall from Kouwenhoven.  This kind of industrial investment does raise some eyebrows, but as long as it doesn't kill publication or hamstring students and postdocs with weird constraints, it's hard to see big downsides.  (Of course, Uber and Carnegie Mellon are a cautionary example of how this sort of relationship may not work out well for the relevant universities.)

More short items, incl. postdoc opportunities

Some additional brief items:

• Rice's Smalley-Curl Institute has two competitive, endowed postdoctoral opportunities coming up, the J. Evans Attwell Welch Postdoctoral Fellowship, and the Peter M. and Ruth L. Nicholas Postdoctoral Fellowship in Nanotechnology.  The competition is fierce, but they're great awards and come with separate travel funds and research supplies resources.  Applying requires working with a Rice faculty sponsor, and the deadline for applications is June 30, 2017, with a would-be start date around the beginning of September, 2017.
• This may be completely academic, but my colleagues at Rice's Baker Institute, including former NSF director and Presidential science adviser Neal Lane, have prepared a report with recommendations to the next science adviser regarding the Office of Science and Technology Policy and how to integrate science into policy making.  Yeah.  Sigh.
• Check out Funsize Physics!  It's a repository of education and broader outreach products from NSF investigators, started by Shireen Adenwalla and Jocelyn Bosely, related to their NSF MRSEC.
• Anyone have strong opinions about Academic Analytics?  The main questions are whether the quality control on the information is good, and whether the information can actually be useful.

short items

A handful of brief items:

• A biologist former colleague has some good advice on writing successful NSF proposals that translates well to other disciplines and agencies.
• An astronomy colleague has a nice page on the actual science behind the much-hyped supermoon business.
• Lately I've found myself recalling a book that I read as part of an undergraduate philosophy of science course twenty-five years ago, The Dilemmas of an Upright Man.  It's the story of Max Planck and the compromises and choices he made while trying to preserve German science through two world wars.  As the Nazis rose to power and began their pressuring of government scientific institutions such as the Berlin Academy and the Kaiser Wilhelm Institutes, Planck decided to remain in leadership roles and generally not speak out publicly, in part because he felt like if he abrogated his position there would only be awful people left behind like ardent Nazi Johannes Stark.   These decisions may have preserved German science, but they broke his relationship with Einstein, who never spoke to Planck again from 1937 until Planck's death in 1947.  It's a good book and very much worth reading.

Lenses from metamaterials

As alluded to in my previous posts on metamaterials and metasurfaces, there have been some recently published papers that take these ideas and do impressive things.

• Khorasaninejad et al. have made a metasurface out of a 2d array of very particularly designed TiO₂ posts on a glass substrate.  The posts vary in size and shape, and are carefully positioned and oriented on the substrate so that, for light incident from behind the glass, normal to the glass surface, and centered on the middle of the array, the light is focused to a spot 200 microns above the array surface.  Each little TiO₂ post acts like a sub-wavelength scatterer and imparts a phase on the passing light, so that the whole array together acts like a converging lens.  This is very reminiscent of the phased array I'd mentioned previously.  For a given array, different colors focus to different depths (chromatic aberration).  Impressively, the arrays are designed so that there is no polarization dependence of the focusing properties for a given color.    
• Hu et al. have made a different kind of metasurface, using plasmonically active gold nanoparticles on a glass surface.  The remarkable achievement here is that the authors have used a genetic algorithm to find a pattern of nanoparticle shapes and sizes that somehow, through phased array magic, produces a metasurface that functions as an achromatic lens - different visible colors (red, green, blue) normally incident on the array focus to the same spot, albeit with a short focal length of a few microns. 
•  Finally, in more of a 3d metamaterial approach, Krueger et al. have leveraged their ability to create 3d designer structures of porous silicon.  The porous silicon frameworks have an effective index of refraction at the desired wavelength.  By controllably varying the porosity as a function of distance from the optical axis of the structure, these things can act as lenses.  Moreover, because of designed anisotropy in the framework, they can make different polarizations of incident light experience different effective refractive indices and therefore have different focal lengths.  Fabrication here is supposed to be considerably simpler than the complicated e-beam lithography needed to accomplish the same goal with 2d metasurfaces.

These are just papers published in the last couple of weeks!  Clearly this is a very active field.

What is a metasurface?

As I alluded in my previous post, metamaterials are made out of building blocks, and thanks to the properties of those building blocks and their spatial arrangement, the aggregate system has, on longer distance scales, emergent properties (e.g., optical, thermal, acoustic, elastic) that can be very different from the traits of the individual building blocks.  Classic examples are opal and butterfly wing, both of which are examples of structural coloration.  The building blocks (silica spheres in opal; chitin structures in butterfly wing) have certain optical properties, but by properly shaping and arranging them, the metamaterial comprising them has brilliant iridescent color very different from that of bulk slabs of the underlying material.

Controlling the relative phases between
antennas in an array lets you steer radiation.
By Davidjessop - Own work, CC BY-SA 4.0,
https://commons.wikimedia.org/
w/index.php?curid=48304978 

This works because of wave interference of light.  Light propagates more slowly in a dielectric (\(c/n(\omega)\), where \(n(\omega)\) is the frequency-dependent index of refraction).  Light propagating through some thickness of material will pick up a phase shift relative to light that propagates through empty space.  Moreover, additional phase shifts are picked up at interfaces between dielectrics.  If you can control the relative phases of light rays that arrive at a particular location, then you can set up constructive interference or destructive interference.

This is precisely the same math that gives you diffraction patterns.  You can also do this actively with radio transmitter antennas.  If you set up an antenna array and drive each antenna at the same frequency but with a controlled phase relative to its neighbors, you can tune where the waves constructively or destructively interfere.  This is the principle behind phased arrays.

An optical metasurface is an interface that has structures on it that impose particular phase shifts on light that either is transmitted through or reflected off the interface.  Like a metamaterial and for the same wave interference reasons, the optical properties of the interface on distance scales larger than those structures can be very different than those of the materials that constitute the structures.  Bear in mind, the individual structures don't have to be boring - each by itself could have complicated frequency response, like acting as a dielectric or plasmonic resonator.  We now have techniques that allow rich fabrication on surfaces with a variety of materials down to scales much smaller than the wavelength of visible light, and we have tremendous computational techniques that allow us to calculate the expected optical response from such structures.  Put these together, and those capabilities enable some pretty amazing optical tricks.  See here (pdf!) for a good slideshow covering this topic.

What is a metamaterial?

(This is part of a lead-in to a brief discussion I'd like to do of two papers that just came out.) The wikipedia entry for metamaterial is actually rather good, but doesn't really give the "big picture".  As you will hopefully see, that wording is a bit ironic.

"Ordinary" materials are built up out of atoms or molecules.  The electronic, optical, and mechanical properties of a solid or liquid come about from the properties of the individual constituents, and how those constituents are spatially arranged and coupled together into the whole.   On the length scale of the constituents (the size of atoms, say, in a piece of silicon), the local properties like electron density and local electric field vary enormously.  However,  on length scales large compared to the individual constituent atoms or molecules, it makes sense to think of the material as having some spatially-averaged "bulk" properties, like an index of refraction (describing how light propagates through the material), or a magnetic permeability (how the magnetic induction \(\mathbf{B}\) inside a material responds to an externally applied magnetic field \(\mathbf{H}\)), or an elastic modulus (how a material deforms in response to an applied stress).

A "metamaterial" takes this idea a step further.  A metamaterial is build up out of some constituent building blocks such as dielectric spheres or metallic rods.  The properties of an individual building block arise as above from their own constituent atoms, of course.  However, the properties of the metamaterial, on length scales long compared to the size of the building blocks, are emergent from the properties of those building blocks and how the building blocks are then arranged and coupled to each other.   The most common metamaterials are probably dielectric mirrors, which are a subset of photonic band gap systems.  You can take thin layers of nominally transparent dielectrics, stack them up in a periodic way, and end up with a mirror that is incredibly reflective at certain particular wavelengths - an emergent optical property that is not at all obvious at first glance from the properties of the constituent layers.

Depending on what property you're trying to engineer in the final metamaterial, you will need to structure the system on different length scales.  If you want to mess with optical properties, generally the right ballpark distance scale is around a quarter of the wavelength (within the building block constituent) of the light.  For microwaves, this can be the cm range; for visible light, its tens to hundreds of nm.  If you want to make an acoustic metamaterial, you need to make building blocks on a scale comparable to a fraction of the wavelength of the sound you want to manipulate.  Mechanical metamaterials, which have large-scale elastic properties far different than those of their individual building blocks, are trickier, and should be thought about as something more akin to a small truss or origami framework.  These differ from optical and acoustic metamaterials because the latter rely crucially on interference phenomena between waves to build up their optical or acoustic properties, while structural systems rely on local properties (e.g., bending at vertices).

Bottom line:  We now know a lot about how to build up larger structures from smaller building blocks, so that the resulting structures can have very different and interesting properties compared to those of the constituents themselves.

Rice has an opening for Dean of Engineering

Just in case anyone out there is interested, Rice is beginning a search for the next dean of our George R. Brown School of Engineering.

Measuring temperature at the milliKelvin scale

How do we tell the temperature of some piece of material?  I've written about temperature and thermometry a couple of times before (here, here, here).  For ordinary, every-day thermometry, we measure some physical property of a material or system where we have previously mapped out its response as a function of temperature.  For example, near room temperature liquid mercury expands slightly with increasing \(T\).  Confined in a thin glass tube, the length of a mercury column varies approximately linearly with changes in temperature, \(\delta \ell \sim \delta T\).  To do primary thermometry, we don't want to have some empirical calibration - rather, we want to measure some physical property for which we think we have a complete understanding of the underlying physics, so that \(T\) can be inferred directly from the measured quantity and our theoretical expressions, with no adjustable parameters.  This is particularly important at very low temperatures, thousandths of a Kelvin above absolute zero, where the number of things that we can measure is comparatively limited, and tiny flows of power (from our measurements, say) can actually produce large percentage temperature changes.

This recent paper shows a nice example of applying three different primary thermometry techniques to a single system, a puddle of electrons confined in 2d at a semiconductor interface, at about 6 mK.  This is all the more impressive because of how easy it is to inadvertently heat up electrons in such 2d layers.  All three techniques rely on our understanding of how electrons behave at low temperatures.  According to our theory of electrons in metals (which these 2d electrons are, as far as physicists are concerned), as a function of energy, electrons are spread out in a characteristic way, the Fermi-Dirac distribution.  From the theory side, we know this functional form exactly (figure from that wikipedia link).  At low temperatures, all of the electronic states below a highest-filled-state are full, and all above are empty.  As \(T\) is increased, the electrons smear out into higher energy states, as shown.  The three effects measured in the experiment all depend on \(T\) through this electronic distribution:

Fig. 2 from the paper, showing excellent, consistent agreement

between experiment and theory, showing electron temperatures 

of ~ 6 mK. 

• Current noise in a quantum point contact, the fluctuations in the average current.  For this particular device, where conduction takes place through a small, controllable number of quantum channels, we think we understand the situation completely.  There is a closed-form expression for what the noise should do as a function of average current, with temperature as the only adjustable parameter (once the conduction has been measured).
• "Coulomb blockade" in a quantum dot.  Conduction through a puddle of electrons connected to input and output electrodes by tunneling barriers ("pinched off" versions of the point contacts) shows a very particular form of current-voltage characteristic that is tunable by a nearby gate electrode.   The physics here is that, because of the mutual repulsion of electrons, it takes energy (supplied by either a voltage source or temperature) to get charge to flow through the puddle.  Again, once the conduction has been measured, there is a closed-form expression for what the conductance should do as a function of that gate voltage.
• "Environmental" Coulomb blockade in a quantum dot.  This is like the situation above, but with one of the tunnel barriers replaced by a controlled resistor.  Again, there is an expression for the particular shape of the \(I-V\) curve where the adjustable parameter is \(T\).  

As shown in the figure (Fig. 2 from the paper - open access and also available on the arxiv), the theoretical expressions do a great job of fitting the data, and give very consistent electron temperatures down to 0.006 K.  It's a very impressive piece of work, and I encourage you to read it - look at Fig. 4 if you're interested in how challenging it is to cool electrons in these kinds of devices down to this level.

What do LBL's 1 nm transistors mean?

In the spirit of this post, it seems like it would be a good idea to write something about this paper (accompanying LBL press release), particularly when popular sites are going a bit overboard with their headlines ("The world's smallest transistor is 1nm long, physics be damned").  (I discuss most of the background in my book, if you're interested.)

What is a (field effect) transistor and how does it work?  A transistor is an electronic switch, the essential building block of modern digital electronics.  A field-effect transistor (FET) has three terminals - a "source" (an input), a "drain" (an output) on either side of a semiconductor "channel", and a "gate" (a control knob).  If you think of electrical current like fluid flow, this is like a pipe with an inlet, and outlet, and a valve in the middle, and the gate controls the valve.  In a "depletion mode" FET, the gate electrode repels away charges in the channel to turn off current between the source and drain.  In an "accumulation mode" FET, the gate attracts mobile charges into the channel to turn on current between the source and drain.   Bottom line:  the gate uses the electrostatic interaction with charges to control current in the channel.  There has to be a thin insulating layer between the gate and the channel to keep current from "leaking" from the gate.   People have had to get very clever in their geometric designs to maximize the influence of the gate on the charges in the channel.

What's the big deal about making smaller transistors?  We've gotten where we are by cramming more devices on a chip at an absurdly increasing rate, by making transistors smaller and smaller.  One key length scale is the separation between source and drain electrode.  If that separation is too small, there are at least two issues:  Current can leak from source to drain even when the device is supposed to be off because the charge can tunnel; and because of the way electric fields actually work, it is increasingly difficult to come up with a geometry where the gate electrode can efficiently (that is, with a small swing in voltage, to minimize power) turn the FET off and on.

What did the LBL team do?  The investigators built a very technically impressive device, using atomically thin MoS₂ as the semiconductor layer, source and drain electrodes separated by only seven nm or so, a ZrO₂ dielectric layer only a couple of nm thick, and using an individual metallic carbon nanotube (about 1 nm in diameter) as the gate electrode.  The resulting device functions quite well as a transistor, which is pretty damn cool, considering the constraints involved.   This fabrication is a tour de force piece of work.

Does this device really defy physics in some way, as implied by the headline on that news article?  No.  That headline alludes to the issue of direct tunneling between source and drain, and a sense that this is expected to be a problem in silicon devices below the 5 nm node (where that number is not the actual physical length of the channel).   This device acts as expected by physics - indeed, the authors simulate the performance and the results agree very nicely with experiment.

If you read the actual LBL press release, you'll see that the authors are very careful to point out that this is a proof-of-concept device.  It is exceedingly unlikely (in my opinion, completely not going to happen) that we will have chips with billions of MoS₂ transistors with nanotube gates - the Si industry is incredibly conservative about adopting new materials.  If I had to bet, I'd say it's going to be Si and Si/Ge all the way down.   (You will very likely need to go away from Si if you want to see this kind of performance at such length scales, though.)   Still, this work does show that with proper fabrication and electrostatic design, you can make some really tiny transistors that work very well!

This year's Nobel in physics - Thouless, Kosterlitz, Haldane

Update:  well, I was completely wrong!  Topology ruled the day.  I will write more later about this, but Congratulations to Thouless, Kosterlitz, and Haldane!

Real life is making this week very busy, so it will be hard for me to write much in a timely way about this, and the brief popular version by the Nobel Foundation is pretty good if you're looking for an accessible intro to the work that led to this.  Their more technical background document (clearly written in LaTeX) is also nice if you want greater mathematical sophistication.

Here is the super short version.  Thouless, Kosterlitz, and Haldane had major roles to play in showing the importance of topology in understanding some key model problems in condensed matter physics.

Kosterlitz and Thouless (and independently Berezinskii) were looking at the problem of phase transitions in two dimensions of a certain type.  As an example, imagine a huge 2d array of compass needles, each free to rotate in the plane, but interacting with their neighbors, so that neighbors tend to want to point the same direction.  In the low temperature limit, the whole array will be ordered (pointing all the same way).  In the very high temperature limit, when thermal energy is big compared to the interaction between needles, the whole array will be disordered, with needles at any moment randomly oriented.  The question is, as temperature is increased, how does the system get from ordered to disordered?  Is it just a gradual thing, or does it happen suddenly in a particular way?  It turns out that the right way to think about this problem is in terms of vorticity, a concept that comes up in fluid mechanics as well (see this wiki page with mesmerizing animations).  It's energetically expensive to flip individual needles - better to rotate needles gradually relative to their neighbors.  The symmetry of the system says that you can't spontaneously create a pattern to the needles that has some net swirliness ("winding number", if you like).  However, it's relatively energetically cheap to create pairs of vortices with opposite handedness (vortex/antivortex pairs).  Kosterlitz, Thouless, and Berezinskii showed that these V/AV pairs "unbind" collectively at some finite temperature in a characteristic way, with testable consequences.  This leads to a particular kind of phase transition in a bunch of different 2d systems that, deep down, are mathematically similar.  2d xy magnetism and superconductivity in 2d are examples.  This generality is very cool - the microscopic details of the systems may be different, but the underlying math is the same, and leads to testable quantitative predictions.

Thouless also realized that topological ideas are critically important in 2d electronic systems in large magnetic fields, and this work led to understanding of the quantum Hall effect.  Here is a nice Physics Today article on this topic.   (Added bonus:  Thouless also did groundbreaking work in the theory of localization, what happens to electrons in disordered systems and how it depends on the disorder and the temperature.)

Haldane, another brilliant person who is still very active, made a big impact on the topology front studying another "model" system, so-called spin chains - 1d arrangements of quantum mechanical spins that interact with each other.  This isn't just a toy model - there are real materials with magnetic properties that are well described by spin chain models.  Again, the questions were, can we understand the lowest energy states of such a system, and how those ordered states go away as temperature is increased.  He found that it really mattered in a very fundamental way whether the spins were integer or half-integer, and that the end points of the chains reveal important topological information about the system.  Haldane has long contributed important insights in quantum Hall physics as well, and in all kinds of weird states of matter that result in systems where topology is critically important.  (Another added bonus:  Haldane also did very impactful work on the Kondo problem, how a single local spin interacts with conduction electrons.)

Given how important topological ideas are to physics these days, it is not surprising that these three have been recognized.   In a sense, this work is a big part of the foundation on which the topological insulators and other such systems are built.


Original post:  The announcement this morning of the Nobel in Medicine took me by surprise - I guess I'd assumed the announcements were next week.  I don't have much to say this year; like many people in my field I assume that the prize will go to the LIGO gravitational wave discovery, most likely to Rainer Weiss, Kip Thorne, and Ronald Drever (though Drever is reportedly gravely ill).    I guess we'll find out tomorrow morning!