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?