|Eric Heller's art piece "Dendrite", based|
on visualization of branching current flow.
Often we are interested in understanding how charge flows through some material or device. The simplest picture taught in courses is an analogy with water flowing through a pipe. The idea is that there is some input for current, some output for current, and that in the material or device, you can think of charge moving like a fluid flowing uniformly along. Of course, you could imagine a more complicated situation - perhaps the material or device doesn't have uniform properties; in the analogy, maybe there are obstacles that block or redirect the fluid flow. Prof. Eric Heller of Harvard is someone who has thought hard about this situation, and how to visualize it. (He's also a talented artist, and the image at right is an example of artwork based on exactly this issue - how the flow of electrons in a solid can branch and split because of disorder in the material.)
There's a different analogy that might be more useful in thinking about how people actually map out the flow of current in real systems, though. Suppose you wanted to map out the roads in a city. These days, one option would be to track all GPS devices (especially mobile phones) moving faster than, say, a few km/h. If you did that you would pretty quickly resolve a decent map of the streets of a city, and you'd find where the traffic is flowing in high volume and at what speed. Unfortunately, with electronic materials and devices, we generally don't have the option of tracking each individual mobile electron.
Some condensed matter experimentalists (like Bob Westervelt, for example) have developed a strategy, however. Here's the traffic analogy: You would set up traffic cameras to monitor the flow of cars into and out of the city. Then you would set up road construction barrels (lanes blocked off, road closures) in known locations in the city, and see how that affected the traffic flow in and out of town. By systematically recording the in/out traffic flow as a function of where you put in road closures, you could develop a rough map of the important routes. If you temporarily close a road that hardly carries any cars, there won't be any effect on the net traffice, but if you close a major highway, you'd see a big effect.
The experimental technique is called scanning gate microscopy. Rather than setting up traffic cones, the experimentalists take a nanoscale-sharp conductive tip and scan it across the sample in question, mapping the sample's end-to-end conduction as a function of where the tip is and what it's doing. One approach is to set the tip at a negative potential relative to the sample, which would tend to repel nearby electrons just from the usual like-charges-repel Coulomb interaction. If there is no current flowing near the tip, this doesn't do much of anything. If the tip is right on top of a major current path, though, this can strongly affect the end-to-end conduction. It's a neat idea, and it can produce some impressive and informative images. I'll write further about another technique for current mapping soon.