Growing up in Ohio, and working as a postdoc in Kansas, I got used to the possibility of having an unplanned University holiday called a snow day. Having moved to Florida, I expected the frequency of snow days to be sharply curtailed. However, today we, along with the Republican National Convention, are “enjoying” an day off thanks to Tropical Storm/Hurricane Isaac.
Speaking of absences, I thought I’d talk about at article in Nature that caught my attention last week. It highlights some of the weirdness of quantum mechanics, and shows how metaphors in science can end up becoming surprisingly real. In short, researchers in the article were able to construct a layered system of two conductive planes separated by an insulating layer so thin that it was comparable to the spacing between electrons in the conducting layers. If a current is driven in one of the conductive layers, electrons flowing near the barrier would would “drag” holes in the other layer.
Holes are are places were electrons could be, but aren’t, as explained below. The attraction between the negatively charged electron and the positively charged hole creates an bound state called an “exciton.” An exciton acts like an atom, in which electrons orbit a positively charged nucleus, but in this case, the electron and hole are in different materials. The surprising part is that, under certain circumstances, the induced “drag” current MUST be exactly equal and opposite to the driving current. This is a quantum mechanical effect, and has surprising implications.
When I was a graduate student at Ohio State, we studied conductive polymers, which, unlike virtually all organic materials, are conductors of electricity. We spoke a lot about excitons, since these were a very important feature in the story of how charge gets transported across the polymer molecules. And “charge transport” is exactly what electrical current is. The amazing thing is that this charge could either be an electron, or, just as easily, a hole, which is really nothing at all! The best way to understand the concept of a hole is to think of a crowded movie theater, where every seat is filled, except for one. If a person wants to shift seats, he or she has to be adjacent to the empty seat. If you watch from the projector room above, you can describe this situation as people moving, but it might be easier to keep track of the empty seat as it “moves” around. This is also like the “15 puzzle” games where only the tiles next to the empty space can move.
Physicists use a similar idea when talking about electrons, or the absence thereof. In materials, there are states available for the electrons to exist in, called orbitals. The famous Pauli exclusion principle dictates that two electrons cannot exist in exactly the same quantum state. This is what keeps all matter from instantly collapsing when all the electrons try to “fall” to the lowest energy orbital. The lowest energy state for this system occurs when the electrons fill the lowest energy levels first, and then higher levels, and so on, until all the electrons have a spot. Sometimes this is called the “Fermi sea,” since all the orbitals below a certain energy are filled, and all the orbitals above are empty. If energy is added, for example, by shining light on the material, a photon can strike one of the electrons and cause it to be “excited” to a higher energy orbital. This leaves an absence, an orbital that could be filled, but isn’t, in the material. When working out the equations that describe the material, it turns out that this “hole” can be treated just like an positively charged “antielectron.” That it, if the electron “falls” back and fills the hole, both are “annihilated,” and energy is released in the form of another photon. In fact, this is a useful way to think about what happens when matter meets actual antimatter – both are annihilated in a flash of energy.
While it might seem that the concept of a hole is just a cute metaphor by scientists who noticed a similarity in the equations, it turns out that holes are much more “real” than that. As indicated before, electric current is the movement of charges. Normally, as in the metal wires that bring electricity to your house, the charges are moving electrons. But in some materials, like many conducting polymers, it is more likely that the moving charges are holes! Yet the electrical current is just as real. You might say that in this case, the holes aren’t really moving, it’s the electrons moving the other way that gives the perception that the holes are shifting around. This is true enough, but these holes, just like electrons, have angular momentum, or spin. In excitons, they also serve as the positively charged “nucleus” that the electron is bound to. Not bad for empty space!
In the paper, the researchers showed that a drag current can be induced in one layer by pushing charges in the other. This doesn’t sound so impressive, besides the technical feat of making two conductive layers that are so closely spaced, but still separated by an insulator. The real surprise comes in the fact that the induced current is required to be equal in magnitude, and opposite in direction. The reason touches on a well-known but still totally non-intuitive aspect of quantum mechanics. That is, the idea of superposition. Superposition means that systems are not always constrained to exist in one state or another. They can be in some linear-combination of possible states. For example, an electron has a spin that, if measured in any direction, will always be either up or down. But the electron itself might have existed as some combination of up and down. In this case, the electron-hole pair existed as a superposition of a state where the electron was in the upper conductor and the hole in the lower one, and a state where the opposite is true, the electron was in the lower conductor, and the hole in the upper one. This symmetry makes the drive and drag currents equal and opposite. So not only are holes “real” in a sense, they can exist in two places at once, just like electrons(!)
So what does it all mean? It is always important to be clear when using metaphors what features are being accurately described, and which are not. Sometimes, however, we come across a metaphor that becomes more than just a way of thinking about a problem, and you get out more than what you put in. This is the hallmark of a successful scientific model.