Electrons, holes and positrons

Ranku

Do positively charged holes have any other quantum numbers assigned to them? What are the similarities and differences between a hole and a positron?

SpectraCat

Electron "holes" are a semantic convenience used to represent electronic vacancies in explanations of physical phenomena. You can think of them like the placeholder zeros in a number like, 18057604. In principle there could be values in the [tex]10^{1}[/tex] and [tex]10^{5}[/tex] places, but in this particular instance, there aren't. Depending on the specific context in which they are used, it sometimes makes sense to associate quantum numbers with holes. For example, a chlorine atom is one 3p electron short of having a complete n=3 shell. Therefore it is semantically consistent to say that it has an "n=3, l=1" hole.

Having said all of that, holes do not really have any independent reality. Positrons, on the other hand, are real particles ... they are the antiparticles of electrons, and have precisely the same set of quantum numbers, but with a positive charge. They have independent reality, that is, they exist and can be isolated experimentally.

Ranku

So holes are independently introduced conceptual constructs, that are not part of the particle standard model?

f95toli

Yes, holes are not "real" as such . They are mathematical constructs that are useful because they simplify our calculations.

Galap

You can think of them pretty much like holes. Imagine a piece of paper with a hole in it. Is the hole a real thing? No, it's just the fact that the paper envelops a region where there is no paper. However, in certain situations, it's more meaningful to talk about the hole than the paper, for example when you are trying to fit it in a 3 ring binder. The same is true about electron holes: they're not real, but sometimes it's better to use that description.

Frame Dragger

Holes are very much like Virtual Particles in that their effect seems obvious, but they are really just a trick of the math. That said, they are a trick which does a good job describing the situation for people who don't think in dimensions higher than 3

Galap

I'd like to hear more in depth about the more-than-3d explanation you imply :)

Frame Dragger

? I mean to say that human beings can't imagine structures in more than the 3 spatial dimensions we experience daily. Given that, we get gravity "wells" and and electron "holes". What else can we say unless people simply spoke in equations?

ArjenDijksman

I see no inconsistency in thinking of holes as ordinary locations left vacant by electrons in a lattice. An electron is attracted to a hole, because there's more place for the electron around holes then elsewhere in the lattice, it can reoccupy the hole ("recombine"), it can "circle" around it (forming an exciton)... It is above all a physical reality and incidentally a mathematical trick...

ZapperZ

I think this is an excellent view of it.

Claiming that holes aren't real is analogous to saying a "bubble" in water isn't real. It is as much a "real" object as the glob of water that left it and went up above the surface. The fact that we can "renormalize" the environment in the filled band and to consider such holes as having not only a positive charge, but also to have spin, etc., means that below the Fermi level, they are as real as the "vacuum excitation" that we call 'electron'.

In condensed matter physics, there is never any demotion of the concept of "holes" with respect to "electrons". YBCO and LACO and BCCO are all hole-doped superconductors, while NCCO is an electron-doped superconductor, for example. In Andreev scattering, it does makes a difference if a hole is reflected at the interface. There are plenty more examples where this came from.

Zz.

Galap

I was just unaware that there was a higher dimension interpretation of specifically electron holes.

SpectraCat

I think this is kind of a "potato/potahtoe" thing, and the differences in description are mostly semantic. Holes are semantically and mathematically convenient for sure, but they are an "extra" concept. What I mean by this is that the properties of what we call a hole or vacancy could be obtained simply from the properties of the electrons that are actually there. This is true in the atomic case (where it is simple to prove), and while I am less familiar with solid-state physics, I suspect it is true there as well, although it is probably *way* less tractable to deal with.

Note that I am not disputing the reality of holes ... of course they are real, as much as the hole in a doughnut is real ... but it requires the doughnut for its existence. If you excite an electron out of a filled band, then you create a higher energy configuration, which has a vacancy in the filled band that "wants" to have an electron in it. Therefore it seems to have a positive charge, and will act as ArjenDijksman described. If the band is spin polarized, then only an electron with a particular spin can fill the hole. The properties of spin and charge are also only relevant with respect to some lower energy reference state. That is what I meant earlier when I said they have no independent reality.

ZapperZ

But within context to condensed matter physics, an "electron" also relies on the vacuum state, i.e. a background of "holes" for its existence! That's why I called an electron a "vacuum excitation"! In fact, both holes and electrons are "quasiparticles" in a many-body interaction. They are not different.

Zz.

Frame Dragger

Hmmm, I've learned to look at Holes in a very new way. Thanks ZapperZ and ArjenDijksman!

Physics Monkey

Although this is certainly speculative, it's amusing to note that even our beloved "real" positrons could themselves be holes in a material we call the vacuum. Imagine a hypothetical person living inside the low energy world of a semiconductor without access to the high energy world of the lattice. Such a person might be inclined to view holes in the same way we view positrons.

And in fact, the analogy isn't just for fun. The low energy electrons and positrons we experience are different from the bare particles that we suppose exist at much higher energies (greater than a TeV say) where the electroweak symmetry is unbroken.

SpectraCat

Ok .. I guess I see what you are saying, but there still seems to be a significant difference to me. Electrons and holes both "exist" in a solid state electrical conductor, however, if we use that conductor as the emission element of a beam source, it is straightforward to make a beam of electrons, but to my knowledge, noone has ever made a beam of holes.

I am a rank novice when it comes to high-energy physics, so I will have to take the word of those more knowledgeable than myself about "vacuum holes". I am also willing to accept that we can only make an electron beam because we live in and experience the "low energy" case, as suggested by Physics Monkey.

Frame Dragger

Well, given the description of holes a la ZapperZ not being able to find holes outside the lattice isn't any odder than not finding free quarks. Doping the material for holes seems to be the equivalent within the medium.