QM in solids works like this:
You take an atom of stuff. It has discrete energy levels according to the
electron shell structure, all that stuff of which is reasonably well
described with atomic spectral theory and whatnot. The energy level
spacings on the order of a few eV, which is convieniently near the visible
spectrum, which means a lot of atoms glow visibly when you put them in a
hot flame (strontium, barium and copper being very important examples), or
a discharge tube (neon, etc.), etc.
When you rub two atoms together, two things can happen: either nothing
happens (noble gasses, pretty much) and they go on their merry way, or
their energy levels start distorting because their electrons 'feel' each
other. When this happens, the energy bands skew, split and squash; total
energy drops and the atoms stick together. Now you have a diatomic
molecule, which has different energy levels, usually lower (fractional to
several eV). But the important part to remember: there are more energy
levels now.
Suppose you keep introducing still more atoms. Sometimes they will
stick -- carbon likes to stick to itself, but only in some ways. Like
nanotubes. Those are produced in great quantity, along with other
carbonaceous bric-a-brak, in a sooty flame (which is rich in diatomic C2,
and various radicals like CH2 and CH, which glow blue, incidentially).
Some won't stick together, like nitrogen and oxygen, which form diatomic
molecules and that's that. But a lot of them (most of the periodic table)
will keep glomming on.
Each additional atom brings more energy levels, and pretty soon you get
big gloms of energy bands -- there are so many atoms and so many energy
levels that they look continuous, even though they are, in principle,
discrete.
Incidentially, as atoms come together, they form wads of levels for some
reason. These are the valence and conduction bands familiar from
semiconductor physics. The conduction bands are comparable to the higher
energy levels of hydrogen (n > 1), they aren't used normally (in "cold"
matter), they're just open, available. These are the conduction and
valence bands.
In reality, the levels are spaced maybe a few neV apart, which is utterly
destroyed by all but the coldest conditions. In principle, you should be
able to do some RF resonance (what's a 1neV photon, the AM radio band? --
oh hey, good guess, it's actually an octave below:
https://www.google.com/search?q=1e-9+elementary+charge+*+volt+/+planck+constant )
with any superultrahypermegacold matter, at least if you can spontaneously
polarize it (e.g., kick an electron into a conduction band in a
semiconductor, I suppose). But at room temperature, those levels are
completely scattered (like having 5 LSBs worth of noise on a 24 bit ADC),
so you can't measure them and they are, in fact, continuous bands at
nonzero temperatures.
Anyways, the thing about QDs is, okay so we started with a quantized
material, and it's still made of the same stuff, but now just by sheer
virtue of it's being huge, it's magically unquantized now. Well, in that
intermediate stage, when you've got gloms of just a few thousand atoms, so
the bands aren't really continuous, at least not at room temperature. And
the bandgap likewise isn't as well defined. In fact, nanoparticles of
familiar things, like copper and gold (which have such a low conduction
band that pretty much every atom contributes a charge carrier!) may have
such unusual band structures that they, too, can glow like molecules and
semiconductors! Well, I don't know if that's true of metal particles, but
it is true of low-bandgap semiconductors, like CdTe. Or they might have
weird chemistry -- it's one thing to form a chemical complex with a single
atom, or a couple, but you get different surface chemistry when you have a
very "round" particle (dozens of atoms across), versus a fairly flat
crystalline surface (typical of bulk solids).
You can pretty easily synthesize a colloidial suspension of CdSe, CdTe,
etc. by precipitation from the salts, and by controlling the particle size
precisely (concentration, temperature, additives), achieve a whole rainbow
of fluorescent colors, because the QD bandgap is much wider. You also get
to do middle-range things with the intra-band levels on the really small
particles, like I suppose, microwave to THz resonances, maybe IR.
Okay, so we can't "do" anything with QDs yet besides shine lasers on them
and make glowy things, but the obvious potential is there -- if we could
organize quantum wires up to them, we could carry electrons with about the
right energy levels to this that and the other thing, and do who knows
what.
Tim
