One of the things with which I am most impressed is the consideration of holes in the Bloch model.
It seems intuitive as it's something that's still flowing, but it's not that something's flowing, it's that something's not flowing.
Considering holes is much like how we consider the movement of air bubbles in water.
If we have our valance band with only few electrons then it would be easier to consider only the movement of the few electrons instead of the many holes.
Similarly with holes.
Intuitive almost, but the holes are a big hole in the Drude and Sommerfeld models where only electrons are considered.
By considering the movement as being from electrons or holes, so negative or positive charges, the signs of constants come out correctly.
Example would be the Hall coefficient where the Drude and Sommerfeld have the wrong sign (since they only consider movement of negative carriers).
The Bloch model considers positive and negative carriers, so the sign of the Hall effect comes out as positive for movement of holes and negative for movement of electrons.
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I like that holes come without an additional assumption. They they are just inherent in the description.
ReplyDeleteI could see how holes could be added into the simpler models to gain some quantitative description of common properties. Like if they assumed that metals also contain some positive particles that with mass m*.
I wonder what can first...
I suppose the only assumption is that (holes + electrons) fill the entire band.
DeleteIt would be difficult to include holes in the Drude and Sommerfeld since they don't acknowledge band structure, hence there would be no way to choose in considering electrons or holes (just add a negative everywhere).
Suppose they considered holes, then everything (all I can think of is hall coefficient) would be positive and for the negative values, we'd have the wrong sign.
The advantage of the Bloch model would that we considered two types of carriers, not just one.
(Sorry, reply got mixed up in your post
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DeleteI agree with Andy that it is rather interesting that holes came out from our calculations using the semiclassical equations of motion in the bloch model. I think this is probably the first quasiparticle introduced in physics. Not only it explains the sign of the hall effect conundrum but it is also useful because in some calculations later on, it would be easier to do them using holes instead of electrons.
DeleteI'm not quite sure your bubbles in water analogy quite matches the situation with holes. AFter all, there we have actual pockets of air, which propogate through the water medium. As a comparison, I would say that probably more matches the situation of electrons passing by heavier ions.
ReplyDeleteNonetheless, I was always amused by how nothingness (ie holes) could have such well defined physical properties! I guess you could make an analogy to general quantum mechanics, where it's not just the particle itself that needs a description, but the state as well.
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