Re: HOLES AS CARRIERS

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:16 PM 10/8/01 -0400, Michael Edmiston wrote:
> Try this out...

I'll try anything once.....

> We know that wavy things like electrons can sometimes appear localized, and
> sometimes appear unlocalized.

Are we talking about wave/particle duality here?  Or real
honest-to-goodness localization?  Or something else??? The word
"localization" means something very specific in modern physics:
  http://www.nobel.se/physics/laureates/1977/anderson-autobio.html
  http://www.nobel.se/physics/laureates/1977/mott-bio.html


> When we speak of "charge carrier" we have in mind some localized entity that
> appears to be moving or propagating.

Boink?
 1) Suppose this means "localized", as in Anderson localization or Mott
localization ... then it's not moving at all.  So this meaning doesn't make
sense.
 2) Suppose this means something else, perhaps some generalized vernacular
notion of "localized" as in spatially-compact.  I can't agree with this
meaning, either.  Things don't need to be spatially-compact to carry charge.

> If the entity does not possess some
> degree of localization then I do not know how to picture "it" as being a
> "charge carrier."

Being hard to visualize isn't the same as being non-existent.

>  For example, I do not know how to describe the Hall
> Effect without some localized charged entities that respond to the magnetic
> field.
>
> In some materials, experiments like the Hall Effect seem to indicate a
> negative charge carrier.  In other materials the same experiment seems to
> indicate a positive charge carrier.  I can picture this in my mind by
> imagining that the charge carrier is the one that seems to have some amount
> of localization to it.  If the electron wave density in the conduction band
> is giving rise to regions of localized negative density, then conduction in
> this material will appear to negative charge carriers.  On the other hand,
> if the electron wave density in the conduction band is giving rise to
> regions of localized positive density then that material will appear to have
> positive charge carriers.

The foregoing seems to be a "just-so story" ...
  http://www.boop.org/jan/justso/leopard.htm
By that I mean that the number of correct predictions it makes is less than
the number of assumptions it makes.

What's worse, it makes tons of incorrect predictions.  For instance, if you
to photoemission spectroscopy from semiconductors, you will find that
electron-emission from an almost-full downward-bending band (where holes
live) is exactly the same as electron-emission from an almost-empty
upward-bending band (where plain old electrons live).

============

Try the following instead:  Forget about "localization".

Holes are just a way of viewing what's going on.  Choosing a viewpoint is
like choosing a reference frame.  Sometimes there are compelling reasons
for choosing a particular reference frame;  for instance, 2-body collisions
are usually much simpler if analyzed in the center-of-mass frame, for
reasons that are well known.  Similarly, there are cases where the hole
viewpoint is really compelling.  In such cases, the reasons include:
 -- particles of interest in the dressed viewpoint (holes) are much less
numerous than the particles of interest in the undressed viewpoint
(electrons), so they're easier to keep track of.
 -- the holes are much closer to the point of symmetry (extremal energy),
so we have first-order expansions that are valid for holes that would not
be valid for electrons.

Tim Folkerts had the right idea.  Correct and to the point.

At 06:00 PM 10/6/01 -0500, he wrote:
> I introduce holes with a couple of (transparent) bottles of shampoo.  Take
> one that is mostly empty and turn is over - watch the shampoo flow down to
> the bottom.  Then take a nearly full bottle and turn it over - watch the
> bubble rise.
>
> Is something moving up in the second case?  Well, not really - shampoo is
> flowing down in both cases, but it seems like a completely different
> phenomenon.  And it is certainly easier to treat the motion of the bubble
> (which moves smoothly) rather than the actual shampoo (which has many parts
> each moving a short way and then stopping).