|Feb23-04, 02:11 PM||#35|
Blog Entries: 27
In condensed matter physics, the ground state of metals at T=0K corresponds to what is known as the "vacuum state" in quantum field theory. In this configuration, the states below the Fermi energy is completely occupied, while the state above the Fermi energy are completely empty.
Now, at finite temperatures, or due to fluctuations, you can have what is known as single-particle excitation above the Fermi energy. When this occure, you have an electron in a state above the Fermi energy, and a hole left behind in the filled states below the Fermi energy. But here's the deal - you can describe this new system EITHER by describing the electron that is above the Fermi energy, OR the hole in the filled states below that.[Refer to Mattuck's "Guide to Feynman Diagram in Many-Body Physics"] In other words, you can set your "universe" to be the empty states and consider the presence of electrons as your elementary excitation, or you can shift your universe to be filled with electrons and consider your elementary excitation to be these positive holes. It is similar in some sort to shifting your "gauge", or potential.
In this respect, the holes behave no different than a positive particle in vacuum (i.e if you shift your "vacuum" to be the level of negative electrons). We give it all the attributes of a particle - it has mass (or effective mass more accurately), charge, spin, etc... In fact, in condensed matter, the holes are the "antimatter" equivalent of the excited electron - i.e. they can anhilate to produce energy.
Now is this nothing more than a mathematical artifact? It isn't. The concepts of holes as a valid entity comes into play in many instances beyond just semiconductors. In high-Tc superconductors, the majority of the families of the cuprates are hole-doped! One actually remove electrons in the filled Mott insulator of the copper-oxide plane. The resulting holes behave like any other positively charged particle. In fact, this is the most common descrption of these family of compounds. Contrast that with the electron-doped cuprates that has generally lower Tc than their hole-doped counterpart, and you can already tell that there are some real physics differences involved here.
Keep in mind that these concepts, and the questions that have been asked in this string, can make more sense if one study a little bit of many-body physics. Only then would one see why things like "holes" and "excitations", etc, are more transparent. It is only within the many-body context would these things have definite meanings.
|Feb23-04, 11:39 PM||#36|
I honestly have no idea what you're talking about. What "tone" am I supposed to change? *What* inflammatory attitude? As far as I know, I'm behaving exactly the same as I always do on numerous forums (several of which I moderate.) You'll have to be far more specific if you want me to understand your complaints.
I certainly am pointing out your physics errors in no uncertain terms. Is this what you're really objecting to? If not, then please quote me the specific sentences in my messages which give you problems. Also please tell me which forum rules they violate.
You're obviously not an internet newbie. You should be well aware that "tone" of messages is frequently all in the mind of the reader, not in the message itself, and therefore is not a reliable indicator. If you're sure that I'm misbehaving in some way, you need to make certain that the "tone" is not all in your own head. It's easy: quote me the specific passages where I break the rules of physicsforums.com
I suggest you take a look at this article:
Email lists: flamewars and psychology
Also this one about electric current that I posted earlier:
Which way does "electricity" flow in circuits?
If you have a few hours, take a look at my collected writings:
Or the rest of my site:
amasci.com: the good stuff
William J. Beaty
University of Washington
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