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Questions regarding the Fermi level of a metal

  1. Apr 13, 2014 #1

    Are the electrons at the fermi level regarded as the "free electrons" of the metal?

    Also, how does one go about calculating the Fermi level? Is there an equation or is it experimentally determined?

    *Bonus question*
    Electrons that undergo phonon exchange and pair up are called "Cooper pairs". Why do these Cooper pairs not experience resistance? I have been looking all over the place for this answer and cannot find out why this is the case.
  2. jcsd
  3. Apr 13, 2014 #2

    Simon Bridge

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    Do you know about the band theory of solids?
    Which band corresponds to the "free" electrons in the metal?
    Where is the fermi-level with regard to this band?

    Do you know the definition of "Fermi level"?

    For whom? Is this homework?

    electrons form cooper-pair at low temperature.
    how does conduction normally happen?
    what is special about a cooper pair?
  4. Apr 14, 2014 #3
    Hi, thanks for taking the time to read my post.

    Yeah I know about band theory, and if I remember correctly there is a valence band and a conduction band and the Fermi level lies somewhere in between. I do not know where the free electrons are.

    I also do know the definition of the Fermi level. Its where electrons reside at absolute zero... i.e. they obey the exchange principle so they dont condense, so there is this Fermi level which is the highest energy state that the electrons occupy.

    as far as bonus question, I was making a joke because it doesn't really have anything to do with the title.

    A cooper pair is a boson, that's whats special about it. I know how conduction normally happens. But I don't understand how at low temperature, cooper pairs don't feel any resistance.
  5. Apr 14, 2014 #4
    The answers to your questions are rather complicated, so I imagine it will be a little bit hard for anyone to answer adequately in a single paragraph or two ;)

    Do you have access to any of the standard physics textbooks? I seem to remember that Chapter 5 of "Introduction to Quantum Mechanics" by Griffiths is pretty accessible in terms of explaining the role of the Fermi level with regard to metals and charge carriers. Ashcroft and Mermin is my favorite solid-state physics book, and will give a more complete explanation. You might check that out, also.
  6. Apr 15, 2014 #5

    Simon Bridge

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    The free electrons are in the conduction band. Hence the name ;)

    Since you know the band theory, you should know what is special about the valence and conduction bands in a conductor. This (and see below) tells you where the fermi level is.


    Close - the Fermi-level is the highest energy level occupied by the electrons at absolute zero. It's a matter of counting the states. Not all electrons are at the Fermi level.

    Fair enough. The questions you ask can show up as part of assignments.

    Please describe how conduction normally happens and how resistance normally occurs.
    The idea here is that it helps me know how to answer your questions effectively.

    Under what conditions do Cooper pairs form?
    Why is it special that a cooper-pair acts as a boson?

    It looks to me like your reading is incomplete all right.
    What education level do you need these replies at?

    Note: the difficulty in providing potted answers is the reason I am, instead, trying to guide your reading and thoughts by asking questions back at you.
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