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Conductivity of a metal approaching absolute zero

  1. Sep 2, 2011 #1
    As a semi conductor approaches absolute zero there should be zero conductivity, the thermal energy that electrons aquire is or can be responsible for promoting electrons from the valence band to the conduction band to provide current flow in a semi conductor ( for t>0).


    My question is shouldn't metals as have zero conductivity as we approach absolute zero?

    Even though the fermi level resides inside the conduction band, the electrons without any thermal energy can not access other vacant higher energies?

    Does the finitie conductivity of metals at absolute zero have something to do with metals being non perfect lattices (realistically) because of entropy forces imperfections on the lattice.

    Can someone explain this better.

    Thank you very much
     
  2. jcsd
  3. Sep 2, 2011 #2

    ZapperZ

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    Not really, because the mechanism for "conductivity" actually depends on not only the number of carriers and the density of empty states, but also the rate of scattering of these carriers due to phonons, electron-electron scattering, impurities, etc. The fact that the conduction band is continuous means that it takes an infinitesimal amount of energy to excite an electron into an empty state. This can easily be accomplished even at 0K due to quantum fluctuation. And the fact that the scattering rates decreases at temperature drops means that while thermal fluctuation gets smaller, the carriers also are being scattered less, and thus, that favors an increase in conductivity.

    Zz.
     
  4. Sep 2, 2011 #3
    Thank you


    What are the difference between the valance band, and the conduction band. I'm confused about when you say continuous.

    I'm thinking as electrons being fermions, they must be built up into higher energy levels. Are there equivalent (empty) energy levels in the conduction band, so that electrons do not necessarily need the thermal energy to occupy different levels (aside from the quantum fluctuations).


    Are these impurities a function of a non perfect lattice?

    THank you!
     
  5. Sep 2, 2011 #4

    ZapperZ

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    Within each band, be it conduction or valence, the available states are continuous, i.e. no discrete levels such as in atoms.

    No. The ground state in the conduction band is when electrons occupied states up to the Fermi energy, with states above that being empty. The fact that there is an exclusion principle means that they all don't occupy the same state in the conduction band.


    It could be a function of a number of things. It could be a lattice imperfection, an external impurity, a dislocation, etc.

    Zz.
     
  6. Sep 2, 2011 #5
    Thank you

    One more please


    In the conduction or valence band, you mention the accessible levels as continuous (non discrete). Is this because we must treat the metal as a collection of atoms, rather than a single atom.

    back to the original question on conductivity,
    If i'm correct, you starting that the conduction is contributed to by phonon electron interaction and scattering of impurities or lattice defects.

    When you approach absolute zero, isn't lattice vibrations prohibited so phonon modes will not be available? wouldn't that only leave quantum mechanical tunneling as a source of electron transport?

    Am i totally wrong? Thank you so much
     
  7. Sep 2, 2011 #6

    ZapperZ

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    Correct. In solids, a lot of the individual behaviors of atoms that make up the material are not longer relevant. Many of the properties of solids are non-existent in individual atoms. Orbitals can hybridize to form other states when atoms are in close proximity to one another, for example.

    I was describing the general properties of conduction via the scattering rates. So yes, as you approach 0K, electron-phonon scattering will diminish, and thus, increase the conductivity. So this can, in principle, counteracts the fact that the temperature is lower and there will be less electrons populating higher empty states.

    Zz.
     
  8. Sep 2, 2011 #7
    Sorry again..


    I just pulled this from Wiki..

    "Starting with an empty system, we then add particles one at a time, consecutively filling up the unoccupied quantum states with the lowest energy. When all the particles have been put in, the Fermi energy is the energy of the highest occupied state. What this means is that even if we have extracted all possible energy from a metal by cooling it to near absolute zero temperature (0 kelvin), the electrons in the metal are still moving around. The fastest ones are moving at a velocity corresponding to a kinetic energy equal to the Fermi energy. This is the Fermi velocity."

    My issue is that I thought at absolute zero, everything stops moving. Is this implying that the the electrons are still moving at absolute zero.

    This is why I thought that electron electron scattering was no possible, the electrons energy was fixed and could only possible "move" to another site via tunneling.

    There would need to be available states of the same energy level for them to tunnel to.

    Is absolute zero only quenching the thermal movement of the atoms? (phonon vibrations), not the electron motion?

    Sorry
    thank you
     
  9. Sep 2, 2011 #8

    ZapperZ

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    This is where you need a bit of quantum mechanics. Note that in a quantum harmonic oscillator, there is still a zero-point energy at the lowest state.

    In a solid, there is such a thing as a 'crystal momentum'. It is really a "momentum" associated with the crystal/band structure. So an electron that occupies a particular band structure, other than at the center of the band, will have a momentum, no matter how low the temperature is.

    What you want to know is getting a bit more involved, and will require that you consult a solid state text.

    Zz.
     
  10. Sep 2, 2011 #9
    Can you recommend one

    I have aschoft & mermin & kittel intro to SS, no one seems to discuss low temperature conductivity of metals, only semiconductors.

    Throughout my physics experience, I've had a hard time relating the complicated mathematics that I've done with the physical explanation.

    Thanks for your help
     
  11. Sep 2, 2011 #10

    ZapperZ

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    Both of those text should contain discussion about crystal momentum. Those should be sufficient, because in most cases, the derivation was done at T=0, i.e. no thermal broadening is taken into account.

    Zz.
     
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