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What is the difference between Mott localization & Anderson loc.?

  1. Jun 30, 2013 #1

    This subject has me confused. I hear a lot about Mott transitions and Anderson localization; then in some papers, I read about Mott localization and I'm not sure what they are referring to.

    Can someone distinguish the following for me?
    1. Mott transition and Anderson transition
    2. Mott localization and Anderson localization

    How are 1 and 2 related to one another?

    The wiki articles have plenty of physics that I haven't encountered before. The papers I'm reading have to do with glasses and electronic states and I'd like to move forward without going off too much on a tangent.

    Thank you!
  2. jcsd
  3. Jun 30, 2013 #2

    Physics Monkey

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    A Mott insulator is an insulator due to interactions. For example, you have a Hubbard model with one electron per site and [itex] U \gg t [/itex]. The picture is very classical in that electrons simply cannot move around, there being no nearby empty sites to hop to.

    An Anderson insulator is an insulator due to the localizing effects of disorder. Usually in this context we think about physics at the single particle level. In particular, with strong disorder, say random onsite energies much larger than hopping, it happens that all single particle energy levels can be localized. In this situation, transport cannot occur because particles cannot move beyond roughly the localization length. However, what is preventing them moving is not interactions but interference.

    Both insulators are localized. Also, Mott worked on a variety of topics including Mott insulators and disorder, so for us to help you disambiguate the meaning of "Mott localization", it would be useful if you could provide some additional context.

    PS Mott transition is a transition from a Mott insulator to a metal while an Anderson transition is a transition from an Anderson insulator to a metal.
  4. Jul 3, 2013 #3
    Hey, thanks for that. I still need to read more about these topics to fully grasp the meaning of your response.

    The following is the context, taken from the following paper: http://prl.aps.org/abstract/PRL/v28/i6/p355_1

    " It appears from Fig. 3 that weak bonds (e.g, As-As) create localized sigma* (anti-bonding) states in the band gap of Se. These are not acceptors, however, because of Coulomb interaction. If the density of weak bonds becomes large enough, the anti-bonding states will become delocalized. The conduction-band edge will then move to lower energy. This is a Mott delocalization because it is due to Coulomb repulsion and correlation.

    Considering, now, admixtures of group-VI elements to group-IV amorphous materials such as Ge, we observe from Fig. 3 that the LP (Lone Pair) states of Se and Te fall near the gap of Ge. It is probably possible to choose a tetrahedral host and a group- VI additive so that the LP states fall in the gap. These lone-pair states will be localized at low concentration. However, when their concentration exceeds a critical value, they become delocalized and we expect an Anderson transition to occur. The LP band arising from these overlapping LP states is fully occupied unless an electron gets trapped into a lower-lying state. "

    If nothing else, I'm trying to interpret that analysis! The rest of the paper is easy enough.

    Thanks again!
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