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Is there a way to make quantitative statements about the conductivity of materials with band theory?

If not I should still be able to get information about the conductivity from Green-Kubo relations of the electron wavefunctions in the material, right?

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What you are asking are transport properties of materials, which represent the response of the system to an external perturbation (such as electric field) so that you cannot obtain just from band structure.

For the transport of the classical particle, you can solve the Boltzmann transport equation, from which you can derive the Drude formula for conductivity. For fully quantum treatment, you can use nonequilibrium Green's function method (or Keldysh formalism), from which you can derive the current formula and transmission coefficient.

From bandstructure, you can obtain mobility, see section3.4 in this paper.

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  • $\begingroup$ so only from band theory without additional input I cannot get it, right? $\endgroup$
    – dan-ros
    Commented Dec 18, 2018 at 12:59
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    $\begingroup$ What you are asking is transport properties, which represent the response of the system to an external perturbation (such as electric field) so that you cannot obtain just from band structure. Boltzmann equation (you can derive Drude formula for conductivity from it) and NEGF (transmission can be obtained, see Suprio Datta or google Keldysh's formalism) are the right ways. $\endgroup$
    – Jack
    Commented Dec 19, 2018 at 1:04
  • $\begingroup$ but a little information about transport properties must be contained in band theory, otherwise you couldn't use it to distinguish between isolators and conductors, no? $\endgroup$
    – dan-ros
    Commented Dec 19, 2018 at 9:35
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    $\begingroup$ You are right. Actually, one can calculate the electron mobility (distinguish with conductivity) of materials from the conduction band minimum. $\endgroup$
    – Jack
    Commented Dec 19, 2018 at 11:05
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    $\begingroup$ See section3.4 pubs.rsc.org/en/content/articlelanding/2016/ta/… $\endgroup$
    – Jack
    Commented Dec 19, 2018 at 12:01

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