Wednesday, July 02, 2014

Many-Body Quantum Fluctuations In Residual Resistivity Of Metals

As a condensed matter physicist by training, the issue of charge transport in matter has always been a topic that I encounter often, especially when I was doing my postdoc many, many years ago. While the physics of charge transport in metals, under "ordinary" situations, can be adequately described by the Drude model, resulting in, for example, the beloved Ohm's Law, there are many other situations where such a simplistic model just doesn't work. And in those situations, that is where the physics gets very interesting and can be quite complicated.

The factors that influences charge transport in matter depends very much on how a charge carrier scatters. So the scattering rate determines the properties of resistivity/conductivity, etc. In a metal, there several types of scattering: electron-phonon scattering, electron-impurity scattering, and electron-electron scattering.[1] The dominant term that has a strong temperature dependence is the electron-phonon scattering, which is the primary mechanism that determines the resistivity of a metal. The electron-electron scattering has a weaker temperature dependence, while the electron-impurity scattering is mostly temperature independent.

What this means is that, as we lower the temperature, at some point, the electron-phonon scattering "freezes out", and no electron-phonon scattering contributes to the resistivity. The resistivity will then be a function of predominantly the electron-electron contribution. As the temperature approaches 0 K, one will notice indication that the resistivity will not be zero. This is the residual resistivity, whereby even at 0 K, there will still be a net resistivity of the material that is due to electron-impurity scattering. Note that this "impurity" need not be foreign atoms that are not part of the material. It can also be crystal defects and deformation that interrupts the long-range order of the crystal structure of the metals. The charge carriers can scatter off these defects as well.

That is how we were taught in solid state courses. we often deal with charge transport using the Boltzmann transport equation, and treating this within the Drude model The full quantum mechanical treatment, via the Kubo formulation, is a BEAST, and often unsolvable.

But now, along comes a new theoretical treatment of charge transport in metals, using DFT, that arrived at a rather unexpected result.[2] The new treatment showed that there is a strong contribution to the electron-impurity scattering due to the electron-electron many-body effects. The electron-impurity scattering is not as simple as we thought. They showed how well this new explanation matches the residual resistivity measured for aluminum.

This is another example where, something that we know very well and for a long time, can often reveal new physics and information when it is examined at the very edge of the boundary of our knowledge. We subject many of our ideas to the extreme case (in this case, very close to 0K) to see how well they work in those situations. It is one of the ways we expand the boundary of our knowledge.


[1] see

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