T2 Resistivity in Perovskites

T2 Resistivity in Perovskites

From e-e interaction?

Perovskite crystals like n-type SrTiO3 show an electronic resistivity that increases with temperature squared \rho \propto T^2, or, for conductivity \sigma \propto T^{-2}. Such T2 resistivity is usually considered a signature for electron-electron scattering, leading to a belief that the electrons in these perovskite crystals behave like a Fermi liquid. A 2015 Science article on this topic generated a lot of interest. But is this the right explanation?

The first red flag to me was the observation of this T2 resistivity at temperatures as high as 1000 K. At this temperature, scattering from lattice vibrations should easily dominate the temperature dependency. Take a look at this plot:

Figure 1: Conductivity of n-type SrTiO3 single crystals with various doping.
Figure 1: Conductivity of n-type SrTiO3 single crystals with various doping. Solid markers are from Ohta et al.; open markers are from Okuda et al.

Also, there were a bunch of other perovskites that behaved similarly, like BaTiO3, KTaO3, etc. These all have the same crystal structure, so shouldn’t that be related to the origin? Indeed, these crystals all have very similar Fermi surface geometries with 2D character (cylinders), rather than 3D character (spheres). So I looked for a connection between deformation potential scattering (the mechanism that seemed more reasonable for high T) and Fermi surface geometries.

From elongated Fermi surfaces!

Turns out, the same mechanism that gives the usual T resistivity in metals gives T2 when the Fermi surface is elongated (relative to phonon vectors in a certain way). I put this understanding into my model and extracted relaxation time from data on several differently doped samples. If the model is consistent, then all curves should collapse onto a single one (relaxation time is energy independent in 2D). Here is the exciting result!

Figure 2: Relaxation time of n-type carriers in SrTiO3 single crystals with various doping.
Figure 2: Relaxation time of n-type carriers in SrTiO3 single crystals with various doping, converted from data in Figure 1 using a 2D Fermi surface model.

There are still some remaining mysteries, like why such a simple deformation potential scattering model works well when the actual deformation potential is supposed to be a lot more complex. Also, it is still possible that at very low temperatures, the origin is simply different than what we discovered for higher temperatures.

Interested? Please take a look at our paper. In another paper, we explain more details about the Fermi-surface geometry that was the origin behind all this. I didn’t have the chance to revisit this topic since then, but I hope I can someday!

Last modified: Jul. 25, 2020

Image Credit: Max T. Dylla
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