Scalable T-square resistivity in dilute metals without Umklapp scattering

The electrical resistivity of Fermi liquids (FLs) displays a quadratic temperature (T) dependence because of electron-electron (e-e) scattering. For such collisions to decay the charge current, there are two known mechanisms: inter-band scattering (identified by Baber) and Umklapp events. However, in two dilute metals: metallic strontium titanate (SrTiO₃) and Bi₂O₂Se, resistivity was found to display T² behavior in absence of either of these two mechanisms. In SrTiO3, the presence of soft phonons and their possible role as scattering centers raised the suspicion that T-square resistivity in SrTiO₃ is not due to e-e scattering. More recently, Bi₂O₂Se, a layered semiconductor with only hard phonons, displayed T-square resistivity well below the degeneracy temperature, denying the possible role played by soft phonons. We observed a universal scaling between the prefactor of T² resistivity and the Fermi energy in SrTiO₃ and Bi₂O₂Se and across various FLs, which is an extension of the Kadowaki-Woods plot. Our results imply the absence of a satisfactory theoretical basis for the ubiquity of e-e driven T-square resistivity in Fermi liquids.

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