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The hallmark of optimal doping cuprates is the linear resistivity term vs. T. This is a very important feature due to the following arguments
- Cuprates are very low density metals, close to a Mott metal-insulator transition
- In high density metals the linear resistivity is typically due to phonons, via the Bloch-Grüneisen rule. This is the typical behaviour of conventional 3d monovalent metals
- In low density 3d monovalent metals, like alkali a {$T^2$} term appears, due to electron-electron umklapp scattering. Lawrence and Wilkins Phys Rev B 7, 2317 calculate the electron-electron scattering and show that it becomes relevant at low temperatures, just before the Matthiesen rule (impurity dominated, temperature independent resistivity) sets in, as {$\rho= m\Delta/ne^2\tau_0$} where {$\Delta$} is the umklapp fraction. The {$T^2$} dependence comes from a Fermi surface integration of the term {$\mathbf{v}_{\mathbf k}\cdot\mathbf E$}
- When {$n$} decreases, even if {$\Delta$} is small like in alkali metals, the electron-electron term dominates
- Therefore cuprates are termed strange metals because the {$T^2$} term is expected to dominate but it is not present.
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