Umklapp scattering as the origin of $T$-linear resistivity in the normal state of high-$T_c$ cuprate superconductors

The high-temperature normal state of the unconventional cuprate superconductors has resistivity linear in temperature $T$, which persists to values well beyond the Mott-Ioffe-Regel upper bound. At low-temperature, within the pseudogap phase, the resistivity is instead quadratic in $T$, as would be expected from Fermi liquid theory. Developing an understanding of these normal phases of the cuprates is crucial to explain the unconventional superconductivity. We present a simple explanation for this behavior, in terms of umklapp scattering of electrons. This fits within the general picture emerging from functional renormalization group calculations that spurred the Yang-Rice-Zhang ansatz: umklapp scattering is at the heart of the behavior in the normal phase.