Low-temperature T -linear resistivity in the strange metal phase of overdoped cuprate superconductors due to umklapp scattering from a spin excitation

The strange-metal phase of overdoped cuprate superconductors exhibits a linear in temperature resistivity in the low temperature, however, the origin of this remarkable anomaly is still not well understood. Here the linear temperature dependence of the resistivity in the strange-metal phase of overdoped cuprate superconductors is investigated. The momentum dependence of the transport scattering rate arising from the umklapp scattering between electrons by the exchange of the spin excitations is derived and employed to calculate the resistivity by making use of the Boltzmann equation. It is shown that the resistivity is mainly dominated by the antinodal and nodal umklapp scattering. In particular, a very low temperature $T_{\rm scale}$ scales with $\Delta^{2}_{p}$, where $\Delta_{p}$ is the minimum umklapp vector at the antinode. In the low temperature above $T_{\rm scale}$, the resistivity is linear in temperature with the temperature linear coefficient that decreases with the increase of doping, however, in the far lower temperature below $T_{\rm scale}$, the resistivity is instead quadratic in temperature. The theory also shows that the same spin excitation that acts like a bosonic glue to hold the electron pairs together also mediates scattering of electrons in the strange-metal phase responsible for the linear in temperature resistivity in the low temperature.