Incoherent transport in a model for the strange metal phase: Memory-matrix formalism

Abstract: We revisit a phenomenological model of fermions coupled to fluctuating bosons that emerges from finite-momentum particle-particle pairs for describing the strange metal phase in the cuprates. The incoherent bosons dominate the transport properties for the resistivity and optical conductivity in the non-Fermi liquid phase. Within the Kubo formalism, the resistivity is approximately linear in temperature with a Drude form for the optical conductivity, such that the Drude lifetime is inversely proportional to the temperature. Additionally, when the bosons emerge from electron pairs with spin-triplet symmetry, the magnetoresistance has a linear magnetic field dependence. Here, we compute the transport properties of such bosons within the memory-matrix approach that successfully captures the hydrodynamic regime. This technique emerges as the appropriate framework for describing the transport coefficients of the strange metal phase. Our analysis confirms the $T$-linear resistivity due to the Umklapp scattering that we obtained for this effective model. Finally, we provide new predictions regarding the variation of the thermal conductivity with temperature and examine the validity of the Wiedemann-Franz law.