Role of many-phonon modes on the high-temperature linear-in-T electronic resistivity

We theoretically consider the possibility that phonons may be playing a role in the observed linear-in-T resistivity in cuprates by focusing on the obvious question: How can phonon scattering be consistent with a linear-in-T resistivity with a constant slope given that cuprates have many phonon modes with different energies and electron-phonon couplings (e.g., 21 phonon modes for LSCO)? We show using an arbitrarily large number of independent phonon modes that, within a model Boltzmann transport theory, the emergent high-T linear-in-T resistivity manifests an approximately constant slope independent of the number of phonon modes except in some fine-tuned narrow temperature regimes. We also comment on the quantitative magnitude of the linear-in-T resistivity in cuprates pointing out the constraints on the effective electron-phonon coupling necessary to produce the observed resistivity.