Kinetic theory of ultrasubsonic fermion systems and applications to flat-band magic-angle twisted bilayer graphene transport

The only kinematically allowed phonon-scattering events for bands of subsonic fermions (vF<vₚ) are interband transitions, leading to different low-T transport physics in nearly flat-band systems (NFBs) than in the typical supersonic case. We apply a kinetic theory of phonon-limited transport to a generic two-band system of subsonic fermions, deriving formulas for relaxation times and resistivity that are accurate in the ``ultrasubsonic'' limit defined by small vF/vₚ and small band separation. We predict regimes of ρ∝T, ρ∝T², and perfect conductivity. Our theory predicts linear-in-T resistivity down to a crossover temperature that is suppressed from its supersonic analog by a factor of vF/vₚ, offering a different explanation for low-T ``strange metal'' behavior observed in NFBs. Understanding NFBs thus requires updated expectations for ``normal'' transport physics.