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 (v(F) < v(p)) 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 v(F)/v(p) and small band separation. We predict regimes of rho infinity T, rho infinity T-2, 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 v(F)/v(p), offering a different explanation for low-T "strange metal" behavior observed in NFBs. Understanding NFBs thus requires updated expectations for "normal" transport physics.