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 $\rho \propto T, \rho \propto T^2$, 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.