The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene

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 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 formulae for relaxation times and resistivity that are accurate in the limit of close bands and small $v_F\mathrm{/}{v}_p$. 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 analogue by a factor of $v_F\mathrm{/}{v}_p$, offering a new explanation for low-$T$ “strange metal” behavior observed in flat band systems.