Self-consistent methods for scattering rate and magnetoresistance in the extreme quantum limit

We theoretically investigate the scattering rate and the magnetoresistance in the extreme quantum limit (EQL), where the kinetic energy becomes significantly smaller than the cyclotron energy, based on the two self-consistent methods, the self-consistent Born approximation (SCBA) and self-consistent T-matrix approximation (SCTMA). We demonstrate that SCTMA successfully captures the crossover of the scattering rate from the Born regime to the unitarity limit. A key finding is the consistency between SCTMA and the T-matrix approximation (TMA), indicating that the renormalization of multiple scattering by a single impurity is the governing factor in EQL transport, surpassing the effects of multi-impurity scattering incorporated by self-consistency.