  We theoretically unveil the unconventional possibility to achieve extremely
high thermoelectric power factors in lightly doped narrow gap semiconductors
with asymmetric conduction/valence bands operated in the bipolar transport
regime. Specifically, using Boltzmann transport simulations, we show that
narrow bandgap materials, rather than suffering from performance degradation
due to bipolar conduction, if they possess highly asymmetric conduction and
valence bands in terms of either effective masses, density of states, or phonon
scattering rates, then they can deliver very high power factors. We show that
this is reached because, under these conditions, electronic transport becomes
phonon scattering limited, rather than ionized impurity scattering limited,
which allows large conductivities. We explain why this effect has not been
observed so far in the known narrow-gap semiconductors, interpret some recent
related experimental findings, and propose a few examples from the half-Heusler
materials family for which this effect can be observed and power factors even
up to 50 mW/m$K^2$ can be reached.
