  The longitudinal nonreciprocal charge transport (NCT) in crystalline
materials is a highly non-trivial phenomenon, motivating the design of next
generation two-terminal rectification devices (e.g., semiconductor diodes
beyond PN junctions). The practical application of such devices is built upon
crystalline materials whose longitudinal NCT occurs at room temperature and
under low magnetic field. However, materials of this type are rather rare and
elusive, and theory guiding the discovery of these materials is lacking. Here,
we develop such a theory within the framework of semiclassical Boltzmann
transport theory. By symmetry analysis, we classify the complete 122 magnetic
point groups with respect to the longitudinal NCT phenomenon. The
symmetry-adapted Hamiltonian analysis further uncovers a previously overlooked
mechanism for this phenomenon. Our theory guides the first-principles
prediction of longitudinal NCT in multiferroic \epsilon-Fe2O3 semiconductor
that possibly occurs at room temperature, without the application of external
magnetic field. These findings advance our fundamental understandings of
longitudinal NCT in crystalline materials, and aid the corresponding materials
discoveries.
