Experimental characterizations of transport phenomena in topological and magnetic materials have mainly been based on linear responses of spin and charge carriers to the applied electric field or current. Far less well understood are emerging nonreciprocal response effects that, in principle, can also be hosted in these materials systems, due to spin-orbit interaction, broken inversion symmetry, and/or band topology.

In this talk, I will present our theoretical works on three representative nonreciprocal transport phenomena that have recently been of particular interests: 1) a unidirectional magnetoresistance effect in conducting ferromagnet|nonmagnet bilayer systems, which is analogous to the current-in-plane giant magnetoresistance effect, but with a current-induced spin density – as opposed to a ferromagnetic metal layer – playing the role of a spin polarizer, 2) a bilinear magneto-electric resistance effect in 3D topological insulators, which may be deemed as a nonlinear version of spin-to-charge conversion, arising from spin-momentum locking of surface Dirac fermions and time-reversal symmetry breaking, and 3) a nonlinear Hall effect in Weyl semimetals, a new transport signature of chiral anomaly – which, in the presence of non-perpendicular electric and magnetic fields, creates an effective chemical potential difference between a pair of Weyl nodes with opposite chiralities and thereby becomes detectable in the nonlinear response regime.