Fig. 1: Chirality-driven magnetoresistance (MR) including the electrical magnetochiral anisotropy (EMCA) and chirality-induced spin selectivity (CISS).

a Transmitted (solid line) and reflected (dashed line) electrons through a chiral molecule get spin-polarized (indicated by small yellow arrows) for unpolarized incident electrons. In a perturbative picture, because the spin polarization relies on the incident direction, the resistance is direction-dependent when the spin polarizer is connected to a ferromagnetic electrode (magnetization indicated by the red/blue arrows), leading to EMCA rather than CISS MR. b, c shows the typical I–V curves for EMCA and CISS MR, respectively. The violation of Onsager’s relation is characterized by the change of zero-bias conductance upon switching the electrode magnetization. d In a CISS device, the ferromagnet-molecule interface exhibits magnetization (M), spin-orbit coupling (SOC), chirality (χ), and dissipation. A chiral chain model (light blue) is adopted to represent the interface with coexisting M, SOC, χ, and dissipation. (e) At the interface, the wave function is exponentially localized to one side due to the non-Hermitian skin effect (NHSE) when the current flows. Merely NHSE leads to EMCA - another interpretation of EMCA besides the spin polarization. If an impurity state(circle) exists on the molecule side, the asymmetric wave function due to NHSE can control this state occupied (electron-trapping) or empty. f Schematics of energy profile for the electron-trapping state and no trap state as two metastable phases. NHSE drives the switch between two phases by reserving M (or χ), i.e. the magnetochiral charge pumping.