Electronic manipulation of polar order in electron crystal

When interaction among atoms or ions is strong enough, they often arrange periodically, forming a crystal. The arrangement patterns of atoms or ions can encode information, a concept that has enabled devices such as ferroelectric memories. It has been found that not only atoms or ions but also electrons in condensed matter can crystallize when Coulomb interaction is strong enough. Typical examples are charge-ordered states in solids, where different valences, or different electron numbers, of an ion spontaneously form a spatial pattern on the lattice. In such electron crystals, information is expected to be encoded into the electron-ordering patterns. Here, we demonstrate electronic manipulation and readout of charge-ordering directions in a paramagnetic semiconductor LuFe$_2$O$_4$. By applying current pulses at room temperature, we observed that the non-reciprocal resistivity of LuFe$_2$O$_4$ is modulated along with a sign reversal, which disappears above the charge-ordering temperature. A numerical calculation incorporating inter-band Berry curvature affected by the charge ordering is consistent with the experimental results. By applying the observed phenomenon, we also demonstrate a non-reciprocal resistance memory operation in the charge-ordered LuFe$_2$O$_4$. This result opens the door to realizing charge-ordering electronics.