Signatures of electronic ordering in transport in graphene flat bands

Recently, a wide family of electronic orders was unveiled in graphene flat bands, such as spin- and valley-polarized phases as well as nematic momentum-polarized phases, stabilized by exchange interactions via a generalized Stoner mechanism. Momentum polarization involves orbital degrees of freedom and is therefore expected to impact resistivity in a way that is uniquely sensitive to the ordering type. Under pocket polarization, carrier distribution shifts in $k$ space and samples the band mass in regions defined by the displaced momentum distribution. This makes transport coefficients sensitive to pocket polarization, resulting in the Ohmic resistivity decreasing with temperature. In addition, it leads to current switching and hysteresis under strong $E$ field. Being robust in the presence of electron-phonon scattering, this behavior can serve as a telltale sign of pocket polarization order. The fast timescale and low dissipation of the switching cycle may be advantageous for highly applicable memory-dependent resistors, i.e., memristors.