Electrical transport near an Ising nematic quantum critical point

Electrical transport properties near an Ising-nematic quantum critical point are of both theoretical and experimental interest. The difficulty of the problem is in part due to the fact that the electronic scattering mediated by critical fluctuations are momentum-conserving, and that one needs to incoporate additional current relaxation mechanisms into the low-energy theory. In this talk, we discuss two mechanisms relevant in such systems, namely Umklapp scattering and compensated metal. We present a memory matrix calculation of the DC resistivity, which treats the quasiparticle density at each patch on the Fermi surface as a slow variable. We work in the temperature regime where electrons are coherent but the fluctuations are Landau-damped. We show that in the case of Umklapp scattering, resistivity shows a smooth crossover from T² at low temperatures to sublinear at high temperatures. For a compensated metal where current and momentum are orthogonal, resistivity shows a surprising T-linear behavior. Connections to recent numerical simulations and experiments will be discussed.