Electrical transport in a two-dimensional disordered non-Fermi liquid

We study the electrical transport of a two-dimensional non-Fermi liquid with disorder, and we determine both the semiclassical dc conductivity and the first quantum correction. We consider a system with N flavors of fermions coupled to SU(N) critical matrix bosons.  Motivated by the SYK model, we employ the bilocal field formalism and derive a set of saddle point equations governing the fermionic and bosonic self-energies in the large-N limit.  Interestingly, disorder smearing induces marginal Fermi liquid (MFL) behavior. Consequently, the resistivity varies linearly with temperature on top of the Drude result. We also consider fluctuations around the saddle points and derive a MFL-Finkel’stein nonlinear sigma model. Using this theory, we evaluate the Altshuler-Aronov correction. In contrast with the Fermi liquid case, our calculation reveals a correction ~ ln^2(\Lambda/T) to the conductivity, which dominates in the low-temperature regime. Our calculations explicitly satisfy the Ward identity at semiclassical and quantum levels. Our results can be tested directly in quantum critical systems via dc transport experiments.