Residual resistivity near a two-dimensional metamagnetic quantum critical point

The behavior of the residual (impurity-dominated) resistivity is computed for a material near a two-dimensional quantum critical point characterized by a divergent $q=0\mathrm{}$ susceptibility. A singular renormalization of the amplitude for back scattering of an electron off of a single impurity is found. When the correlation length of the quantum critical point exceeds the mean free path, the singular renormalization is found to convert the familiar “Altshuler-Aronov” logarithmic correction to the conductivity into a squared-logarithmic form. Impurities can induce unconventional Friedel oscillations, which may be observable in scanning tunneling microscope experiments. Possible connections to the metamagnetic quantum critical end point recently proposed for the material ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ are discussed.