Effects of quenched non-magnetic disorder on a spin-density-wave quantum critical metallic system

We investigate effects of general quenched non-magnetic disorder on a spin-density-wave(SDW) quantum critical metallic system using a renormalization group method. As effects of quenched non-magnetic disorder, (i) random charge potential and (ii) random mass of a SDW boson order parameter are considered. Two regularization methods; co-dimensional regularization and a correlated random mass method are used in our renormalization group analysis. In one-loop result, there is no stable fixed and low energy RG-flows are governed by the large random charge potential vertices and an effective Yukawa interaction. Beyond the one-loop results, possiblity of the another strongly disordered phase due to the random boson mass vertex is discussed. Regarding to the physical properties, low energy behavours of the two point Green's functions and anomalous dimensions of several superconducting channels are discussed. It is found zero momentum d-wave superconducting channel is suppressed due to the effects of the disorder. We hope that our research give guidance and intuition about effects of quenched non-magnetic disorder on non-Fermi liquid states.