Abstract

In this work, we investigate effects of general disorder on a spin-density-wave(SDW) quantum critical metallic system which is known to show non-fermi liquid states using a renormalization group method. As effects of disorder, we consider two effects: (i) random charge impurity potential and (ii) random mass of SDW boson order parameter. To tame strong quantum fluctuation, both a co-dimensional regularization and a correlated random mass method have been used in our renormalization group calculation. In one-loop result, we find that a stable fixed point in a clean system obtained by Sur and Lee(Phys. Rev. B 91, 125136) become unstabilized by the disorder and two different strongly disordered phases appear in low energy limit depending on which disorder effect among the random charge impurity potential and the random mass disorder is stronger. One of two phases is `random charge impurity potential dominant' phase. In this phase, Fermion fields are strongly localized and Yukawa-interaction and both disorder effects are strong while a boson-self interaction is weak. The phase discussed in the paper(Phys. Rev. B 103, 235157) recently belongs to this phase and our results are consistent with their results. The other phase is a `random-mass disorder dominant' phase. In this phase, Boson fields are strongly localized and boson-self interaction and both disorder effects are strong while a Yukawa-interaction is weak which is opposite to the `random charge impurity potential dominant' phase. For both phases, we studied properties of Green's functions and four superconducting channels discussed by Sur and Lee. Additionally, partial two loop diagrams consists of only charge impurity disorder vertices are calculated and it turns out that there is no qualitative difference compared to the one-loop result. We hope that our research give guidance and intuition about effects of disorder on non-Fermi liquid states.