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Non-magnetic impurities are known as strong pair breakers in superconductorswith pure d-wave pairing symmetry. Here we discuss d-wave states under thecombined influence of impurities and competing instabilities, such as pairingin a secondary channel as well as lattice symmetry breaking. Using theself-consistent T-matrix formalism, we show that disorder can strongly modifythe competition between different pairing states. For a d-wave superconductorin the presence of a subdominant local attraction, Anderson's theorem impliesthat disorder always generates an s-wave component in the gap at sufficientlylow temperature, even if a pure d_{x^2-y^2} order parameter characterizes theclean system. In contrast, disorder is always detrimental to an additionald_{xy} component. This qualitative difference suggests that disorder can beused to discriminate among different mixed-gap structures in high-temperaturesuperconductors. We also investigate superconducting phases with latticesymmetry breaking in the form of bond order, and show that the addition ofimpurities quickly leads to the restoration of translation invariance. Ourresults highlight the importance of controlling disorder for the observation ofcompeting order parameters in cuprates.Comment: 13 pages, 10 figure

Impact of disorder on unconventional superconductors with competing ground states