We show that a localized bosonic mode acts as a new type of "defect" in s-and d x 2 −y 2 -wave superconductors. The mode induces bound or resonance states, whose spectral signature are peaks in the superconductor's density of states (DOS). We study the peaks' shape and energy as a function of temperature and the mode's frequency and lifetime. We identify several characteristic signatures of the localized mode that qualitatively distinguishes its effects from those of magnetic or nonmagnetic impurities.PACS numbers: 72.10. 72.10.Fk, 74.25.Jb The study of local defects or impurities in superconductors has attracted significant experimental [1, 2] and theoretical [3,4,5] interest over the last few years. These studies have proven particularly important for further elucidating the nature of the superconducting (SC) pairing mechanism in unconventional superconductors. In particular, recent scanning tunnelling microscopy (STM) experiments provided a detailed picture of the frequency and spatial dependence of defect induced resonance states in the high-temperature superconductor (HTSC) Bi 2 Sr 2 CaCu 2 O 8+δ [2], and the triplet superconductor Sr 2 RuO 4 [6]. Several theoretical scenarios for the physical origin of these impurity states have been proposed, ranging from electronic scattering off classical impurities [3,5] to the onset of .

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We propose a scanning tunneling spectroscopy experiment to identify the nature and relative strength of collective modes in the high-temperature superconductors ͑HTSCs͒. To this end, we show that the pinning of diverse collective modes by impurities leads to qualitatively different fingerprints in the local density of states. These fingerprints directly reflect the modes' magnetic or nonmagnetic character, as well as their wave vectors and correlation lengths. These results provide an alternative method for identifying collective modes not only in the HTSCs but also in other correlated electron systems.Identifying the collective mode that is responsible for the emergence of the superconducting phase and the unconventional normal-state properties of the high-temperature superconductors ͑HTSCs͒ is one of the key issues in understanding these complex materials and the focus of an intense scientific debate. The problem in resolving this issue arises from the fact that each proposal for a candidate mode, 1 such as spin or charge modes, or phonons, possesses some experimental support. For example, prominent features in the electronic excitation spectrum of the HTSCs, as observed by angle-resolved photoemission ͑ARPES͒ ͑Refs. 2 and 3͒ and tunneling 4,5 experiments, were argued to arise from a coupling either to a magnetic resonance mode, 2,4 seen in inelastic-neutron-scattering experiments, 6-8 or to phonons. 3,5 The interpretation of these experiments is further complicated by the coupling between various modes. 7,9 Clearly, new experiments are required that can unambiguously identify the collective mode giving rise to the complex behavior of the HTSCs.In this article, we propose such an experiment based on the idea that different collective modes, when pinned by impurities, exert qualitatively different effects on the local electronic structure of a d x 2 −y 2-wave superconductor. These effects can be measured via scanning tunneling spectroscopy ͑STS͒ and hence allow us to directly identify the nature of the pinned mode. In particular, we show that the pinning of spin ͑charge͒ modes by impurities induces static spin ͑charge͒-density droplets which act as scattering potentials for the fermionic degrees of freedom and thereby affect the superconductor's local density of states ͑LDOS͒. Indeed, static spin droplets around Ni and Zn impurities have been observed in nuclear-magnetic-resonance ͑NMR͒ experiments. 10-13 By using the T -matrix 14,15 and Bogoliubov-de Gennes ͑BdG͒ ͑Ref. 16͒ formalisms, we demonstrate that spin and charge droplets lead to qualitatively different fingerprints in the LDOS. For example, in contrast to a pinned charge mode, a pinned ͑antiferromag-netic͒ spin mode prevents the creation of resonant impurity states, leads to complementary spatial patterns in the spinresolved LDOS, and gives rise to a strong magnetic-field dependence of the LDOS. These differences are a direct consequence of the modes' quantum numbers and momentum structures, and thus are robust features that are insensitive to the detai...