Impurity resonances and the origin of the pseudo-gap

Abstract

We study the structure of resonance states localized around nonmagnetic impurities in the CuO 2 planes of the cuprate superconductors within a potential scattering formalism. In particular we show that strong quantum interference effects arise between several impurities. This interference can be utilized to distinguish the dwave superconducting state from the phase with d-density wave order. This is important if the origin of the pseudo-gap state in the underdoped regime of the High Tc superconductors is caused by preformed Cooper pairs or staggered orbital currents. Furthermore impurity interference can be utilized to reveal subdominant superconducting order parameters and to pose further constraints on the potential scattering scenario.For conventional superconductors Yu and Shiba[1] first showed that as a result of the interaction between a magnetic impurity and the spin density of the conduction electrons, a bound state located around the magnetic impurity is formed inside the gap in the strong-scattering (unitary) limit. For anisotropic superconductors a number of authors generalized the Yu-Shiba approach to study the effects of single impurities [2].Many important questions concerning the electronic structure of the High T c materials still need to be answered. The study of single impurity effects provide a promising path to yield some answers. This is mainly due to the large experimental progress in low temperature scanning tunneling microscopy (STM). In particular, STM measurements have provided detailed local density of states (LDOS) images around single nonmagnetic [3,4] (Zn) and magnetic [5] (Ni) impurities on the surface of the high temperature superconductor Bi 2 Sr 2 CaCuO 4+δ (BSCCO). More recently the energy dependence of the Fourier transformed LDOS images was measured in the superconducting state of optimally doped BSCCO[6]. The dispersive features were explained by elastic quasi-particle interference resulting from a single weak, nonmagnetic impurity [7]. This gives credence that a scattering potential picture can yield valuable predictions in the superconducting state of these materials. Furthermore, it was recently shown by Martin et al. [8] that both the energetics of the resonance state and its spatial dependence around a strong potential scatterer (e.g. Zn) can be accounted for by including the tunnelling (the filter) through excited states from the CuO 2 planes to the top BiO layer probed by the STM tip. In order to obtain agreement with the measured LDOS one needs to attribute a large negative potential to the Zn site in agreement with the filled d shell of this atom; the potential will strongly repel holes, i.e. attract the electrons.Experimentally there is also evidence from NMR measurements that magnetic moments are induced around nonmagnetic impurities [9]. In this paper we assume, however, that the large potential scattering off the impurity site itself is dominating the final LDOS.Future experimental ability to control the position of the impurities on the surface of a superconduc...