Zero temperature phase diagram of a d-wave superconductor with Anderson impurities

Magnetic and nonmagnetic impurities in correlated electron systems are an important probe of the properties of the host material. There is large and growing body of research on impurities in high-temperature superconductors.[1, 2] The refinement of experimental techniques probing local properties stimulated the theoretical work on defects in those systems. The investigation of the effects of Zn, Ni and other dopants in YBCO and BSCCO answered some important questions and raised new ones. Measurements on some compounds show that the superconducting order parameter is not uniform over the entire sample.[3]-[7] Scanning tunnelling spectroscopy measurement showed that modulation of the structure of Bi2Sr2CaCu2O8+x is correlated locally with the magnitude of the energy gap.[8] The spatial variation of ∆0(r) may result e.g. from the structural supermodulation affecting the strength of local pairing interaction.[9] The intrinsic spatial variation of the superconducting gap raises the possibility of observing impurity states on both sides of the quantum phase transition in the same sample. Theoretical work on magnetic impurities in systems with reduced density of states near the Fermi surface[11]-[18] showed that the resonant impurity states may be viewed as a sensitive probe of the superconducting state. If the coupling to the magnetic impurity is small compared to the energy scale associated with the gap, the impurity is decoupled from conduction electrons. This impurity quantum phase transition occurs at finite coupling, provided the particle-hole symmetry is broken, and may be studied by STM techniques. The low-energy behavior of the model depends on the exponent r in the conduction electron density of states, N(ǫ) ∼ |ǫ|, where the Fermi level is fixed at ǫ = 0.