Magnetic impurity induced states in superconducting Bi$_{2}$Sr$_{2}$CaCuO$_{8+\delta}$

We revisit the Ni impurity problem in superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (BSCCO-2212) using the Bogoliubov- de Gennes (BdG)-Wannier approach [1, 2]. We solve the self-consistent BdG equations on a square lattice and use first principle-based Wannier function to compute the local density of states (LDOS) with sub-atomic resolution in the vicinity of a magnetic impurity. We find two spin-resolved virtual bound states localized around the impurity position. The spatial LDOS patterns at the resonance energies are found to be in excellent agreement with STM experiment [3], and can be understood by accounting for the tails of Cu Wannier function.\\[4pt] [1] Peayush Choubey, T. Berlijn, A. Kreisel, C. Cao and P. J. Hirschfeld, Phys. Rev. B. 90, 134520 (2014).\\[0pt] [2] A. Kreisel, Peayush Choubey, T. Berlijn, B. M. Andersen and P. J. Hirschfeld, arxiv: 1407.1846 (2014).\\[0pt] [3] E. W. Hudson, K. M. Lang, V. Madhavan, S. H. Pan, H. Eisaki, S. Uchida and J. C. Davis, Nature, 411, 920 (2001).