Impurity States and Interlayer Tunneling in High Temperature Superconductors

Abstract

We argue that the scanning tunneling microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tunneling matrix elements. We find that the optimal tunneling path between the STM tip and the metal (Cu, Zn, or Ni) Although it appears that on a gross scale these findings can be understood in terms of a conventional d-wave superconductor perturbed by potential scattering, upon closer inspection problems of principle seem to arise. The impurity states observed by STM are characterized by two main features: (1) energy and width of the impurity-induced resonance in the density of states (DOS), and (2) the spatial structure of the resonance. While the DOS seems to be satisfactorily described by a single-site impurity model [3], the real space distribution of intensity cannot be fit by this model. The main problem with the Zn impurity image seen in the STM experiments is that the intensity of the signal on the impurity site is very bright, which is at odds with the unitary scattering off Zn. We remind the reader that Zn 21 has a closed d shell and hence, exactly on the impurity site the scattering potential is very strong. Unitary scattering is equivalent to the hard wall condition for the conduction states and therefore no or very little intensity of electron states is expected on the Zn site. A similar problem arises also with explaining the Ni-induced resonance.Here we demonstrate that these problems find a natural resolution in terms of the specific way in which the local density of states of the cuprate planes is probed in the STM experiments. We argue that the quantum-mechanical nature of the tunneling from the STM tip into the Cu-O layer that hosts impurity requires tunneling through the uppermost insulating Bi-O layer which effectively filters the signal. Surprisingly, similar filtering should also take place even in the case of "direct" tunneling into Cu-O plane. Such nonlocal tunneling has profound consequences for the real space image of the impurity state seen by STM.There are two major types of tunneling routes between the STM tip and the conducting orbitals in the Cu-O plane:

Impurity resonances and the origin of the pseudo-gap

“…The tunnelling filter shifts the LDOS maximum from the nearest neighbors to the impurity site and induce a second maximum on the nextnearest neighbors. This weight redistribution is identical to the situation in the DSC phase [8]. Thus when comparing Fig.…”

“…Here {i} denotes the set of lattice sites hosting the impurities and U i is the strength of the corresponding effective potential. In agreement with the above discussion the impurities are modelled with a potential, U = −15t, corresponding to -4.5eV, which generates resonances at a few meV for a single nonmagnetic impurity [8]. The large scale of this potential renders the effects on the LDOS from corrections to other energy scales around the impurity site less important.…”

“…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.…”

“…Any difference in the impurity modified LDOS between the DSC and DDW states may reveal the hidden DDW order and distinguish between the scenario of preformed pairs versus staggered orbital currents as the origin for the pseudo-gap state [15]. Recently, there has been several other proposals to probe the DDW order in the cuprates [14,16].In attempting to make better contact to the experiments we include the tunneling through excited states from the CuO 2 planes to the BiO layer probed by the STM tip [8]. This effect modifies the LDOS, ρ(r, ω) = n |ψ n (r)| 2 δ(ω − n ), by including the four nearest Cu…”

“…In attempting to make better contact to the experiments we include the tunneling through excited states from the CuO 2 planes to the BiO layer probed by the STM tip [8]. This effect modifies the LDOS, ρ(r, ω) = neighbors in the underlying CuO 2 plane, ψ n (r) −→ ψ n (r + e x )+ψ n (r−e x )−ψ n (r+e y )−ψ n (r−e y ).…”