Dirk Morr: "Impurities, collective modes, and magnetic droplets in the cuprate superconductors"

Dirk Morr noted that there has been much interest recently in analyzing the spectroscopic signatures of collective modes in superconductors. He pointed out that if a collective mode is close to critical, pinning it on impurities creates a local droplet of locally ordered state, and cited Alloul/Bobroff NMR experiments in Ni doped high-Tc as an example. Dirk therefore suggested that STM spectra obtained near impurity sites depend on the type of the collective mode, and have the potential to distinguish between different types of short-range order.

He considered two examples of such droplets: small-q charge density wave order, and the spin-density wave order at Q=(pi.pi). The interaction with the conduction electrons is local, and the question Dirk asked whether a spin droplet looks different from a charge droplet when viewed from an STM tip. He showed the results of both T-matrix and Bogoliubov-de Gennes calculations for the spectra on the impurity site. An important point is that the local value of the spin/charge polarization that enters the calculations of the density of states is proportional to the static part of the spin/charge susceptibility, and therefore one may read off spatial dependence of the susceptibility.

The spectra for the two cases are different. The charge droplet is essentially an extended potential impurity, the potential varies slowly, and therefore in this case there exists a resonance state inside a gap. In contrast, for the AFM SDW droplet the oscillatory spin polarization (on the scale of the lattice spacing) reduces the scattering, and leads to overall suppression of the density of states with no sign of the local resonant state on the impurity site. Dirk emphasized that these qualitative different effects of charge and spin droplets on the local density of states allow one to identify the nature of collective modes via STM experiments.

Dirk also pointed out that for the spin droplet spin-polarized tunneling will give unequivocally distinct results from the charge droplet, and discussed with Hartmut Monien what the time scale for such measurements may be.