2D map of the magnitude of the spectral gap on the surface of Bi-2212, a high-Tc cuprate superconductor. The red dots represent O dopant atoms, which are also imaged.

A new wrinkle is introduced when one studies superconductors with sign-changing order paramters
on distinct Fermi surface sheets, as appears to be realized in the Fe-based superconductors, for
example. If a so-called s_{+/-} state is realized, with + gap on one pocket and - gap on
another, * intraband* scattering doesn't affect the gap ("Anderson's theorem"), but *interband*
scattering can break pairs. The effect on T_{c} was calculated relative
to the increase of residual resistivity in Wang et al, Phys. Rev. B
87, 094504 (2013). More information is provided below.

Scanning Tunneling Microscopy (STM) has always provided essential insight into the local impurity states on the surfaces of metals and superconductors. In the case of superconductors, until recently modeling was restricted to lattice simulations, where resolution was much lower than actual (subatomic) experimental resolution. We recently pioneered a technique to image impurity states using the Wannier function information typically discarded in the derivation of the tight-binding Hamiltonian (Choubey et al, Phys. Rev. B 90, 134520 (2014)), see below.

In recent years, the Hirschfeld group also been interested in the role of residual interactions in the superconducting state and their interplay with disorder. In particular, many unconventional superconducting materials have strong antiferromagnetic correlations which give rise to magnetic droplets around impurities of size equal to the antiferromagnetic correlation length. When these droplets overlap, long range order can be created. Many of these phenomena were reviewed in a paper (Rev. Mod. Phys. 81, 45 (2009)) written with the Orsay group of Henri Alloul, Julien Bobroff, and Marc Gabay. A picture of a magnetic droplet is shown on the right.

Wolfgang Pauli: "Solid state physics is `dirty physics'"

magnetic droplet induced around impurity

d_{x2-y2} Wannier function for BSCCO-2212, cut 5 A above the surface of the sample.

Top: conductance map at resonance for Zn impurity in BSCCO. Bottom: QPI map of weak scatterer.

Fermi surface of disordered
KFe_{2}Se_{2}

Suppression of T_{c} in s_{+/-} superconductor depending on
the ratio of inter to intraband
scattering u/v between two Fermi surfaces, vs. residual resistivity due
to disorder (Wang
et al., Phys. Rev. B 87, 094504 (2013) )