Department of Physics | University of Florida

Electronic Disorder

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.

Disorder in unconventional superconductors

All materials contain defects, and d-wave superconductivity is particularly sensitive to disorder. Simple nonmagnetic defects can break pairs in a d-wave superconductor, in contrast to a conventional superconductor. In addition, the physics of disordered interacting electrons is a fundamental unsolved problem in condensed matter physics. This is why we study this problem, despite (or perhaps because of) Pauli's remark (right).

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 Tc 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

Bogoliubov-de Gennes + Wannier method of visualizing STM data: BSCCO

Theoretical calculations of STM images on cuprate superconductors have been confined almost exclusively to models of electrons hopping on a square lattice corresponding to the Cu sites in the CuO2 plane; this is a clear disadvantage. We developed a method that started with the Bogoliubov-de Gennes lattice calculations and used the Wannier functions generated in the process of downfolding a renormalized DFT band structure onto a tight-binding model to calculate the continuum instead of the lattice Green's function. The crucial aspect was found to be the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. The results compare nearly perfectly to experimental findings that have puzzled the community for more than 10 years.

dx2-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.

Ab initio Wannier-based approach to disordered electronic structure

In most cases when DFT groups try to simulate doped or disordered materials, disorder is treated on the average by virtual crystal approximation or similar. One can in principle perform crude disorder averages by doing many DFT calculations with large supercells and then averaging over them, but these methods are very expensive. Recently Tom Berlijn and Wei Ku pioneered a method to downfold a few DFT calculations using supercells onto tight-binding models, and then disorder average over impurity supercells, yielding a relatively cheap rendition of the disorder-averaged bandstructure or self-energy. The Hirschfeld group and Ku worked together to apply these ideas to Fe-based superconductors. Right is one example, from the intrinsically disordered material KFe2Se2, which has a rather conventional pnictide Fermi surface except the hole pockets have been moved below the Fermi level. The parent compound has a set of ordered Fe vacancies in a root-5 by root-5 structure. The DFT calculation of the Fermi surface of this material, K2Fe4Se5, is shown at right, and is rather complex. When one disorder averages over the Fe vacancies, however, the simple effective Fermi surface is obtained ( Berlijn et al., PRL 109, 147003 (2012)). surface on the far right is obtained.

Fermi surface of disordered KFe2Se2

Tc suppression and other disorder effects in Fe-based superconductors

Even after several years of intensive study, there is relatively little direct evidence for sign-changing order parameters predicted by theories of pairing due to repulsive electronic interactions, and some theoretical work (Kontani) to suggest that orbital fluctuations are important in these systems, and lead to conventional s-symmetry (s++) pairing. The critique provided by these alterative approaches includes the claim that impurities are observed suppress Tc more slowly than one would expect in a system where the order parameter changed sign significantly. To counter this claim, the Hirschfeld group performed explicit calculations of Tc relative to an experimentally observable measure of disorder, the residual resistivity change, and showed that "slow" suppression is quite possible if interband scattering is weak. We also showed that if the system has nodes, a possible strange evolutionof the low-energy quasiparticle structure is possible, whereby the residual DOS at the Fermi level initially increases, then vanishes, then reappears as bound states are formed-only if the system is s+/- . This behavior has been observed in the magnetic penetration depth of electron-irradiated samples of BaFe2(As1-xPx)2 by the Kyoto group.

Suppression of Tc 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) )

© 2015 Peter J. Hirschfeld. All rights reserved.

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