Unconventional Disorder Effects in Correlated Superconductors

Maria N. Gastiasoro, Fabio Bernardini, and Brian M. Andersen

Phys. Rev. Lett. 117, 257002 – Published 15 December 2016

Abstract

We study the effects of disorder on unconventional superconductors in the presence of correlations, and explore a novel correlated disorder paradigm dominated by strong deviations from standard Abrikosov-Gor’kov theory due to generation of local bound states and cooperative impurity behavior driven by Coulomb interactions. Specifically we explain under which circumstances magnetic disorder acts as a strong poison destroying high- $T_{c}$ superconductivity at the sub-1% level, and when nonmagnetic disorder, counterintuitively, hardly affects the unconventional superconducting state while concomitantly inducing an inhomogeneous full-volume magnetic phase. Recent experimental studies of Fe-based superconductors have discovered that such unusual disorder behavior seems to be indeed present in those systems.

Received 18 July 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.257002

Physics Subject Headings (PhySH)

Antiferromagnetism Impurities in superconductors Magnetic interactions Magnetic order Magnetism Multiband superconductivity Phase diagrams Superconducting order parameter Superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Maria N. Gastiasoro¹, Fabio Bernardini², and Brian M. Andersen¹

¹Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
²CNR-IOM-Cagliari and Dipartimento di Fisica, Università di Cagliari, 09042 Monserrato, Italy

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Vol. 117, Iss. 25 — 16 December 2016

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Images

Figure 1
Experimentally obtained superconducting $T_{c}$ and magnetic $T_{m}$ transition temperatures in OD La-1111 (a),(c) and Sm-1111 (b),(d) vs magnetic disorder (a),(b) and nonmagnetic disorder (c),(d). The data were adapted from Refs. [11, 12, 41, 42, 44].
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Figure 2
Superconducting critical temperature $T_{c}$ vs magnetic (a) and nonmagnetic (b) impurity concentrations. (a) Effect of electronic correlations on $T_{c} / T_{c}^{0}$ ( $T_{c}^{0} = 3.6 meV$ ), compare $u = 0$ and $u = 0.97$ , for a case with orbital independent impurities modeled by $I S_{μ} = 0.38 eV$ . The $u = 0$ curve agrees with standard AG theory (gray stars). (b) $T_{c}$ (red squares) and magnetic critical temperature $T_{m}$ (green triangles) induced by nonmagnetic disorder. Dashed curve in (b) shows $T_{c}$ for the clean system $T_{c}^{0}$ where only a band-widening effect has been included (i.e. no disorder) as discussed in the main text.
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Figure 3
(a) Induced magnetic potential, $I_{ind} s_{i μ}$ , along a cut through a magnetic impurity and as a function of $u$ . Correlations renormalize local magnetic potentials as shown in (b) where the orange (blue) arrows show the induced (bare) parts for $u = 0.97$ . (c) Local suppression of $Δ_{i μ}$ relative to its value in the clean system $Δ_{μ}^{0}$ vs $u$ . (d) Real-space map of $Δ_{i μ} / Δ_{μ}^{0}$ in the presence of 0.55% magnetic disorder. The blue surface shows the suppression from only the bare moments, i.e. $u = 0$ , but self-consistently obtained gaps beyond AG theory. Including the local correlation-enhanced magnetic moments leads to the green surface, and only by including both local and nonlocal effects is superconductivity fully destroyed (orange). (e),(f) Real-space maps of the 0.55% (e) bare $I S_{μ}$ and (f) induced magnetic potential $I_{ind} s_{i μ}$ for $u = 0.97$ . For all results in this figure, the bare moments are the ones used in Fig. 2 and $μ = d_{x z}$ orbital.
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Figure 4
(a) Positions of a random set of 15% nonmagnetic disorder. The red tiles highlight favorable dimerlike arrangements, defined by all the impurity sites with an occupied NNN site but not more than one occupied NN site. (b) Real-space map of the LDOS of the $d_{3 z^{2} - r^{2}}$ orbital at $T > T_{c}$ at the Fermi level. (c) Local dipolar field $B (r) = \sum_{i} (m_{i} / | r_{i} |^{3})$ ( $r_{i}$ is the distance between the muon site $r$ and the moment position $m_{i}$ of the itinerant electrons) with orange (blue) color indicating regions with field strength larger (smaller) than 0.5 mT ( $- 0.5 mT$ ). (d) Real-space map of the dimer-induced magnetization of the $d_{3 z^{2} - r^{2}}$ orbital. (e) Average dimer concentration (blue dots) and the bandwidth renormalization parameter $1 / (1 + x)$ (orange circles) as a function of disorder concentration $x$ . (f) Superconducting order parameter of the $d_{3 z^{2} - r^{2}}$ orbital $Δ_{i d_{3 z^{2} - r^{2}}} / Δ_{d_{3 z^{2} - r^{2}}}^{0}$ relative to its value in the clean system. For all results in this figure, $V_{d_{3 z^{2} - r^{2}}} = 0.7 eV$ and $μ = d_{3 z^{2} - r^{2}}$ orbital.
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