Strong correlations generically protectd-wave superconductivity against disorder

Abstract

We address the question of why strongly correlated d-wave superconductors, such as the cuprates, prove to be surprisingly robust against the introduction of non-magnetic impurities. We show that, very generally, both the pair-breaking and the normal state transport scattering rates are significantly suppressed by strong correlations effects arising in the proximity to a Mott insulating state. We also show that the correlation-renormalized scattering amplitude is generically enhanced in the forward direction, an effect which was previously often ascribed to the specific scattering by charged impurities outside the copper-oxide planes. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Introduction.-For many classes of unconventional superconductors, such as the cuprates 1-4 , heavy fermion superconductors 5 , organic materials 6,7 and iron pnictides 8 , electronic interactions are believed to be essential. Among the many puzzling features of these systems is their behavior in the presence of disorder 9,10 . In weakly interacting d-wave superconductors, Abrikosov-Gor'kov (AG) theory predicts that a small concentration of non-magnetic impurities should bring the transition temperature T c to zero. In the case of the cuprates, however, experiments have shown that these d-wave superconductors are very robust against disorder 3,11-13 . This feature was frequently ascribed to scattering by charged offplane impurities, which is mostly in the forward direction (see, e.g., 14 ). It has also been attributed to the frequency dependence of the pairing interactions in spin-fluctuation theories 15 . The puzzle was partially clarified, however, once strong electronic interactions were shown to give rise to the impurity screening effects seen in these experiments, especially as captured by the Gutzwiller-projected wave function [16][17][18][19][20][21][22][23][24] . Despite this progress, it would be desirable to understand both qualitatively and quantitatively whether disorder screening has any significant influence on T c as well as on the normal state transport properties. In other words, can a physically transparent answer be given to the following question: how do strong correlations and Mott physics affect the predictions of AG theory?The transition temperature in the under-doped region of the hole-doped cuprates is believed to be influenced by phase fluctuations, various types of competing orders (such as chargeand spin-density waves), stripe formation, etc. Consequently, impurities act as nucleations centers, which complicates the analysis considerably. In the over-doped region, however, T c is dominated by the superconducting gap opening, thus offering a particularly favorable window into the interplay between disorder and interactions. This regime will be the focus of the present work.In the presence of impurities, the strongly correlated state readjusts itself and creates a renormalized disorder potential. In the dilute limit, the AG theory can be extended to describe the effect of this renormalized potential on T c degrad...

Effects of strong disorder in strongly correlated superconductors

“…A surprising result of RIMT [15,[26][27][28] is that in-spite of the d-wave nature of the order parameter, strong correlations make superconductivity robust up to moderate disorders. This is ascribed to the electronic repulsions that modify the hopping amplitudes based on local density and smear out charge accumulation near deep potential wells, leading to a much weaker effective disorder.…”

“…A semianalytic approach, where effects of projection are kept in terms of renormalization of Hamiltonian parameters, is the Gutzwiller approximation [24], which is known [25] to match the more sophisticated Monte Carlo results [22] for the homogeneous system. This approach is easily extended to inhomogeneous situations to get a renormalized inhomogeneous mean field theory (RIMT) [15,[26][27][28], which tries to capture effects of both strong correlations and disorder in the system.A surprising result of RIMT [15,[26][27][28] is that in-spite of the d-wave nature of the order parameter, strong correlations make superconductivity robust up to moderate disorders. This is ascribed to the electronic repulsions that modify the hopping amplitudes based on local density and smear out charge accumulation near deep potential wells, leading to a much weaker effective disorder.…”

“…A semianalytic approach, where effects of projection are kept in terms of renormalization of Hamiltonian parameters, is the Gutzwiller approximation [24], which is known [25] to match the more sophisticated Monte Carlo results [22] for the homogeneous system. This approach is easily extended to inhomogeneous situations to get a renormalized inhomogeneous mean field theory (RIMT) [15,[26][27][28], which tries to capture effects of both strong correlations and disorder in the system.…”

Unconventional Disorder Effects in Correlated Superconductors

“…[15,16] By contrast, for non-magnetic disorder the s± superconducting state is largely immune to disorder, in agreement with earlier one-band studies, finding that correlations enhance the screening of disorder potentials and thereby reduce pair-breaking and scattering rates compared to the non-interacting case. [17][18][19][20][21] In the current multi-orbital case, however, additional impuritygenerated bound states play an important unexpected role in supporting T c . This resilience to non-magnetic disorder is remarkable since favorable clusters of impurities locally pin magnetic order, eventually causing a volume-full inhomogeneous magnetic state which coexists with superconductivity.…”

“…How may one understand this result which appears at odds with the expectation that correlations screen disorder and limit their damaging effects? [17][18][19][20][21] The answer to this question necessitates a deeper understanding of correlation effects at both the local scale (immediate vicinity of the impurity sites) and non-local scale (inter-impurity regions). Both effects are intimately tied to the fact that magnetic impurity moments induce spin polarizations of the surrounding itinerant electrons m iµ , which renormalize the exchange coupling such thatH imp =Ĩ iµσ σS iµ c † iµσ c iµσ , wherẽ…”