We study the impurity effects on the transition temperature Tc with use of the T-matrix approximation. We propose a way to visualize the multi-orbital effect by introducing the hybridization function characterizing the multi-orbital effect for the impurity scattering. Characterizing function does not depend on the superconducting pairing symmetry, since this function is defined by the eigenvectors in normal states. The result indicates that an impurity-robust superconductivity does not necessarily imply a sign- preserving pairing. Visualizing the hybridization effect in the effective five-band model for LaFeAsO, we show that the impurity effect on Tc is relatively weaker than that in single-band models.
We investigate the impurity scattering rates for quasi-particles in vortex cores of sign-reversing s-wave superconductors as a probe to detect the internal phase difference of the order parameters among different Fermi surfaces. The impurity scattering rates and coherence factors are related to quasiparticle interference effect by the scanning tunneling microscopy and spectroscopy technique. With use of the Born and Kramer-Pesch approximations for the Andreev bound states, we show that the sign-reversed forward scatterings are dominant in vortex cores. Owing to the coherence factor in vortex c…
To understand the impurity effect on Tc in FeAs superconductors, we analyze a simple two-band BCS model with repulsive interband interaction. The realized fully-gapped superconducting state with sign reversal, which is predicted by spin fluctuation theories in this compound, is suppressed by impurities due to the interband hopping of Cooper pairs, if the interband impurity scattering $I'$ is equal to the intraband one $I$. When $|I'/I| < 1$, in highly contrast, Tc is almost unchanged by strong impurity scattering since the interband scattering is almost prohibited by the multiple scattering ef…
The sign-reversing fully gapped superconducting state, which is expected to be realized in oxypnictide superconductors, can be prominently affected by nonmagnetic impurities due to the interband scattering of Cooper pairs. We study this problem based on the isotropic two-band BCS model: In oxypnictide superconductors, the interband impurity scattering $I'$ is not equal to the intraband one $I$. In the Born scattering regime, the reduction in Tc is sizable and the impurity-induced density of states (DOS) is prominent if $I\sim I'$, due to the interband scattering. Although impurity-induced DOS …
We explain that the study of impurity effect in iron pnictides are correctly calculated based on the T-matrix approximation, contrary to the Comment by Bang. The replacement T with T-I proposed by Bang breaks the perturbation theory and is therefore erroneous.
We pointed out that the main claim of Ref.[1] that the presence of the orbital degree of freedom is essential to describe the correct impurity effects for Iron-based superconductors is incorrect and demonstrated the equivalent results of Tc suppression due to impurities by both the band basis model and the orbital basis model.
Based on the five-orbital model, we study the effect of local impurity in iron pnictides, and find that the interband impurity scattering is promoted by the d-orbital degree of freedom. This fact means that the fully-gapped sign-reversing s-wave state, which is predicted by spin fluctuation theories, is very fragile against impurities. In the BCS theory, only 1% impurities with intermediate strength induce huge pair-breaking, resulting in the large in-gap state and prominent reduction in Tc, contrary to the prediction based on simple orbital-less models. The present study provides a stringent …
Thermal transport measurements have been performed on single-crystalline Co-doped BaFe2As2 down to 0.1 K and under magnetic fields up to 7 T. Significant peak anomalies are observed in both thermal conductivity and thermal Hall conductivity below Tc as an indication of the enhancement of the quasiparticle mean-free path. Moreover, we find a sizable residual T-linear term in thermal conductivity, possibly due to a finite quasiparticle density of states in the superconducting gap induced by impurity pair breaking. Our findings support a pairing symmetry compatible with the theoretically predicte…
A single impurity problem is investigated for multiband s-wave superconductors with different sign order parameters (+-s-wave superconductors) suggested in Fe-pnictide superconductors. Not only intraband but also interband scattering is considered at the impurity. The latter gives rise to impurity-induced local boundstates close to the impurity. We present an exact form of the energy of the local boundstates as a function of strength of the two types of impurity scattering. The essential role of the impurity is unchanged in finite number of impurities. The main conclusions for a single impurit…
What is the fundamental reason for Hall Anomaly in Type II Superconductors: Independent Vortex Dynamics Effect or a Manifestation of Vortex Many-Body Effect? For a long time researchers in this field had not realized the importance of vortex many-body effects in the understanding of the so-called anomalous Hall effect. In this note I give a brief account of the situation in the light of a recent Phys Rev Lett.
We respond to P. Ao's comment in arXiv:1907.09263, which suggests that vortex many-body effects are the origin of Hall sign reversal in few-unit-cell thick Bi-2212 cuprate crystals (Phys. Rev. Lett. 122, 247001 (2019)). Our experimental results are incompatible with the theoretical predictions detailed in Ao's comment.
We discuss the surface Andreev bound states in Fe-based superconductors with the use of an effective five-band model and investigate the surface-angle dependence of the tunneling spectroscopy by a quasiclassical approach for an isotropic and an anisotropic /pm s-wave gap superconductivity. We show that information on the normal state is important for the Andreev bound state and its peak positions do not depend on the gap amplitude anisotropy.
We report an 75As-nuclear quadrupole resonance (NQR) study on heavily electron-doped LaFeAsO_1-xF_x(La1111) with Tc=5 K. Nuclear spin relaxation rate (1/T1) measurement has revealed that a Hebel-Slichter (HS) peak partially recovers in heavily electron-overdoped regimes where the nesting condition of hole and electron Fermi surfaces(FSs) becomes significantly worse. This is in contrast to previous results reported in optimally doped La1111 with Tc=28 K where a lack of the HS peak was reported. It indicates that the interband scattering between the hole and electron FSs is strongly suppressed b…
We argue that the newly discovered superconductivity in a nearly magnetic, Fe-based layered compound is unconventional and mediated by antiferromagnetic spin fluctuations, though different from the usual superexchange and specific to this compound. This resulting state is an example of extended s-wave pairing with a sign reversal of the order parameter between different Fermi surface sheets. The main role of doping in this scenario is to lower the density of states and suppress the pair-breaking ferromagnetic fluctuations.
To understand the nematicity in Fe-based superconductors, nontrivial $k$-dependence of the orbital polarization ($ΔE_{xz}(k)$, $ΔE_{yz}(k)$) in the nematic phase, such as the sign reversal of the orbital splitting between $Γ$- and X,Y-points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole- and electron-pockets are elongated along the $k_y$- and $k_x$-axes respectively, consistently with experi…
The low energy band structure of the FeAs based superconductors is fitted by a tight binding model with two Fe ions per unit cell and two degenerate orbitals per Fe ion. Based on this, superconductivity with extended s-wave pairing symmetry of the form $\cos k_x +\cos k_y$ is examined. The local density of states near an impurity is also investigated by using T-matrix approach. For the nonmagnetic scattering potential, we found that there exist two major resonances inside the gap. The height of the resonance peaks depends on the strength of the impurity potential. These in-gap resonances are o…
We perform large-scale numerical calculations self-consistently solving the Bogoliubov-de Gennes (BdG) equations in the magnetic field together with random impurities to directly demonstrate the typical quasi-particle interference (QPI) in the presence of vortices as observed by scanning tunneling microscopy/spectroscopy experiments in unconventional superconductors. The calculations reveal that vortex itself never works as a scatter causing the QPI pattern but vortex core containing impurity brings about the enhancement of the sign-preserving QPI peaks. Its origin is Andreev bound-states dist…
The insertion of a magnetic impurity in a superconductor induces a first order quantum phase transition as the coupling to the electronic spin density increases. As the transition is crossed, a discontinuity is exhibited by various quantities, like the total spin density, the total gap function and the gap function at the impurity location. The location of other quantum phase transitions have been detected by singularities in entanglement measures of the system. In this work we show that the single-site and two-site von Neumann entropies, the mutual information and the Meyer-Wallach measure sh…
We have investigated the in-gap bound states (IGBS) induced by a single nonmagnetic impurity in multiband superconductors with incipient bands. Contrary to the naive expectation, we found that even if the superconducting (SC) order parameter is sign-preserving s-wave on the Fermi surfaces, the incipient bands may still affect the appearance and locations of the IGBS, although the gap between the incipient bands and the Fermi level is much larger than the SC gap. Therefore in scanning tunneling microscopy experiments, the IGBS induced by a single nonmagnetic impurity are not the definitive evid…
We study a single impurity effect on the local density of states in a d-wave superconductor accounting for the momentum-dependent impurity potential. We show that the anisotropy of the scattering potential can alter significantly the spatial dependence of the quasiparticle density of states in the vicinity of the impurity.
We study the Kondo physics of a quantum magnetic impurity in two-dimensional topological superconductors (TSCs), either intrinsic or induced on the surface of a bulk topological insulator, using a numerical renormalization group technique. We show that, despite sharing the p + ip pairing symmetry, intrinsic and extrinsic TSCs host different physical processes that produce distinct Kondo signatures. Extrinsic TSCs harbor an unusual screening mechanism involving both electron and orbital degrees of freedom that produces rich and prominent Kondo phenomena, especially an intriguing pseudospin Kond…
We investigate the Josephson transport through a thin semiconductor barrier containing impurity centers with the on-site Hubbard interaction $u$ of an arbitrary sign and strength. We find that in the case of the repulsive interaction the Josephson current changes sign with the temperature increase if the energy of the impurity level $ε$ (measured from the Fermi energy of superconductors) falls in the interval $(-u,0)$. We predict strong temporal fluctuations of the current if only a few centers present within the junction. In the case of the attractive impurity potential ($u<0$) and at low tem…
Recent experiments reported the puzzling zero energy modes associated with ferromagnetic impurities in some iron-based superconductors with topological band structures. Here, we show that the sufficiently strong exchange coupling between a ferromagnetic impurity and substrate can trigger a quantum phase transition, beyond which, the phase of the topological surface superconducting order parameter around the impurity acquires a sign-change. In such a case, we prove that a Kramers degenerate pair of Majorana modes can be induced at the boundary separating the two sign-change regimes and trapped …
Probing Sign-Changing Order Parameters via Impurity States in unconventional superconductors: Implications for La$_3$Ni$_2$O$_7$ Superconductors with interlayer pairing
Tunneling conductance spectra between a normal metal / d-wave superconductor junction under the presence of bulk impurities in the superconductor are studied. The quasiclassical theory has been applied to calculate the spatial variation of the pair potential and the effect of impurity scattering has been introduced by t-matrix approximation. The magnitude of a subdominant s-wave component at the interface is shown to robust against the impurity scattering while that for a subdominant $d_{xy}$-wave component is largely suppressed with the increase of the impurity scattering rate. The zero-bias …
We investigate the role of a finite potential range of a nonmagnetic impurity for the local density of states in a d_{x^2-y^2} superconductor. Impurity induced subgap resonances are modified by the appearance of further scattering channels beyond the $s$--wave scattering limit. The structure of the local density of states (DOS) in the vicinity of the impurity is significantly enhanced and therefore improves the possibility for observing the characteristic anisotropic spatial modulation of the local DOS in a d_{x^2-y^2} superconductor by scanning tunneling microscopy.
We fabricate van der Waals heterostructure devices using few unit cell thick Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ for magnetotransport measurements. The superconducting transition temperature and carrier density in atomically thin samples can be maintained to close to that of the bulk samples. As in the bulk sample, the sign of the Hall conductivity is found to be opposite to the normal state near the transition temperature but with a drastic enlargement of the region of Hall sign reversal in the temperature-magnetic field phase diagram as the thickness of samples decreases. Quantitative analysis of …
Multiband superconductivity with dominant two-gap features are recently proposed to challenge the earlier accepted nodal $d$-wave pairing in the first unconventional superconductor CeCu$_{2}$Si$_{2}$. Here we obtain multiband Fermi-surface topology of CeCu$_{2}$Si$_{2}$ via first-principles calculations, and study the problem within an effective two hybridization band model including detailed band-structure. Within T-matrix approximation, our calculations reveal that different pairing candidates could yield qualitatively distinct features characterised by impurity-induced bound states. Except …
A short review of the optical and far-infrared measurements on MgB$_{2}$ is given. Multiband and multigap effects are analyzed by comparing optical properties with other experiments and {\em ab initio} calculations. The covered topics are: the plasma frequency, electron-phonon interaction, impurity scattering, the effects of C and Al substitution, interband transitions and the far-infrared signatures of the superconducting gaps.
The effect of weak anisotropic (momentum-dependent) impurity scattering in unconventional superconductors has been investigated. It is shown that the anisotropic scattering can lead either to a small reduction or a small enhancement of the isotropic pair-breaking effect. The influence of the anisotropy of the scattering potential becomes significant for the order parameters with large Fermi surface average values. In that case an unexpected enhancement (up to 10%) of the critical temperature over the critical temperature in the absence of impurities is predicted for a small impurity concentrat…
The pointlike impurity scattering is studied for a superconductor with different pairing symmetries based on a minimal two band model proposed by S. Raghu $et$ $al.$ [Phys. Rev. B {\bf 77}, R220503 (2008)], and the self-consistent Bogoliubov-de Gennes equations. Two intra-gap resonance peaks are found at or near the nonmagnetic impurity site for a typical $s_{x^2y^2}$ symmetry and strong scattering potentials. Such intra-gap resonance peaks are absent for the sign unchanged s-wave and $d_{x^2-y^2}$-wave order parameter. Thus we propose that a non-magnetic impurity with strong scattering potent…
By measuring the spatial distribution of differential conductance near impurities on Fe sites, we have obtained the quasi-particle interference (QPI) patterns in the (Li$_{1-x}$Fe$_x$)OHFe$_{1-y}$Zn$_y$Se superconductor with only electron Fermi surfaces. By taking the Fourier transform on these patterns, we investigate the scattering features between the two circles of electron pockets formed by folding or hybridization. We treat the data by using the recent theoretical approach [arXiv:1710.09089] which is specially designed for the impurity induced bound states. It is found that the supercond…
We discuss the weak-coupling BCS theory of a superconductor with the impurities, accounting for their anisotropic momentum-dependent potential. The impurity scattering process is considered in the t-matrix approximation and its influence on the superconducting critical temperature is studied in the Born and unitary limit for a d- and (d+s)-wave superconductors. We observe a significant dependence of the pair-breaking strength on the symmetry of the scattering potential and classify the impurity potentials according to their ability to alter T_c. A good agreement with the experimental data for …
The effect of a nonmagnetic impurity on the subgap electronic spectrum in a d-wave superconductor in the Fulde-Ferrell-Larkin-Ovchinnikov state is investigated. In a pure system, the spatial variation of the order parameter (OP) of the FFLO state forms a two-dimensional lattice, and there exist two types of sub-gap quasi-particle states. Our numerical iterations indicate that an OP saddle point, and slightly less so energetically, an OP extremum favor to be pinned at the impurity site. The local density of states and the fixed-bias map reveal the subtle effects of an impurity on the subgap ene…
Recent experiments on Sr_2RuO_4 have indicated the presence of linear nodes in the superconducting order parameter. Among the possible spin triplet states, 2D p-wave superconductivity with E_u symmetry appears to be inconsistent with the experiments, whereas the 2D f-wave order parameter with B_1g x E_u symmetry turns out to be a more likely candidate. Here it is shown how the quasi-particle bound state wave functions around a single impurity provide a clear signature of the symmetry of the underlying superconducting order parameter.
The impurity effects are studied for the BiS_{2}- layered superconductors based on a two orbital model with the Bogoliubov-de-Gennes technique. The superconducting critical temperature (T_{c}) as a function of the mpurity concentration is calculated. Significant reduction of T_{c} is found for spin singlet nearest-neighboring paring d-wave state and the spin triplet next-nearest-neighboring (NNN) paring p-wave state, while no depression of T_{c} for isotropic s-wave state. The single impurity effects for various paring states are also explored. The impurity resonance peak in the local density …
We report theoretical and experimental studies of the effect of Zn-impurity in Fe-based superconductors. Zn-impurity is expected to severely suppress sign reversed s$_\pm$ wave pairing. The experimentally observed suppression of T$_c$ under Zn-doping strongly depends on the materials and the charge carrier contents, which suggests competition of $s_{++}$ and $s_{\pm}$ pairings in Fe-base superconductors. We study a model incorporating both $s_{++}$ and $s_{\pm}$ pairing couplings by using Bogoliubov de-Gennes equation, and show that the Zn-impurity strongly suppresses $s_{\pm}$ pairing and may…
Using both the self-consistent Bogoliubov-de Gennes formulation and non-self-consistent T-matrix approach, we perform a comprehensive investigation of the in-gap bound states induced by a localized single impurity in iron-based superconductors. We focus on studying signatures associated with the unconventional sign-changed s-wave pairing symmetry. For a non-magnetic impurity, we find that there are two in-gap bounds, symmetric with respect to zero energy, only in the sign changed s-wave pairing state, not in the sign-unchanged s-wave state, due to the existence of non-trivial Andreev bound sta…
In a recent Letter [PRL 103, 186402 (2009)], the energy band structure of Fe-As-based superconductors is fitted with a tight-binding model with two Fe ions per unit cell and two degenerate xz and yz orbitals per Fe ion. The author claims that the proposed model, which differs markedly from a model previously used by other authors for the same two orbitals in the same compounds, possesses the symmetry required to describe the Fe-As planes in iron-pnictide superconductors. In this comment we argue that this is not the case.
We report muon-spin relaxation measurements of highly homogeneous samples of FeAs and FeAs2, both previously found as impurity phases in some samples of recently synthesized pnictide superconductors. We observe well defined muon precession in the FeAs sample with two precession frequencies of 38.2(3) and 22.7(9) MHz at 7.5 K, with the majority of the amplitude corresponding to the lower frequency component. In FeAs2 we confirm previous measurements showing that no long-ranged magnetic order occurs above 2 K and measure the muon spin relaxation rate, which increases on cooling. Our results excl…
We discuss the universal theory of localized impurities in the paramagnetic state of 2D antiferromagnets where the spin gap is assumed to be significantly smaller than a typical exchange energy. We study the impurity spin susceptibility near the host quantum transition from a gapped paramagnet to a Neel state, and we compute the impurity-induced damping of the spin-1 mode of the gapped antiferromagnet. Under suitable conditions our results apply also to d-wave superconductors.
We argue that the Scanning Tunneling Microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tunneling matrix elements. We find that the optimal tunneling path between the STM tip and the metal (Cu, Zn, or Ni) $d_{x^2 - y^2}$ orbitals in the Cu-O plane involves intermediate excited states. This tunneling path leads to the four-fold nonlocal filter of the impurity state in C…
The concepts, which have traditionally been useful in understanding the effects of the electron--phonon interaction in optical spectroscopy, are based on insights obtained within the infinite electronic band approximation and no longer apply in finite band metals. Impurity and phonon contributions to electron scattering are not additive and the apparent strength of the coupling to the phonon degrees of freedom is substantially reduced with increased elastic scattering. The optical mass renormalization changes sign with increasing frequency and the optical scattering rate never reaches its high…
We apply the unbiased weak-coupling continuous time quantum Monte Carlo (CTQMC) method to review the physics of a single magnetic impurity coupled to s-wave superconducting leads described by the BCS reduced Hamiltonian. As a function of the superconducting gap $Δ$, we study the signature of the first order transition between the singlet and doublet (local moment) states on various quantities. In particular we concentrate on the Josephson current with 0 to $π$ phase shift, the crossing of the Andreev bound states in the single particle spectral function, as well as the local dynamical spin str…
Non-magnetic impurities in iron-based superconductors can provide an important tool to understand the pair symmetry and they can influence significantly the transport and the superconducting behaviour. Here, we present a study of the role of strong impurity potential in the Fe plane, induced by Cu substitution, on the electronic and superconducting properties of single crystals of FeSe. The addition of Cu quickly suppresses both the nematic and superconducting states, and increases the residual resistivity due to enhanced impurity scattering. Using magnetotransport data up to 35 T for a small …
We present a systematic investigation of the effects of "nonmagnetic" impurities on the $s$-wave BCS-BEC crossover in atomic Fermi gases within a pairing fluctuation theory. Both pairing and impurity scattering $T$-matrices are treated self-consistently at the same time. While the system is less sensitive to impurity scattering in the Born limit, for strong impurity scatterers, both the frequency and the gap function are highly renormalized, leading to significant suppression of the superfluid $T_c$, the order parameter and the superfluid density. We also find the formation of impurity bands a…
