We investigate effects of disorder on the density of states, the single particle response function and optical conductivity in multiband superconductors with s_{+-} symmetry of the order parameter, where s_{+-} -> s_{++} transition may take place. In the vicinity of the transition the superconductive gapless regime is realized. It manifests itself in anomalies in the above mentioned properties. As a result, intrinsically phase-insensitive experimental methods like ARPES, tunneling and terahertz spectroscopy may be used for revealing of information about the underlying order parameter symmetry.
We examine the effect of a single, non-magnetic impurity in a multiband, extended s-wave superconductor allowing for anisotropy of the gaps on the Fermi surfaces. We derive analytic expressions for the Green's functions in the continuum and analyse the conditions for the existence of sharp impurity-induced resonant states. Underlying band structure is more relevant for the multiband than for single band case, and mismatch between the bands generically makes the formation of the impurity states less likely in the physical regime of parameters. We confirm these conclusions by numerically solving…
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 impurity effects on the transition temperature Tc and the isotope effect are examined in multiband superconductors with magnetic and nonmagnetic impurities, where the effect of Coulomb repulsion is considered. It is shown that an internal transition of the superconducting state is induced by impurity doping, and that the transition is accompanied by a jump of the isotope-effect coefficient alpha. In particular, the transition is illustrated in a system with two electron bands. In some special cases, extended Abrikosov and Gor'kov (AG) equations for Tc and the expressions of the isotope-eff…
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 …
The optical conductivity of MgB$_2$ has been determined on a dense polycrystalline sample in the spectral range 6 meV - 4.6 eV using a combination of ellipsometric and normal incidence reflectivity measurements. $σ_{1}(ω)$ features a narrow Drude peak with anomalously small plasma frequency (1.4 eV) and a very broad "dome" structure, which comprises the bulk of the low-energy spectral weight. This fact can be reconciled with the results of band structure calculations by assuming that charge carriers from the 2D $σ$-bands and the 3D $π$-bands have principally different impurity scattering rates…
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…
We consider the effect of isotropic impurity scattering on the exotic superconducting states that arise from the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface contains inequivalent but degenerate pockets (e.g. around several points of high symmetry). As examples we look at CeCo$_2$, CeRu$_2$, and LaB$_6$; all of which have such Fermi surface topologies and the former exhibits unconventional superconducting behavior. We find that while these non s-wave states are suppressed by non-magnetic impurities, the suppression is much weaker than would be expec…
We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurit…
In multiband superconductors, multiple collective modes exist associated with the multiple order parameters. Oscillations of the amplitude and the relative phase of the order parameters are called Higgs and Leggett modes, respectively. Recently, it has been suggested that nonmagnetic impurity scattering would enhance nonlinear coupling between the Higgs mode and an electromagnetic wave with a frequency located in the superconducting gap region, while its effect on the Leggett mode is still unresolved. Here, we theoretically investigated the nonlinear optical response of multiband Bardeen-Coope…
We study inelastic (dynamical) impurity scattering effects in two-band superconductors with the same ($s_{++}$ wave) or different ($s_\pm$ wave) sign order parameters. We focus on the enhancement of the superconducting transition temperature $T_{\rm c}$ by magnetic interband scattering with the interchange of crystal-field singlet ground and multiplet excited states. Either the $s_{++}$-wave or $s_\pm$-wave state is favored by the impurity-mediated pairing, which depends on the magnetic and nonmagnetic scattering strengths derived from the hybridization of the impurity states with the conducti…
Motivated by the recent experimentally observed manifestations of the quantum critical point fluctuations in the thermodynamic properties of multiband superconductors, we derive a general expression for the Josephson current of various junctions between two superconductors in the phase of superconductivity coexistence with the spin-density-wave. We demonstrate that the critical current peaks at the quantum critical point that separates pure and mixed superconducting phases. We argue that our results are generic and, in particular, can be adopted to explain the recent observations of a nonmonot…
We report the results of an ab initio modeling of substitutional impurities such as zinc, copper and zirconium ions incorporated into the magnesium sublattice of MgB2. The goal of computational studies was to gain an atomistic understanding of how the structural and bonding properties of the local ionic environment are affected by a change in the host cation. The simulations performed for the given set of substituents indicate that at a low doping level, the induced lattice distortions and additional forces are noticeable small. At the same time, the electron redistributions around the impurit…
We study the vortex lattice in a two-dimensional s-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations self-consistently for the superconducting order parameter. We find that when spin-orbit coupling is relatively weak, one of the two underlying chiralities in the topological superconducting state can be strongly manifest in the vortex core structure and govern the response of the system to vorticity and a nonmagnetic impurity where the vortex is pinned. The Majorana zero mode in the vortex core is found to be robust ag…
We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the $s_\pm$ state with the sign-changing gaps. Scattering by nonmagnetic impurities leads to the change of sign of the smaller gap thus resulting in a transition from the $s_{\pm}$ to the $s_{++}$ state with the sign-preserving gaps. We show here that the transition is temperature-dependent, thus, there is a line of $s_\pm \to s_{++}$ transition in the temperature-disorder phase diagram. There exists a narrow range…
We study the generation of excitations due to an ''impurity''(static perturbation) placed into an oscillating Bose-condensed gas in the time-dependent trapping field. It is shown that there are two regions for the position of the local perturbation. In the first region the condensate flows around the ''impurity'' without generation of excitations demonstrating superfluid properties. In the second region the creation of excitations occurs, at least within a limited time interval, revealing destruction of superfluidity. The phenomenon can be studied by measuring the damping of condensate oscilla…
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 analyze how the magnetic disorder affects the properties of the two-band $s_\pm$ and $s_{++}$ models, which are subject of hot discussions regarding iron-based superconductors and other multiband systems like MgB$_2$. We show that there are several cases when the transition temperature $T_c$ is not fully suppressed by magnetic impurities in contrast to the Abrikosov-Gor'kov theory, but a saturation of $T_c$ takes place in the regime of strong disorder. These cases are: (1) the purely interband impurity scattering, (2) the unitary scattering limit. We show that in the former case the $s_\pm$…
We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from s_{+-} state to s_{++} state induced by interband impurity scattering. Using a Ginzburg-Landau theory, derived from microscopic equations, we demonstrate that close to T_c this transition is necessarily a direct one, but deeper in the superconducting state an intermediate complex state appears. This state has a distinct order parameter, which breaks the time-reversal symmetry, and is separated from the s_{+-} and s_{++} states by phase transitions. Based on our resul…
In multiband systems, such as iron-based superconductors, the superconducting states with locking and anti-locking of the interband phase differences, are usually considered as mutually exclusive. For example, a dirty two-band system with interband impurity scattering undergoes a sharp crossover between the $s_{\pm}$ state (which favors phase anti locking) and the $s_{++}$ state (which favors phase locking). We discuss here that the situation can be much more complex in the presence of an external field or superconducting currents. In an external applied magnetic field, dirty two-band supercon…
In high-superconducting transition temperature ($T_{\rm c}$) iron-based superconductors, interband sign reversal ($s_{\rm \pm}$) and sign preserving ($s_{\rm ++}$) $s$-wave superconducting states have been primarily discussed as the plausible superconducting mechanism. We study Co impurity scattering effects on the superconductivity in order to achieve an important clue on the pairing mechanism using single crystal Fe$_{1-x}$Co$_x$Se and depict a phase diagram of a FeSe system. Both superconductivity and structural transition / orbital order are suppressed by the Co replacement on the Fe sites…
A pronounced step-like (kink) behavior in the temperature dependence of resistivity $ρ(T)$ is observed in the optimally-doped $Sm_{1.85}Ce_{0.15}CuO_4$ thin films around $T_{sf}=87K$ and attributed to manifestation of strong spin fluctuations induced by $Sm^{3+}$ moments with the energy $\hbar ω_{sf}=k_BT_{sf}\simeq 7meV$. In addition to fluctuation induced contribution $ρ_{sf}(T)$ due to thermal broadening effects (of the width $ω_{sf}$), the experimental data are found to be well fitted accounting for residual (zero-temperature) $ρ_{res}$, electron-phonon $ρ_{e-ph}(T)=AT$ and electron-electr…
We report on novel superconducting characteristics of the heavy fermion (HF) superconductor CePt3Si without inversion symmetry through 195Pt-NMR study on a single crystal with T_c= 0.46 K that is lower than T_c= 0.75 K for polycrystals. We show that the intrinsic superconducting characteristics inherent to CePt3Si can be understood in terms of the unconventional strong-coupling state with a line-node gap below T_c= 0.46 K. The mystery about the sample dependence of T_c is explained by the fact that more or less polycrystals and single crystals inevitably contain some disordered domains, which …
Distinguishing impurity-induced bound states from Majorana-like zero-energy peaks in strained CsCa2Fe4As4F2 by scanning tunneling microscopy
Hefei National Research Center for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China（中国科学技术大学物理系和微尺度物质科学国家研究中心）；School of Physics, Zhejiang University（浙江大学物理学院）；New Cornerstone Science Laboratory, Hefei National Laboratory（合肥国家实验室新 cornerstone 科学实验室）
We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced in Phys. Rev. Lett. 108, 036803 (2012). We show how, in the presence of time-reversal symmetry, Z_2 invariants that distinguish between trivial and non-trivial quantum phases can be constructed by considering only one of the Kramers' sectors in which the Hamiltonian decouples into. We find that the main features identified in our original 2D setting remain qualitatively unchanged in 1D and 3D, with non-trivial topological superconducting phases supporting an odd number of Kramers' p…
We consider a model of multiband superconductivity, inspired by iron pnictides, in which three bands are connected via repulsive pair-scattering terms. Generically, three distinct superconducting states arise within such a model. Two of them are straightforward generalizations of the two-gap order parameter while the third one corresponds to a time-reversal symmetry breaking order parameter, altogether absent within the two-band model. Potential observation of such a genuinely frustrated state would be a particularly vivid manifestation of the repulsive interactions being at the root of iron-b…
I study the effects of disorder on the superconductivity of a three-band model with repulsive interband pairing. Such a model can support several possible superconducting order parameters, including a complex time-reversal symmetry breaking (TRSB) state. Impurity scattering suppresses the critical temperature of all these states, but the complex state survives, and remains a part of the phase diagram of the model even in the presence of moderate amount of disorder. This means that the TRSB states could be experimentally accessible in multiband materials like iron pnictides and chalcogenides.
Direct Evidence of Unconventional Superconductivity in Doped Kagome system RV$_3$Sb$_5$
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
We investigate the evolution of superconducting properties by doping non-magnetic impurity in single crystals of YNi2-xPtxB2C (x=0-0.2). With increasing Pt doping the critical temperature (Tc) monotonically decreases from 15.85K and saturates to a value ~13K for x>0.14. However, unlike conventional s-wave superconductors, the upper critical field (HC2) along both crystallographic directions a and c decreases with increasing Pt doping. Specific heat measurements show that the density of states (N(EF)) at the Fermi level (EF) and the Debye temperatures (Theta_D) in this series remains constant w…
To probe manifestations of multiband superconductivity in oxypnictides, we measured the angular dependence of the magnetic torque $τ(θ)$ in the mixed state of LaO$_{0.9}$F$_{0.1}$FeAs single crystals as a function of temperature $T$ and magnetic fields $H$ up to 18 T. The paramagnetic contribution of the Fe ions is properly treated in order to extract the effective mass anisotropy parameter $γ=(m_c/m_{ab})^{1/2}$ from $τ(θ)$. We show that $γ$ depends strongly on both $T$ and $H$, reaching a maximum value of $\sim$ 10 followed by a decrease towards values close to 1 as $T$ is lowered. The obser…
To probe manifestations of multiband superconductivity in oxypnictides, we measured the angular dependence of magnetic torque $τ(θ)$ in the mixed state of SmO$_{0.8}$F$_{0.2}$FeAs single crystals as functions of temperature $T$ and high magnetic field $H$ up to 30 T. We show that the effective mass anisotropy parameter $γ$ extracted from $τ(θ)$, can be greatly overestimated if the strong paramagnetism of Sm or Fe ions is not properly taken into account. The correctly extracted $γ$ depends on both $T$ and $H$, saturating at $γ\simeq 9$ at lower temperatures. Neither the London penetration depth…
We report B_c2 data for LaO_{0.9}F_{0.1}FeAs_{1-delta} in a wide T and field range up to 60 Tesla. The large slope of B_c2 approx ~ -6 Tesla/K near an improved T_c = 28.5 K of the in-plane B_c2(T) contrasts with a flattening starting at 23 K above 30 Tesla we regard as the onset of Pauli-limited behavior (PLB) with B_c2(0) about 65 Tesla. We interpret a similar hitherto unexplained flattening of the B_c2(T) curves reported for at least three other disordered closely related systems as also as a manifestation of PLB. Their Maki parameters have been estimated analyzing their B_c2(T) data within …
