Static spin susceptibility of superconductors with spin-orbit relaxation has been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov. Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the ordinary and spin-orbit scattering. Using the developed formalism we study the linear spin pumping effect between the ferromagnet and the adjacent superconducting film. The consequences for understanding recent experiments demonstrating the modification of Gilbert damping by the superconducting correlations are discussed.
Ising superconductivity has been recently discovered in 2D transition metal dichalcogenides. We report that such superconductors have unusual optical properties controlled by the in-plane Zeeman field. First, we find several optical gaps visible as peaks of the conductivity and the Raman susceptibility. Moreover, we find that the Ising spin splitting in the spectrum of Bogolubov quasiparticles enables strong population inversion generated by the time-dependent Zeeman field. Ultimately this leads to the possibility of the superconducting laser with magnonic pumping which can be realized in the …
We show that the spin pumping from ferromagnetic insulator into the adjacent metallic spin sink can be strongly stimulated by the superconducting correlations. The key physical mechanism responsible for this effect is the presence of quasiparticle surface states at the ferromagnetic insulator/superconductor interface. We consider the minimal model when these states appear because of the suppressed pairing constant within the interfacial normal layer. For thin normal layers we obtain a strongly peaked temperature dependence of the Gilbert damping coefficient which has been recently observed in …
We calculate the spin susceptibility of a superconductor without inversion symmetry, both in the clean and disordered cases. The susceptibility has a large residual value at zero temperature, which is further enhanced in the presence of scalar impurities.
We present a formalism to study adiabatic pumping through a superconductor - normal - superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.
We calculate the specific heat and susceptibility of rare-earth magnetic superconductors in the context of the Ginzburg-Landau theory. The specific heat and susceptibility are calculated both at the coexistence phase of antiferromagnetism and superconductivity and normal phase. Theoretical results are compared with experimental results, which agree excellently well.
We investigate charge pumping in ferromagnet/triplet superconductor junctions where the magnetization of the ferromagnet is inhomogeneous and dynamical. It is shown that charge current is pumped due to the coupling of the localized spin with triplet vector spin chirality, vector spin chirality formed by the triplet vector of Cooper pairing. Physical mechanism of the charge pumping is also discussed.
This paper demonstrates the method of estimation of critical temperature Tc value of high-temperature superconductors from the dispersive part of AC susceptibility measurement using a pair of neural networks.
ARPES measurements on HiTc superconductors such as BiSrCaCuO reveal a quasiparticle peak, a broad background and a dip. The background may originate from inelastic spin fluctuation emission. Calculations of the spectral weight are presented incorporating these inelastic processes. Superconducting correlations have been included in the magnetic susceptibility. The dip feature in the spectral weight is evidence for a spin gap in the superconducting state.
Finite-difference time-domain methods are increasingly being used to develop, model and analyze the response of materials, including engineered metamaterials that may contain superconductors. Though simple and useful expressions for the time-domain susceptibility exist for basic metals and dielectrics, the time-domain response for a superconductor has not been developed, mainly because the frequency-dependent expressions themselves are rather complex. In this paper we present a simple approximate expression for the time-domain susceptibility of a superconductor for the hbar/2Delta time scale (…
Recent experiments indicate that the Bechgaard salts (TMTSF)$_2$ ClO$_4$ and (TMTSF)$_2$ PF$_6$ may be unconventional triplet superconductors. The quasiparticle density of states and the uniform spin susceptibility tensor are computed at low temperatures for order parameter symmetries, as an attempt to narrow the number of possibilities based on experimental evidence.
Experiment and analytical calculations show that the demagnetizing field of a superconductor is a sensitive probe of quantities otherwise difficult to measure, such as the sample-probe distance in flux-density imaging experiments, and the field of first flux penetration Hp. In particular, the ratio of the maximum field measured above the superconductor edge and the applied field can be determined unambiguously so as to define a linear "geometric" susceptibility. The evolution of this susceptibility with field depends on the regime of flux penetration, and can be used as a means to determine Hp…
Experiment and theory indicate that UPt3 is a topological superconductor in an odd-parity state, based in part from temperature independence of the NMR Knight shift. However, quasiparticle spin-flip scattering near a surface, where the Knight shift is measured, might be responsible. We use polarized neutron scattering to measure the bulk susceptibility with H||c, finding consistency with the Knight shift but inconsistent with theory for this field orientation. We infer that neither spin susceptibility nor Knight shift are a reliable indication of odd-parity.
The nematic susceptibility of hole-doped Ba1-xKxFe2As2 and electron-doped Ba(Fe1-xCox)2As2 iron-based superconductors is obtained from measurements of the elastic shear modulus using a three-point bending setup in a capacitance dilatometer. Nematic fluctuations, although weakened by doping, extend over the whole superconducting dome in both systems, suggesting their close tie to superconductivity. Evidence for quantum critical behavior of the nematic susceptibility is, surprisingly, only found for Ba(Fe1-xCox)2As2, the system with the lower maximal Tc value.
We calculate the wave-vector dependent electronic spin susceptibility $χ_{αβ}(\mathbf q, \mathbf H_0)$ of a d-wave superconductor in uniform magnetic field $\mathbf{H}_0$ with Pauli pair-breaking. We find that the transverse component of the susceptibility tensor can be greater than its normal state value; the longitudinal component also slightly increases but in a very limited range of $q$s. We identify several wave vectors $\{\mathbf q_\perp,\mathbf q_\parallel\}$, that correspond to the maxima of either $χ_\perp$ or $χ_\parallel$. We compare our results with available data on the high-field…
We show that in some trigonal and hexagonal crystals the Zeeman coupling of band electrons with an external magnetic field is strongly anisotropic and necessarily vanishes along the main symmetry axis. This leads to qualitative changes in the temperature dependence of the electron spin susceptibility in the superconducting state. In particular, the power-law exponents at low temperatures due to the contribution of the nodal quasiparticles are considerably modified compared to their textbook values.
We study theoretically spin pumping in bilayers consisting of superconductors and antiferromagnetic insulators. We consider both compensated and uncompensated interfaces and include both the regular scattering channel and the Umklapp scattering channel. We find that at temperatures close to the critical temperatures and precession frequencies much lower than the gap, the spin-current is enhanced in superconductors as compared to normal metals. Otherwise, the spin-current is suppressed. The relevant precession frequencies where the spin-current in SC/AFI is enhanced compared to NM/AFI is much l…
Spin pumping refers to the microwave-driven spin current injection from a ferromagnet into the adjacent target material. We theoretically investigate the spin pumping into superconductors by fully taking account of impurity spin-orbit scattering that is indispensable to describe diffusive spin transport with finite spin diffusion length. We calculate temperature dependence of the spin pumping signal and show that a pronounced coherence peak appears immediately below the superconducting transition temperature Tc, which survives even in the presence of the spin-orbit scattering. The phenomenon p…
The non-centrosymmetric superconductors Li2Pd3B and Li2Pt3B show different superconducting properties despite having the same crystal symmetry. Motivated by experimental results, we investigate the spin susceptibility of non-centrosymmetric superconductors accompanied by the topological transition of Fermi surfaces due to antisymmetric spin-orbit coupling, which is indicated by the first-principles band structure calculation for Li2Pt3B. We study three types of topological transition, namely, (A) the disappearance of the Fermi surface, (B) crossing the Dirac point, and (C) crossing the saddle …
The spin susceptibility of noncentrosymmetric superconductors is studied when the gap function has line nodes. As examples, d-wave states, where the gap function has an additional odd-parity phase factor, are examined. The curve of the spin susceptibility $χ(T)$ is upward convex when all line nodes are parallel to the magnetic field, while it is downward convex in the other d-wave states and an s-wave state. For polycrystalline powder samples, the temperature dependences of $χ(T)$ are predicted by assuming three explicit conditions of the powder particles. The results are compared with the exp…
A theoretical study is presented on the odd-frequency spin-singlet pairing that arises in nonuniform even-frequency superconductors as a consequence of broken translation symmetry. The effect of the odd-frequency pairing on the superfluid density and the spin susceptibility is analyzed by using the quasiclassical theory of superconductivity. It is shown that (1) the superfluid density is reduced by the formation of the odd-frequency singlet pairs and (2) the odd-frequency pairing increases the spin susceptibility even though its spin symmetry is singlet. The two unusual phenomena are related t…
We propose that the orbital angular momentum of the conduction electrons in the Iron-based superconductors is activated in their low energy physics. Using a five-band tight-binding model derived from fitting the LDA band structure, we find that the orbital magnetic susceptibility of the conduction electrons in such a multi-orbital system is several times larger than the Pauli spin susceptibility and is comparable in magnitude to the observed total magnetic susceptibility. The orbital magnetic susceptibility in the Fe-As plane($χ^{x}_{L}$) is found to be larger than that perpendicular to the Fe…
We demonstrate that a new tool, a model independent numerical Eliashberg inversion of the optical self-energy, based on maximum entropy considerations can be used to extract the magnetic excitation spectra of high-transition-temperature superconductors. In Bi-2212 we explicitly show that the magnetic mode that dominates the self-energy at low temperatures directly evolves out of a smooth transfer of spectral weight to the mode from the continuum just above it. This redistribution starts already at 200 K in optimally doped materials but is much weaker in overdoped samples. This provides evidenc…
The iron-based superconductor FeTe$_{1-x}$Se$_{x}$ has attracted considerable attention as a candidate topological superconductor owing to a unique combination of topological surface states and bulk high-temperature superconductivity. The superconducting properties of as-grown single crystals, however, are highly variable and synthesis dependent due to excess interstitial iron impurities incorporated during growth. Here we report a novel physicochemical process for pumping this interstitial iron out of the FeTe$_{1-x}$Se$_{x}$ matrix and achieving bulk superconductivity. Our method should have…
Magnetic Field Dependence of the Spin Susceptibility on Conventional s-wave Superconductor LaRu$_4$P$_{12}$ Revealed by $^{31}$P-NMR and $^{139}$La-NMR
We review our recent experimental results on the electronic nematic phase in electron- and hole-doped BaFe$_2$As$_2$ and FeSe. The nematic susceptibility is extracted from shear-modulus data (obtained using a three-point-bending method in a capacitance dilatometer) using Landau theory and is compared to the nematic susceptibility obtained from elastoresistivity and Raman data. FeSe is particularly interesting in this context, because of a large nematic, i.e., a structurally distorted but paramagnetic, region in its phase diagram. Scaling of the nematic susceptibility with the spin lattice rela…
Anomalous spin-pumping behavior of half-metallic ferromagnet/d-wave superconductor heterostructures
Laboratoire Albert Fert, CNRS, Thales, Université Paris Saclay（阿尔贝·费朗实验室，法国国家科学研究中心，泰雷兹集团，巴黎萨克雷大学）；ICTS - Centro Nacional de Microscopía Electrónica, Universidad Complutense de Madrid（综合微观技术中心-国家电子显微镜中心，马德里康普顿斯大学）；Condensed Matter Theory Group, University Bordeaux I, CPMOH UMR-CNRS 5798（波尔多第一大学凝聚态理论组，CPMOH UMR-CNRS 5798）；GFMC, Dept. Física de Materiales, Facultad de Física, Universidad Complutense（物质材料物理系，物理学院，马德里康普顿斯大学）
We here examine the relation between odd-frequency spin-triple even-parity (OTE) Cooper pairs and anomalous surface magnetic response in time-reversal invariant (TRI) spin-triplet superfluids and superconductors. The spin susceptibility generally consists of two contributions: Even-frequency odd-parity pair amplitudes and odd-frequency even-parity pair amplitudes. The OTE pair amplitudes are absent in the bulk region, but ubiquitously exist in the surface and interface region as Andreev bound states. We here clarify that additional discrete symmetries, originating from the internal symmetry an…
We have studied the interplay of magnetism and superconductivity in LaFeAsO$_{1-x}$F$_x$ and Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$. While antiferromagnetic spin density wave formation is suppressed and superconductivity evolves, all samples show a doping independent strong increase of the normal state susceptibility upon heating which appears a general feature of iron pnictides. The data provide evidence for robust local antiferromagnetic correlations persisting even in the superconducting regime of the phase diagram.
A phenomenological theory to describe the electromagnetic properties of granular superconductors, based on known bulk superconductors expressions and conventional Josephson's junctions tunneling currents, is presented and succesfully used to fit distinct experimental results for the magnetic susceptibility as a function of the temperature and the applied magnetic field of rather different samples.
We propose a microscopic explanation of the pseudogap features discovered in the normal state specific heat and magnetic susceptibility of cuprates. In the framework of the bipolaron theory of high-Tc superconductors we explain the magnitude of the carrier specific heat and susceptibility as well as their universal scaling with temperature over a wide range of doping.
The magnetic ac susceptibility of high-temperature superconductors is shown to obey some scaling relations.We try to ananlyse this behavior within the framework of a common nonlinear response function of mixed state.The derived equations for critical current and ac susceptibility (x(T)) agree with the scaling relations of experimental data.
The AC susceptibility at zero DC magnetic field of a polycrystalline sample of LaFeAsO_{0.94}F_{0.06} (T_c = 24 K) has been investigated as a function of the temperature, the amplitude of the AC magnetic field (in the range Hac = 0.003 - 4 Oe) and the frequency (in the range f = 10 kHz - 100 kHz). The temperature dependence of the AC susceptibility exhibits the typical two-step transition arising from the combined response of superconduncting grains and intergranular weak-coupled medium. The intergranular part of the susceptibility strongly depends on both the amplitude and the frequency of th…
We analyze theoretically adiabatic quantum pumping through a normal conductor that couples the normal regions of two superconductor/normal metal/superconductor Josephson junctions. By using the phases of the superconducting order parameter in the superconducting contacts as pumping parameters, we demonstrate that a non zero pumped charge can flow through the device. The device exploits the evolution of the superconducting phases due to the ac Josephson effect, and can therefore be operated at very high frequency, resulting in a pumped current as large as a few nanoAmperes. The experimental rel…
We calculate the diamagnetic susceptibility in zero external magnetic field above the phase transition from ferromagnetic phase to phase of coexistence of ferromagnetic order and unconventional superconductivity. For this aim we use generalized Ginzburg-Landau free energy of unconventional ferromagnetic superconductor with spin-triplet electron pairing. A possible application of the result to some intermetallic compounds is briefly discussed.
In this work, we investigated the nonadiabatic transport properties of the one-dimensional time-dependent superconductor-normal metal-superconductor (SNS) Josephson junction biased by a current source and driven by a high-frequency-ac-gate-potential applied to the normal-metal layer. BCS superconductors are considered and treated with the time-dependent Bogoliubov-de Gennes equation. Using Floquet theory, we compute the transmission coefficients and the Wigner-Smith delay times as a function of the incident energy and find that they display resonances when one of the electron or hole Floquet w…
Nuclear magnetic resonance (NMR) and Knight shift measurements are critical tools in the identification of spin-triplet superconductors. We discuss the effects of spin orbit coupling on the Knight shift and susceptibilities for a variety of spin triplet multi-orbital gap functions with orbital-singlet character and compare their responses to "traditional" single band spin-triplet ($p_x+ip_y$) superconductors. We observe a non-negligible residual spin-susceptibility at low temperature.
We study the spin susceptibility of the orbital-singlet pairings, including the spin-triplet/orbital-singlet/$s$-wave $E_g$ representation proposed by Suh \textit{et al}., [H.\ G.\ Suh \textit{et al}., Phys.\ Rev.\ Research \textbf{2}, 032023 (2020)], for a three-orbital model of superconducting Sr$_2$RuO$_4$ in three dimensions. For the pseudospin-singlet states represented in the band basis, the spin susceptibility decreases when reducing the temperature, irrespective of the direction of the applied magnetic fields, even if they are spin-triplet/orbital-singlet pairings in the spin-orbital s…
We review recent work on the theory for pump/probe photoemission spectroscopy of electron-phonon mediated superconductors in both the normal and the superconducting states. We describe the formal developments that allow one to solve the Migdal-Eliashberg theory in nonequilibrium for an ultrashort laser pumping field, and explore the solutions which illustrate the relaxation as energy is transferred from electrons to phonons. We focus on exact results emanating from sum rules and approximate numerical results which describe rules of thumb for relaxation processes. In addition, in the supercondu…
We perform calculations relating the order parameter symmetry of organic quasi-one-dimensional superconductors to the bulk quasiparticle density of states and the bulk uniform spin susceptibility tensor at finite temperatures. Current experimental results suggest that some organic quasi-one-dimensional superconductors may exhibit triplet pairing symmetry. The purpose of our analysis is to attempt to narrow down the number of possibilities for the symmetry of the order parameter based on the experimental evidence.
We have investigated the pressure dependence of ac and dc susceptibilities of the heavy-fermion superconductor CePt3Si (Tc= 0.75 K) that coexists with antiferromagnetism (TN = 2.2 K). As hydrostatic pressure is increased, Tc first decreases rapidly, then rather slowly near the critical pressure Pc = 0.6 GPa and shows a stronger decrease again at higher pressures, where Pc is the pressure at which TN becomes zero. A transition width and a difference in the two transition temperatures defined in the form of structures in the out-of-phase component of ac susceptibilities also become small near Pc…
In materials without spatial inversion symmetry the spin degeneracy of the conduction electrons can be lifted by an antisymmetric spin-orbit coupling. We discuss the influence of this spin-orbit coupling on the spin susceptibility of such superconductors, with a particular emphasis on the recently discovered heavy Fermion superconductor CePt3Si. We find that, for this compound (with tetragonal crystal symmetry,) irrespective of the pairing symmetry, the stable superconducting phases would give a very weak change of the spin susceptibility for fields along the c-axis and an intermediate reducti…
The order parameter of High-T$_{c}$ superconductors through a series of experiments has been quite conclusively demonstrated to not be of the normal $s-wave$ type. It is either a pure $d_{x^{2}-y^{2}}$-wave type or a mixture of a $d_{x^{2}-y^{2}}-wave$ with a small imaginary $s-wave$ or $d_{xy}-wave$ component. In this work a distinction is brought out among the four types, i.e., $s- wave$, $d_{x^{2}-y^{2}}- wave$, $d_{x^{2}-y^{2}}+is - wave$ and $d_{x^{2}-y^{2}}+id_{xy}- wave$ types with the help of quantum pumping spectroscopy. This involves a normal metal double barrier structure in contact…
We propose a setup to realize time-reversal invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is $ϕ=π$ a Kramers' pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in presence of both time-reversal invariant and time-reversal breaking perturbations. In addition, we show that the system forms a natural realization o…
In an attempt to clarify conflicting published data, we report new measurements of specific heat, resistivity, magnetic susceptibility, and thermal expansivity up to room temperature for the 6 K superconductor ZrB12, using well-characterized single crystals with a residual resistivity ratio >9. The specific heat gives the bulk result 2*delta(0)/(k_B*Tc)=3.7 for the superconducting gap ratio, and excludes multiple gaps and d-wave symmetry for the Cooper pairs. The Sommerfeld constant gamma_n = 0.34 mJ K-2 gat-1 and the magnetic susceptibility xsi = -2.1 x 10^-5 indicate a low density of states …
Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quant…
For assemblies of superconductor nanograins, the magnetic response is analyzed as a function of both temperature and magnetic field. In order to describe the interaction energy of electron pairs for a huge number of many-particle states, involved in calculations, we develop a simple approximation, based on the Richardson solution for the reduced BCS Hamiltonian and applicable over a wide range of the grain sizes and interaction strengths at arbitrary distributions of single-electron energy levels in a grain. Our study is focused upon ultra-small grains, where both the mean value of the nearest…
Local magnetic properties around a nonmagnetic impurity are investigated in high-Tc cuprate superconductors. We consider a model two-dimensional d-wave superconductor with strong antiferromagnetic (AF) spin fluctuations and calculate the spin susceptibility around the impurity. We show that the uniform susceptibility, which is usually suppressed in spin-singlet superconductivity, is enhanced at low temperatures around the impurity when the impurity scattering is in the unitarity limit. This anomalous behavior is more remarkable when the impurity potential is extended spatially and the AF spin …
