Multigap Superconductivity Research Articles

Coherence Lengths for Superconductivity in the Two-Orbital Negative-U Hubbard Model

Multi-component superconductivity models, developed more than fty years starting from the papers [1 3], include rather varied physics. In connection with the presence of interacting order parameters the main properties of the multi-band systems are quite di erent from the corresponding characteristics in single-band superconductors. The examination of theses peculiarities has been an object of growing interest. The various multi-component theoretical scenarios have been applied for a number of superconducting materials (see [4 7] and references therein). The research activity in this direction has been especially stimulated by the acceptance of the multi-gap superconductivity in MgB2 [8], cuprates [9] and iron arsenic compounds [10]. In particular, the derivation of high-quality superconducting regions from oxygen ordering, observed recently in La2CuO4+y [11], supports the multi-band theoretical scenario of superconductivity in cuprates. In the present contribution we study the coherency of the superconducting ordering of a two-band (two-orbital) system with the negative-U Hubbard intra-orbital pairing and inter-orbital pair-transfer interaction. One can distinguish here two characteristic length scales [12] in the spatial behaviour of superconducting uctuations. One of these lengths as a function of temperature behaves critically diverging at the phase transition point. The other one remains nite and its temperature dependence is weaker. The formation of these length scales is caused by the interband interaction mixing the superconducting order parameters of initially non-interacting bands. The critical and non-critical coherence lengths associate also with critical and non-critical uctuations (see e.g. Refs. [13, 14]) which appear as the certain linear combinations of the deviations from the equilibrium band superconducting orders. Consequently, these length scales cannot be attributed to di erent bands involved [15] (see also Refs. [16 18]). Our results have been obtained using the superconducting negative-U Hubbard model [19] for a two-orbital system on a two-dimensional lattice.

Quasiparticle relaxation across the multiple superconducting gaps in the electron-doped BaFe1.85Co0.15As2

We study the quasiparticle relaxation dynamics in the electron-doped superconductor, BaFe1.85Co0.15As2 (BFCA) by using optical spectroscopy in both time and frequency domains. The estimate of the electron−phonon (el–ph) coupling constant from quasiparticle relaxation rate in time domain gives a value of ∼0.16 that is much too small to give a TC of 25 K. We obtain a negative value of the Coulomb pseudopotential that implies that the el−ph interaction alone is not strong enough to induce a superconducting transition in BFCA. More importantly, the electron-boson spectral function determined from optical scattering rate in frequency domain does not resemble the measured phonon density of states and has a dominant peak (at 53 meV) beyond the phonon frequencies. Our results support that the BFCA is a multi-gap s-wave superconductor and that its electron pairing is based on a spin-mediated pairing mechanism.

Robust accidental nodes and zeros and critical quasiparticle scaling in iron-based multiband superconductors

We study multigap superconductivity, with strong angular variations of one of the gaps, as appropriate for certain iron-based high-temperature superconductors. We solve the gap equations of this model and find that the nodes or zeros in the gap function present at ${T}_{c}$---although purely accidental---typically survive down to $T=0$. Based on this result, we investigate the line of quantum transitions at which gap zeros first appear. The peculiar ``zero-point'' quantum critical scaling emanating from this line dominates quasiparticle thermodynamics and transport properties over much of the phase diagram and supplants more familiar forms of scaling associated with the accidental nodes.

Microwave Study of ${\rm FeSe}_{0.3}{\rm Te}_{0.7}$ Thin Film by ${\rm TE}_{011}$-Mode Sapphire Dielectric Resonator

High quality epitaxial thin films of FeSe1-xTex (x=0-1) have been successfully fabricated. Their superconducting transition temperatures are around 8-13 K. Microwave properties of a film (x=0.7) was studied by a sapphire dielectric cavity at 9.315 GHz. The cavity, which has a quality factor of 45000 in room temperature with TE011-mode, is specially designed for the measurement of small samples with the sapphire cylinder having a small hole in the center. Thin film samples with dimension of 1-2 mm can be put in the middle of the hole, supported by a very thin sapphire rod. The cavity is sealed in a vacuum chamber soaked in the liquid 4He and the temperature of the thin sapphire rod (hence the sample) can be controlled from 1.6 K to 60 K with a stability about ±1 mK. Temperature dependence of transmission response and Q-factors were measured by a network analyser (Agilent N5230C). The results showed a clear signature of multi-gap superconductivity. No evidences of existence of node in the energy gap were found as the normalized change in the surface reactance and the corresponding normalized change in the in-plane penetration depth have flat dependence at low temperatures.

Microwave surface impedance measurements of LiFeAs, LiFe(As,P) and FeSe1−xTex single crystals

We study microwave surface impedance measurements of LiFeAs, LiFe(As,P) and FeSe1−xTex single crystals. The in-plane penetration depths of LiFeAs and LiFe(As,P) depend on temperature exponentially at low temperatures, which is a strong indication that these two materials have the nodeless superconducting gap. The temperature dependence of the superfluid density indicates that LiFeAs and LiFe(As,P) are multi-gap superconductors with at least two isotropic gaps. In FeSe1−xTex, on the other hand, the quadratic temperature dependence of the in-plane penetration depth appears, which indicates the existence of some sort of quasiparticle excitations. In addtion, the real part of the microwave conductivity exhibits a large enhancement below Tc in all three materials, which results from the increase of the quasiparticle relaxation time, τ, below Tc.

Variety ofc-Axis Collective Excitations in Layered Multigap Superconductors

We present a dynamical theory for the phase differences along a stacked direction of intrinsic Josephson junctions (IJJ's) in layered multigap superconductors, motivated by the discovery of highly anisotropic iron-based superconductors with thick perovskite-type blocking layers. The dynamical equations describing ac and dc intrinsic Josephson effects peculiar to multigap IJJ's are derived, and collective Leggett mode excitations in addition to the Josephson plasma established in single-gap IJJ's are predicted. The dispersion relations of their collective modes are explicitly displayed, and the remarkable peculiarity of the Leggett mode is demonstrated.

Magnetic field-induced martensite–austenite transformation in Fe-substituted NiMnGa ribbons

We report As-75 nuclear quadrupole resonance (NQR) studies on oxypnictide superconductors LaFeAsO1-xFx (x=0.08, 0.15) and LaNiAsO1-xFx (x=0, 0.06, 0.10, 0.12). In LaFeAsO0.92F0.08 (T-c=23 K), nuclear spin-lattice relaxation rate 1/T-1 shows no coherence peak just below T-c and decreases with decreasing temperature accompanied by a hump structure at T similar to 0.4T(c), which is a characteristic of the multigap superconductivity. In the normal state, the quantity 1/T1T increases with decreasing temperature to T-c, indicating that the existence of antiferromagnetic correlation originating from its multiple electronic band structure. On the other hand, LaNiAsO1-xFx shows a clear Hebel-Slichter (coherence) peak just below T-c, evidencing that the LaNiAsO1-xFx is a BCS superconductor. In the normal state, 1/T-1 T is constant in the temperature range 4 <= T <= 10 K for all LaNiAsO1-xFx, which indicates electron correlations are weak. We suggest that the contrasting behavior of both superconductivity and electron correlations in LaFeAsO0.92F0.08 and LaNiAsO1-xFx between them relate to the difference of electronic band structure configuration. We also provide a possible interpretation for the pseudogap-like behavior in the normal state observed in both compounds. (C) 2010 Elsevier Ltd. All rights reserved.

Enhanced Quasiparticle Heat Conduction in the Multigap SuperconductorLu2Fe3Si5

Thermal transport measurements have been made on the Fe-based superconductor Lu2Fe3Si5 (T(c) ∼ 6 K) down to a very low temperature T(c)/120. The field and temperature dependences of the thermal conductivity confirm the multigap superconductivity with fully opened gaps on the whole Fermi surfaces. In comparison to MgB2, Lu2Fe3Si5 reveals a remarkably enhanced quasiparticle heat conduction in the mixed state. The results can be interpreted as a consequence of the unequal weight of the Fe 3d-electron character among the distinct bands.

Observation of multi-gap superconductivity in GdO(F)FeAs by Andreev spectroscopy

We have studied current-voltage characteristics of Andreev contacts in polycrystalline GdO0.88F0.12FeAs samples with bulk critical temperature T c = (52.5 ± 1) K using break-junction technique. The data obtained can- not be described within the single-gap approach and suggests the existence of a multi-gap superconductivity in this compound. The large and small superconducting gap values estimated at T = 4.2 K are Δ L = 10.5 ± 2 meV and Δ s = 2.3 ± 0.4 meV, respectively.

Calorimetric evidence for nodes in the overdoped Ba(Fe0.9Co0.1)2As2

We present low-temperature specific heat of the electron-doped Ba(Fe0.9Co0.1)2As2, which does not show any indication of an upturn down to 400 mK, the lowest measuring temperature. The lack of a Schottky-like feature at low temperatures or in magnetic fields up to 9 T enables us to identify enhanced low-temperature quasiparticle excitations and to study anisotropy in the linear term of the specific heat. Our results cannot be explained by a single or multiple isotropic superconducting gap, but are consistent with multi-gap superconductivity with nodes on at least one Fermi surface sheet.

Microwave Surface Impedance Measurements of LiFeAs Single Crystals

We report results of microwave surface impedance measurements of LiFeAs single crystals. The in-plane penetration depth depends on temperature exponentially at low temperatures, which strongly suggests that this material has the nodeless superconducting gap. The temperature dependence of the superfluid density indicates that LiFeAs is a multi-gap superconductor with at least two isotropic gaps. In addtion, the real part of the microwave conductivity exhibits a large enhancement below $T_\mathrm{c}$, indicating that the quasi-particle relaxation time, $\tau$, increases rapidly below $T_\mathrm{c}$. We believe that this enhancement is rather common to all superconductors where an inelastic scattering is dominant above $T_\mathrm{c}$, irrespective of the strength of the electron correlation.

Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: theeffect of electron hopping between layers

Multigap superconductivity modulated by quantum confinement effects in a superlattice ofquantum wells is presented. Our theoretical BCS approach captures the low-energyphysics of a shape resonance in the superconducting gaps when the chemicalpotential is tuned near a Lifshitz transition. We focus on the case of weak Cooperpairing coupling channels and strong pair exchange interaction driven by repulsiveCoulomb interaction that allows us to use the BCS theory in the weak-couplingregime neglecting retardation effects, like in quantum condensates of ultracoldgases. The calculated matrix element effects in the pairing interaction are shownto yield a complex physics near the particular quantum critical points due toLifshitz transitions in multigap superconductivity. Strong deviations of the ratio2Δ/Tc from the standard BCS value as a function of the position of the chemical potential relativeto the Lifshitz transition point measured by the Lifshitz parameter are found. The responseof the condensate phase to the tuning of the Lifshitz parameter is compared with theresponse of ultracold gases in the BCS–BEC crossover tuned by an external magnetic field.The results provide the description of the condensates in this regime where matrix elementeffects play a key role.

Theory of Josephson effects in iron-based multi-gap superconductor junctions

We revisit the theory for Josephson effects in Josephson junctions with multiple tunneling channels, which can be realized when multi-gap superconductors, e.g., iron-based superconductors or MgB2 are employed as the electrodes. We mainly re-examine a hetero (multi-band)superconductor- insulator-(single-band)superconductor junction. Deriving an effective Lagrangian density based on the time-dependent Ginzburg-Landau model, we discuss how the relative fluctuations between multiple gaps (i.e., Leggett's excitation modes) and the pairing symmetry modify the Shapiro steps.

Electrodynamics and intrinsic Josephson effects in multi-gap superconductors

We develop a theory for the Josephson effects in 2-gap intrinsic Josephson junction stacks (IJJ's). The coupled dynamical equations for the phase differences are derived from the low-energy effective Lagrangian. The equations can describe the longitudinal Josephson plasma and the Josephson–Leggett (JL) mode propagating in the direction perpendicular to the junctions. Numerical results for the I – V characteristics are presented. The I – V characteristics shows multiple-branch structure similar to that in Bi-2212 IJJ's. When the Josephson frequency is approached to the JL mode frequency in non-uniform voltage branches, the JL mode is resonantly excited. At the resonant voltage a step-like structure appears in the I – V curves in low-voltage branches.

Two-Gap Superconductivity in 2H-NbS2

We performed specific heat measurements of the superconducting single crystal of 2H-NbS2 in the temperature range down to 0.6 K and magnetic fields up to 14 T. The temperature and magnetic field dependence of the electronic specific heat consistently indicate existence of two superconducting energy gaps in the system. The superconducting anisotropy depends on both temperature and magnetic field. Moreover, the angular dependence of the upper critical field deviates from the Ginzburg-Landau behavior and rather reminds that of MgB2. All these features point to a multigap superconductivity in 2H-NbS2. Our measurements are in a perfect agreement with the previous scanning tunneling spectroscopy of Guillamon et al.

As-NQR study of superconductivity in LaRAsO1−xFx (R=Fe and Ni)

We report 75As nuclear quadrupole resonance (NQR) studies on oxypnictide superconductors LaFeAsO1−xFx (x=0.08, 0.15) and LaNiAsO1−xFx (x=0, 0.06, 0.10, 0.12). In LaFeAsO0.92F0.08 (Tc=23K), nuclear spin-lattice relaxation rate 1/T1 shows no coherence peak just below Tc and decreases with decreasing temperature accompanied by a hump structure at T∼0.4Tc, which is a characteristic of the multigap superconductivity. In the normal state, the quantity 1/T1T increases with decreasing temperature to Tc, indicating that the existence of antiferromagnetic correlation originating from its multiple electronic band structure. On the other hand, LaNiAsO1−xFx shows a clear Hebel–Slichter (coherence) peak just below Tc, evidencing that the LaNiAsO1−xFx is a BCS superconductor. In the normal state, 1/T1T is constant in the temperature range 4≤T≤10K for all LaNiAsO1−xFx, which indicates electron correlations are weak. We suggest that the contrasting behavior of both superconductivity and electron correlations in LaFeAsO0.92F0.08 and LaNiAsO1−xFx between them relate to the difference of electronic band structure configuration. We also provide a possible interpretation for the pseudogap-like behavior in the normal state observed in both compounds.

Leggett mode in a strong-coupling model of iron arsenide superconductors

Using a two-orbital model of the superconducting phase of the pnictides, we compute the spectrum of the Leggett mode -- a collective excitation of the phase of the superconducting gap known to exist in multi-gap superconductors -- for different possible symmetries of the superconducting order parameter. Specifically, we identify the small regions of parameter space where the Leggett mode lies below the two-particle continuum, and hence should be visible as a sharp resonance peak. We discuss the possible utility of the Leggett mode in distinguishing different momentum dependencies of the superconducting gap. We argue that the observation of a sharp Leggett mode would be consistent with the presence of strong electron-electron correlations in iron-based superconductors. We also emphasize the importance of the orbital character of the Leggett mode, which can result in an experimental observation of the mode in channels other than $A_{1g}$.

Publisher's Note: Signatures of multigap superconductivity in tunneling spectroscopy [Phys. Rev. B82, 014531 (2010)

Publisher's Note: Signatures of multigap superconductivity in tunneling spectroscopy [Phys. Rev. B<b>82</b>, 014531 (2010)

Multi-gap superconductivity in a BaFe1.84Co0.16As2 film from optical measurements at terahertz frequencies

We measured the THz reflectance properties of a high quality epitaxial thin film of the Fe-based superconductor BaFe$_{1.84}$Co$_{0.16}$As$_2$ with T$_c$=22.5 K. The film was grown by pulsed laser deposition on a DyScO$_3$ substrate with an epitaxial SrTiO$_3$ intermediate layer. The measured $R_S/R_N$ spectrum, i.e. the reflectivity ratio between the superconducting and normal state reflectance, provides clear evidence of a superconducting gap $\Delta_A$ close to 15 cm$^{-1}$. A detailed data analysis shows that a two-band, two-gap model is absolutely necessary to obtain a good description of the measured $R_S/R_N$ spectrum. The low-energy $\Delta_A$ gap results to be well determined ($\Delta_A$=15.5$\pm$0.5 cm$^{-1}$), while the value of the high-energy gap $\Delta_B$ is more uncertain ($\Delta_B$=55$\pm$7 cm$^{-1}$). Our results provide evidence of a nodeless isotropic double-gap scenario, with the presence of two optical gaps corresponding to 2$\Delta/kT_c$ values close to 2 and 7.

Ambegaokar-Baratoff relations for Josephson critical current in heterojunctions with multigap superconductors

An extension of the Ambegaokar-Baratoff relation to a superconductor-insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Appling the resultant relation to a SIS Josephson junction formed by an iron-based (five-band) and a single-band Bardeen-Cooper-Schrieffer (BCS) type superconductors, a theoretical bound of the Josephson critical current ($I_{\rm c}$) multiplied by the resistance of the junction ($R_{\rm n}$) is given. We reveal that such a bound is useful for identifying the pairing symmetry of iron-pnictide superconductors. One finds that if a measured value of $I_{\rm c}R_{\rm n}$ is smaller than the bound then the symmetry is $\pm s$-wave, and otherwise $s$-wave without any sign changes. In addition, we stress that temperature dependence of $I_{\rm c}R_{\rm n}$ is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.