Two-gap Superconductivity Research Articles

Two-band analysis on the upper critical field for superconductor NbS2

Based on two-band Ginzburg-Landau theory, we study the temperature and angular dependences of upper critical field for superconducting crystal NbS2. All the results fit the experimental data well. We thus conclude that NbS2 is another example of two-gap superconductors. Our calculations also indicate that the larger gap opens in the quasi-two-dimensional Nb-derived bands.

Composite vortices in two-component Bose-Einstein condensates

Motivated by the recent observation of composite vortices in two-gap superconductors, we investigate the occurrence and stability of composite vortices in a two-component Bose condensate. As a function of the inter-component interaction strength, the vortices in the two components of the Bose mixture can overlap and form a composite vortex object. However, when two such composite vortices approach each other, their mutual interaction may cause the composite object to dissociate in its component vortices. We derive the phase diagram for the stability of composite vortices as a function of the interaction strengths of the Bose condensates, based on a variational calculation. The effective forces between the component vortices of the composite object are also derived within this approach, and allow for an interpretation of the phase diagram.

Numerical simulation of vortex structure in mesoscopic two-gap superconductor

In this paper, the evolution of vortex configuration for mesoscopic two-gap superconductor is investigated by the time-dependent Ginzburg-Landau theory in the presence of an externally applied field. The vortex configurations of s-wave and d-wave, and the distribution of magnetic field are given when the temperature is between critical temperatures of s-wave and d-wave. In theory, the over-cold and the over-hot field, and the boundary effect on vortex are simulated when the magnetic flux penetrates the superconductor.

Single crystal growth and characterization of tetragonal FeSe1−x superconductors

The plate-like single crystals of tetragonal (P4/nmm) FeSe1−x superconductors were grown using the KCl–AlCl3 flux technique which produced single crystalline tetragonal samples of about 4 × 4 × 0.1 mm3 dimensions. The energy dispersive X-ray spectroscopy established a ratio of Fe : Se = 1 : 0.96 ± 0.02. The resistivity and magnetization measurements revealed a sharp superconducting transition at Tc = 9.4 K. Multiple Andreev reflections spectroscopy pointed to the existence of two-gap superconductivity with the gap values ΔL = 2.4 ± 0.2 meV and ΔS = 0.75 ± 0.1 meV at 4.2 K.

Comparative studies of the scanning tunneling spectra in cuprate and iron-arsenide superconductors

We report scanning tunneling spectroscopic studies of cuprate and iron-arsenic superconductors, including YBa2Cu3O7-δ (Y-123, Tc = 93 K), Sr0.9La0.1CuO2 (La-112, Tc = 43 K), and the “122” compounds Ba(Fe1-xCox)2As2 (Co-122 with x = 0.06, 0.08, 0.12 for Tc = 14, 24, 20 K). In zero field (H = 0), spatially homogeneous coherence peaks at energies ω = ± ΔSC flanked by spectral “shoulders” at ±Δeff are found in hole-type Y-123. In contrast, only a pair of spatially homogeneous peaks is seen in electron-type La-112 at ± Δeff. For H > 0, pseudogap (ΔPG) features are revealed inside the vortices, with ΔPG = [(Δeff)2-(ΔSC)2]1/2 > ΔSC in Y-123 and ΔPG < ΔSC in La-112, suggesting that the physical origin of ΔPG is a competing order coexisting with superconductivity. Additionally, Fourier transformation (FT) of the Y-123 spectra exhibits two types of spectral peaks, one type is associated with ω-dependent quasiparticle interference (QPI) wave-vectors and the other consists of ω-independent wave-vectors due to competing orders and (π,π) magnetic resonances. For the multi-band Co-122 compounds, two-gap superconductivity is found for all doping levels. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps are also identified. These findings, together with the ω- and x-dependent QPI spectra, are consistent with a sign-changing s-wave pairing symmetry in the Co-122 iron arsenides. Our comparative studies suggest that the commonalities among the cuprate and the ferrous superconductors include the proximity to competing orders, antiferromagnetic (AFM) spin fluctuations and magnetic resonances in the superconducting (SC) state, and the unconventional pairing symmetries with sign-changing order parameters on different parts of the Fermi surface.

Study of the Two-Gap Superconductivity in GdO(F)FeAs by ScS-Andreev Spectroscopy

Current-voltage characteristics and dynamic conductance of the superconductor -constriction - superconductor junctions in GdO(F)FeAs polycrystalline samples with critical temperatures TlocalC = 46 ÷ 53 K were investigated. Two superconducting gaps, the large ΔL = 10.5±2 meV, and the small one Δs = 2.3 ± 0.4 meV were clearly observed at T = 4.2 K. The 2ΔL/kBTlocalC = 5.5 ± 1 ratio gives support to the strong coupling mechanism which is responsible for the high Tc value. Temperature dependence of the large gap ΔL(T) indicates the presence of intrinsic proximity effect (in κ-space) between two superconducting condensates.

NANOSCALE SUPERCONDUCTIVITY

We deal with the problem of nanoscale superconductivity. Nanoscale superconductivity remains to be one of the most interesting research areas in condensed mater. Recent technology and experiments have fabricated high-quality superconducting MgB 2 nanoparticles. We consider the two-band superconductivity in ultrasmall grains, by extending the Richardson exact solution to two-band systems, and develop the theory of interactions between nano-scale ferromagnetic particles and superconductors. The properties of nano-sized two-gap superconductors and the Kondo effect in superconducting ultrasmall grains are investigated as well. The theory of the Josephson effect is presented, and his application to quantum computing are analyzed.

Correlation functions and coherence lengths in a two-gap superconductor

We derive analytically the spatial correlation functions for gap fluctuations in two-band scenario with intra- and interband pair-transfer interactions. These functions demonstrate the changes in spatial functionality due to the presence of two channels of coherency described by the divergent and finite correlation lengths. Even at the phase transition point both channels are essential for two-band superconductivity. Generally their relative contributions depend on the temperature and system parameters.

Theoretical analysis of two-gap superconductivity of magnesium diborades and iron pnictides in the generalized α model

A generalized α model for computing the superconducting parameters of real two-band superconductors is proposed based on an analysis of the properties of two-band equations in the theory of superconductivity. Using this model, we calculate the heat capacity and optical properties of Ba(Fe1 − xCox)2As2 superconducting compound and obtain the temperature dependences of the gaps and energies of the Leggett modes in the Mg1 − xAlxB2 superconducting system. Good quantitative coincidence of the calculated data and experimental results is demonstrated.

Critical and Non-Critical Coherence Lengths in a Two-Band Superconductor

We study the peculiarities of coherency in a two-gap superconductor. The both intraband couplings, inducing superconductivity in the independent bands, and interband pair-transfer interaction have been taken into account. On the basis of the Ginzburg-Landau equations derived from the Bogoliubov-de Gennes equations and the relevant self-consistency conditions for a two-gap system, we find critical and non-critical coherence lengths in the spatial behaviour of the fluctuations of order parameters. The character of the temperature dependencies of these length scales is determined by the relative contributions from intra- and interband interaction channels.

Two-band superconductivity featuring different anisotropies in the ternary iron silicide Lu2Fe3Si5

We report detailed studies of the upper critical field and low-temperature specific heat in the two-gap superconductor Lu$_{2}$Fe$_{3}$Si$_{5}$. The anisotropy of the upper critical field suggests that the active band is quasi-one-dimensional. Low-temperature specific heat in magnetic fields reveals that the virtual $H_{c2}$ in the passive band is almost isotropic. These results strongly indicate that the two bands have two different anisotropies, similar to the typical two-gap superconductor MgB$_{2}$, and their interplay may be essential to the two-gap superconductivity in Lu$_{2}$Fe$_{3}$Si$_{5}$.

Fluxon dynamics of a long Josephson junction with two-gap superconductors

We investigate the phase dynamics of a long Josephson junction (LJJ) with two-gap superconductors. In this junction, two channels for tunneling between the adjacent superconductor (S) layers as well as one interband channel within each S layer are available for a Cooper pair. Due to the interplay between the conventional and interband Josephson effects, the LJJ can exhibit unusual phase dynamics. Accounting for excitation of a stable 2$\ensuremath{\pi}$-phase texture arising from the interband Josephson effect, we find that the critical current between the S layers may become both spatially and temporally modulated. The spatial critical current modulation behaves as either a potential well or barrier, depending on the symmetry of the superconducting order parameter, and modifies the Josephson vortex trajectories. We find that these changes in phase dynamics result in emission of electromagnetic waves as the Josephson vortex passes through the region of the 2$\ensuremath{\pi}$-phase texture. We discuss the effects of this radiation emission on the current-voltage characteristics of the junction.

Scanning Hall probe microscopy of unconventional vortex patterns in the two-gap MgB2superconductor

The low magnetic field vortex patterns nucleation and evolution in a high-quality two-gap superconductor MgB${}_{2}$ single crystal have been investigated by low-temperature scanning Hall probe microscopy. Large areas have been imaged with single-vortex resolution while changing systematically the thermodynamic parameters for field and temperature. The obtained patterns have been studied and compared with those of a reference 2H-NbSe${}_{2}$ single crystal. We found that the observed vortex patterns in MgB${}_{2}$ (e.g., stripes, clusters) appear due to competing vortex-vortex interactions as suggested by the theory of type-1.5 superconductivity.

Non-magnetic impurity effect on suppression of Tc and gap evolution in the two-gap superconductor Lu2Fe3Si5

We report the suppression of Tc and the evolution of amplitudes of the two gaps with the introduction of non-magnetic impurities in a two-gap superconductor Lu2Fe3Si5. While Tc rapidly decreases by a small amount of substitution of Sc for Lu, the suppression of Tc is more than ten times slower than that expected from the Abrikosov–Gor’kov equation describing the reduction of Tc in a superconductor with sign reversal in the gap function. The evolution of two distinct gaps by the introduction of non-magnetic impurities does not show merging the amplitude of two gaps, which is strikingly different from the typical two-gap superconductor MgB2.

The healing lengths in two-band superconductors in extended Ginzburg–Landau theory

We study the vortex profiles in two-gap superconductors using the extended Ginzburg–Landau theory. The results shed more light on the disparity between the effective length scales in two bands. We compare the behavior expected from the standard Ginzburg–Landau theory with this new approach, and find good qualitative agreement in the case of LiFeAs.

10B–11B isotope substitution and superconductivity in ZrB12

The specific heat of the ZrB12 compound in the normal and superconducting states (T C ≈ 6 K) has been studied in the 1.9–7 K temperature range for high-quality single crystals with different relative contents of boron isotopes. For Zr10B12, ZrnatB12, and Zr11B12 dodecaborides, the electron density of states and the electronphonon coupling constant, λe-ph ∼ 0.4, are found. The dependence of the thermodynamic and upper critical fields, as well as of the Ginzburg-Landau parameter (κ = 0.8–1.14) on temperature and isotope composition is determined. The results suggest the existence of the magnetic field induced phase transition at T* = 4–5 K, which is not related to the transition from type-I to type-II superconductivity. The possibilities of the existence of two-gap superconductivity and a structural phase transition at T* in zirconium dodecaboride are discussed.

Temperature and angular dependence of some superconducting state parameters of Lu 2Fe 3Si 5 in two-band anisotropic Ginzburg–Landau theory

Based on the two-band anisotropic Ginzburg–Landau theory, we studied the temperature and angular dependence of the coherence length, the critical velocity of Cooper pairs and the penetration depth of the two-gap superconductor Lu 2Fe 3Si 5. The theoretical results are agreement with the experimental data very well.

Evidence for conventional superconducting behavior in noncentrosymmetric Mo3Al2C

We report on measurements of the magnetic penetration depth of polycrystalline samples of nonmagnetic Mo${}_{3}$Al${}_{2}$C (${T}_{c}=9$ K) without inversion symmetry. Two previous specific-heat measurements in this compound found different anomalous peaks in the low-temperature limit. One of these peaks was attributed to the superconducting transition at 3 K of the impurity phase Mo${}_{2}$C. We argue here that the second anomalous peak may be caused by the superconducting transition of SiC:Al at 1.45 K, another impurity phase possibly present in Mo${}_{3}$Al${}_{2}$C samples. The temperature-independent behavior of the penetration depth observed below 0.5 K is taken as firm evidence for the presence of a nodeless superconducting gap in Mo${}_{3}$Al${}_{2}$C. Numerical calculations using the BCS expression for the penetration depth give qualitative support for an isotropic energy gap in Mo${}_{3}$Al${}_{2}$C. The present results suggest that Mo${}_{3}$Al${}_{2}$C is a conventional $s$-wave superconductor, although two-gap or anisotropic-gap superconductivity cannot be ruled out.

Vortex matter in mesoscopic two-gap superconductor square

In mesoscopic superconductors with low intrinsic pinning, the boundary plays the most important role in the stabilization of the vortex patterns. Especially in the case of symmetric sample shape, very distinct vortex locations inside the sample are defined, for the different vorticity states. The study of two-component superconductors with the Ginzburg-Landau equation implies the introduction of a coupling term between the two condensates, changing the linear part of the potential. This article presents the analysis of the impact of the competition between the coupling term and the geometry of confinement on the vortex patterns of thin mesoscopic square samples made from a two-gap superconductor. For a simple case presented here, it was found that the appearance of the noncomposite vortices is accompanied by an unusual shape of the component of the order parameter associated with the passive band as a function of the temperature. This shape is a distinct fingerprint for materials with noncomposite vortices.

Different length scales for order parameters in two-gap superconductors: Extended Ginzburg-Landau theory

Using the Ginzburg-Landau theory extended to the next-to-leading order we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that those can be significantly different even in the strict domain of applicability of the Ginzburg-Landau theory. This justifies the use of this theory to describe relevant physics of two-gap superconductors, distinguishing them from their single-gap counterparts. The calculational degree of complexity increases only slightly with respect to the conventional Ginzburg-Landau expansion, thus the extended Ginzburg-Landau model remains numerically far less demanding compared to the full microscopic approaches.