Two-gap Superconductivity Research Articles

Two kinds of magnetic gauge potentials due to coherent effect in two-gap superconductor

Two-component Ginzburg–Landau model with one magnetic gauge potential can be used to describe the physical properties of two-gap superconductor. When the order parameters in two-gap superconductor have different phases, the gauge invariance will be destroyed. In order to preserve gauge invariance, two kinds of gauge potentials must be introduced. For seeking the origins of two kinds of gauge potentials, one suggests two kinds of order parameters are in the coherent state. Therefore, two different gauge potentials and masses of the order parameters arise through deducing the super-current of the coherent state. As a result, two different gauge potentials lead to different magnetic fields at the zero points of the order parameters. In other places, the gauge potentials have no contributions to the magnetic field. Moreover, the topological properties of two different gauge potentials are discussed in detail.

Two-Band Calculations on the Upper Critical Field of Sc2Fe3Si5

The ternary compound Sc2Fe3Si5 has attracted much attention because of the various anomalous physical properties. The specific heat experiment and energy band structure calculation suggest that Sc2Fe3Si5 is a two-gap superconductor. Based on this, we analyze the upper critical field for superconducting Sc2Fe3Si5 crystals using the two-band Ginzburg-Landau theory. A two-parameter variational approach is adopted to obtain the upper critical field in arbitrary direction. The temperature and angular dependences of the upper critical field are plotted. The results reproduce the experimental data in a very broad temperature range and strongly support previous specific heat data and theoretical calculation, pointing to the existence of two energy gaps in Sc2Fe3Si5. The anisotropy of the upper critical field is also studied and is about 2, in accordance with the experimental result. Moreover our calculations indicate that Sc2Fe3Si5 has rather a three-dimension character, in agreement with the energy band calculation.

Two-Gap Superconductivity in LaNiGa_{2} with Nonunitary Triplet Pairing and Even Parity Gap Symmetry.

The nature of the pairing states of superconducting LaNiC_{2} and LaNiGa_{2} has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a nonunitary triplet pairing state. However, all the allowed nonunitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC_{2}. Here we probe the gap symmetry of LaNiGa_{2} by measuring the London penetration depth, specific heat, and upper critical field. These measurements demonstrate two-gap nodeless superconductivity in LaNiGa_{2}, suggesting that this is a common feature of both compounds. These results allow us to propose a novel triplet superconducting state, where the pairing occurs between electrons of the same spin, but on different orbitals. In this case the superconducting wave function has a triplet spin component but isotropic even parity gap symmetry, yet the overall wave function remains antisymmetric under particle exchange. This model leads to a nodeless two-gap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results.

Coupling of Higgs and Leggett modes in non-equilibrium superconductors.

In equilibrium systems amplitude and phase collective modes are decoupled, as they are mutually orthogonal excitations. The direct detection of these Higgs and Leggett collective modes by linear-response measurements is not possible, because they do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump–probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes, which is absent in equilibrium. Moreover, we propose a type of pump–probe experiment, which allows to probe and coherently control the Higgs and Leggett modes, and thus the order parameter directly. These findings go beyond two-band superconductors and apply to general collective modes in quantum materials.

Theoretical analysis of the upper critical field of two-band superconductor LaNiC2

LaNiC2 is one of ternary RNiC2 compounds, where R is a rare earth or Y. Its space group is Amm2. the symmetry along the c-axis of the crystal structure lacks inversion symmetry along the c-axis. In 2009, Hillier et al. performed the muon spin relaxation experiment (upSR) which implied that time-reversal symmetry is broken in LaNiC2. As a weak correlation noncentrosymmetric superconductor, LaNiC2 has attracted wide research interest in recent years. Though a lot of theoretical and experimental studies have been carried out, the order parameter of this compound remains highly controversial. The measurements of specific heat and nuclear quadrupole relaxation suggest that LaNiC2 is normally BCS-like, which is further supported by theoretical calculations. But recently another study showed that the London penetration depth depends on T2 below 0.4 Tc indicative of nodes in the energy gap. Evidence of possible nodal superconductivity can also be inferred from the early measurements of specific heat given by Lee et al. However, the experimental results obtained by Chen et al. supported the existence of two-gap superconductivity in LaNiC2.Based on the above case, the two-band Ginzburg-Landau theory is used to study the temperature dependence of the upper critical field for the superconductor LaNiC2 in this paper. Choosing the Ginzburg-Landau theory for calculating the upper critical field is just because Ginzburg-Landau theoretical model is simple, easy to understand, low-calculation, and the clear physical meanings of the parameters. The theoretical results in this paper accord with the experimental data very well in the whole temperature range. The curve of Hc2 (T) has an obvious positive curvature near the critical temperature, which is typical feature of multi-gap superconductor. Therefore, our results show strong evidence that two-gap scenario is better to account for the superconductivity of LaNiC2, consistent with the results of Chen Jian et al. The influences of two different energy bands on the upper critical field are also studied. It is found that the relatively small coherent length has a grester influence on the upper critical magnetic field of LaNiC2. So if we want to improve the upper critical field of LaNiC2, reducing the relatively small coherence length can be achieved in theory.

Weak interband-coupling superconductivity in the filled skutteruditeLaPt4Ge12

The superconducting pairing state of LaPt$_{4}$Ge$_{12}$ is studied by measuring the magnetic penetration depth $\lambda(T,B)$ and the superfluid density $\rho_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($\mu$SR) spectroscopy. $\lambda(T)$ follows an exponential-type temperature dependence at $T\ll T_{c}$, but its zero-temperature value $\lambda(0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $\lambda(T)$ and the corresponding $\rho_{s}(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $\gamma$ model with gap sizes of $\Delta_1(0)=1.31k_{B}T_c$ and $\Delta_2(0)=1.80k_{B}T_c$ and a very weak interband coupling. In contrast, $\rho_s(T)$, derived from the $\mu \rm{SR}$ data taken in a small field, can be fitted by a single-gap BCS model with a gap close to $\Delta_2(0)$. We conclude that LaPt$_{4}$Ge$_{12}$ is a marginal two-gap superconductor and the small gap $\Delta_1$ seems to be destroyed by a small magnetic field. In comparison, in PrPt$_4$Ge$_{12}$ the $4f$-electrons may enhance the interband coupling and, therefore, give rise to more robust multiband superconductivity.

Tunneling and electronic structure of the two-gap superconductorMgB2

A combined experimental (superconductor-insulator-superconductor tunneling spectra) and theoretical (density functional theory) study of the two-gap superconductor ${\mathrm{MgB}}_{2}$ is reported. The calculations confirm that the small gap is associated with a $\ensuremath{\pi}$ band mostly based on the boron ${p}_{z}$ orbitals leading to the three-dimensional band component of the Fermi surface. This channel almost completely dominates the tunneling images and spectra for $c$-axis-oriented samples and not the two-dimensional $\ensuremath{\sigma}$ band. The origin of this effect is due to the faster decay of the electronic states associated with the boron ${p}_{x}$ and ${p}_{y}$ orbitals compared to those associated with the boron ${p}_{z}$ orbitals, together with the symmetry properties of the wave functions. The calculated tunneling channels and partial density of states for each band agree with the values deduced from precise fits of experimental tunneling spectra. The present approach provides a framework for the understanding of tunneling spectra and the nature of superconducting gaps of other multigap superconductors.

Analysis of experimental data for two-band superconductors at T ≈ Tc using the GL theory in the presence of a self-consistent vortex line

We study the two-component Ginzburg–Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB 2, V 3 Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V 3 Si and LiFeAs , while is T-dependent for the compound MgB 2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V 3 Si and LiFeAs seems to be different from the one in MgB 2. The use of this parameter, κ, as a new way to "study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism.

Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions

Low-temperature characters of superconducting devices yield definite probes for different superconducting phenomena. We study the macroscopic quantum tunneling (MQT) in a Josephson junction, composed of a single-gap superconductor and a two-gap superconductor. Since this junction has two kinds to the superconducting phase differences, calculating the MQT escape rate requires the analysis of quantum tunneling in a multi-dimensional configuration space. Our approach is the semi-classical approximation along a 1D curve in a 2D potential- energy landscape, connecting two adjacent potential (local) minimums through a saddle point. We find that this system has two plausible tunneling paths; an in-phase path and an out-of-phase path. The former is characterized by the Josephson-plasma frequency, whereas the latter is by the frequency of the characteristic collective mode in a two-band superconductor, Josephson- Leggett mode. Depending on external bias current and inter-band Josephson-coupling energy, one of them mainly contributes to the MQT. Our numerical calculations show that the difference between the in-phase path and the out-of-phase path is manifest, with respect to the bias- current-dependence of the MQT escape rate. This result suggests that our MQT setting be an indicator of the Josephson-Leggett mode.

Specific heat of Nb3Sn: The case for a single gap

The important influence of multiple gaps in the superconductivity of MgB2 and Fe-based compounds, especially because of the possibility that manipulation of a second gap can significantly raise the upper critical field Hc2, has refocused attention on Nb3Sn because anomalies in both specific heat and point-contact tunneling studies have led to the proposal that Nb3Sn is also a two-gap superconductor. Here, we search for evidence of the second gap in a careful study of the influence of the homogenization temperature on the sample uniformity. We show that it is very difficult to fabricate samples that are both homogeneous and stoichiometric. We find so-called “second-gap” anomalies disappear only after high temperature and long-term annealing. Such a well-annealed sample shows only a strong, electron-phonon-coupled, single-gap behavior. In contrast, samples reacted and annealed at lower temperatures, as in the earlier two-gap studies, show small chemical composition variations of the A15 phase. We propose that the second gap sightings are actually due to variation of Tc within very difficult-to-fully homogenize samples. A curiosity of the A15 Nb3Sn phase is that almost any mixture of Nb and Sn tries to form a stoichiometric A15 composition, but the residue of course contains off-stoichiometric A15, Nb, and other phases when the Nb:Sn ratio departs from the true 3:1 stoichiometry.

Theoretical Study on the Upper Critical Field of a Layered Superconductor NbSe $$_2$$ 2

Based on two-band Ginzburg-Landau theory, we study the temperature and angular dependences of the upper critical field for superconducting NbSe $$_2$$ crystals. We introduce two variational parameters in our approach, and provide the explicit equations to determine the upper critical field in arbitrary direction. Our analyses strongly support previous scanning tunneling microscopy results and specific heat data, pointing to the existence of two energy gaps in this compound. Our results thus suggest that besides MgB $$_{2}$$ , NbSe $${_2}$$ is another example of two-gap superconductors.

Gauge invariance and spontaneous symmetry breaking in two-gap superconductors

The gauge symmetry of the Ginzburg-Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg-Landau hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region.

Determination of the electron-phonon coupling constants from the experimental temperature dependences of superconducting gaps in MgB2

Experimental temperature dependences Δσ, π(T) of the energy of superconducting gaps for MgB2 samples with the critical temperatures 22 K < T c < 41 K have been fitted by selecting the renormalized electron-phonon coupling constants λ ij with the use of the Moskalenko-Shul system of equations, the expression for the frequency of collective plasma oscillations obtained by Leggett for two-gap superconductors, and two fitting parameters. We previously obtained the dependences Δσ, π(T) by the multiple Andreev reflection spectroscopy of superconductor-constriction-superconductor junctions based on MgB2 with various degree of disorder of the crystal structure. It has been shown that the intraband pairing constants are decisive for the superconductivity mechanism in MgB2; in this case, √V σσ V ππ/V σπ = 8–22 and the ratio of the interband constants α can range from 3 to 11. The set of the Eliashberg coupling constants λ 0 has been qualitatively determined for relatively pure MgB2 with maximum values T c ≈ 40 K. The leading constant is 0.7 < λ σσ 0 ≈ λ eff 0 < 0.9 and depends on the choice of the upper integration limit in the Bardeen-Cooper-Schrieffer (BCS) model and the effective Coulomb repulsion μ iff * . The characteristic ratio for the gap in the σ band is 2Δσ/k B T c = 5.0–6.5.

Direct measurement of the temperature dependence of the magnetic penetration depth in Ba(Fe1−xNix)2As2 superconductors

The temperature dependence of the in-plane magnetic penetration depth λab of Ba(Fe1−xNix)2As2 single crystals is determined directly from the shielding magnetic susceptibility, measured in the Meissner region with the field parallel to the ab layers. The doping levels studied cover the underdoped, optimally doped and overdoped regimes. At temperatures below 0.5Tc a well-defined power-law behavior λab(T) − λab(0) = ATn (with n ≈ 2.5) is observed. At lower temperatures (T < 0.3Tc) the data are still consistent with n = 2 and , as predicted by the strong pair-breaking scenario proposed by Gordon et al (2010 Phys. Rev. B 81, 180501(R)). The temperature dependence of the superfluid density presents a marked positive curvature just below Tc, which is a sign of two-gap superconductivity. The analysis of ρs(T) in terms of a two-gap model allowed estimation of parameters like the in-band and inter-band couplings, the relative weight of each band, and their dependence on the doping level. A comparison with ρs(T) data obtained by using other techniques in compounds with a similar composition is also presented.

On the mixed character of superconductivity fluctuations in two-band systems

We demonstrate that spatially inhomogeneous superconductivity fluctuations in both electron bands coupled via Josephson-type interaction consist of two components scaled by different characteristic lengths not related to the definite bands. Such mixed nature of fluctuations is a specific feature of two-gap superconductivity.

Condensation Energy for a Two-Gap Superconducting State in Nanoparticles

Recent technology and experiments have fabricated high-quality superconducting MgB2 nanoparticles. We investigate properties of two-gap superconductivity in nanosized systems by using a two-sublevel model. In the present work, we analyze the results obtained for superconducting granules in the case of multiband superconductivity. We discuss the finite size effect in multiband superconductors. A definition of the critical level spacing of two-gap superconductivity is also presented, and we discuss the condensation energy and the parity gap of two-gap superconductivity in relation to the size dependence of those properties with two bulk gaps and the effective pair scattering process between two sublevels.

AN ATTEMPT AT A RESONATING MEAN-FIELD THEORETICAL DESCRIPTION OF THERMAL BEHAVIOR OF TWO-GAP SUPERCONDUCTIVITY

The resonating mean-field theory (Res-MFT) has been applied and shown to effectively describe two-gap superconductivity (SC). Particularly at T = 0 using a suitable chemical potential, the two-gap SC in MgB2 has been well described by the Res-Hartree-Bogoliubov theory (Res-HBT). The Res-HB ground state generated with HB wavefunctions almost exhausts the ground-state correlation energy in all the correlation regimes. In this paper we make an attempt at a Res-MF theoretical description of thermal behavior of the two-gap SC. In an equal energy-gap case we find a new formula leading to a higher critical temperature Tc than the Tc of the usual HB formula.

Current-phase relation of double-barrier Josephson junctions with a two-gap superconductor as intermediate electrode

The current-phase (I-ϕ) relation of a double-barrier Josephson junction with a two-gap superconductor as intermediate electrode is derived by means of a simplified version of Ohta’s model. As in conventional double-barrier Josephson junctions, a marked skewness in the I-ϕ curves is present. Moreover, as in heterotic Josephson devices, a reduction of the maximum Josephson current is predicted. An appropriate experiment to verify the rich behavior of this type of Josephson device is suggested.

Evidence for two-gap superconductivity in the non-centrosymmetric compound LaNiC2

We study the superconducting properties of the non-centrosymmetric compound LaNiC2 by measuring the London penetration depth Δλ(T), the specific heat C(T,B) and the electrical resistivity ρ(T,B). Both Δλ(T) and the electronic specific heat Ce(T) exhibit behavior at low temperatures that can be described in terms of a phenomenological two-gap Bardeen–Cooper–Schrieffer (BCS) model. The residual Sommerfeld coefficient in the superconducting state, γ0(B), shows a rapid increase at low fields and then an eventual saturation with increasing magnetic field. A pronounced upturn curvature is observed in the upper critical field Bc2(T) near Tc. All these experimental observations support the existence of two-gap superconductivity in LaNiC2.

Two-gap superconductivity: interband interaction in the role of an external field

We show that weak interband pair-transfer interaction affects the weaker-superconductivity component of a two-gap system as an external field associated with the order parameter, similarly to an external magnetic field for ferromagnetics or an external electric field for ferroelectrics.