Two-band Superconductor Research Articles

Soliton states in mesoscopic two-band-superconducting cylinders

In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the presence of “Josephson-type” interband coupling, when phase winding numbers are different for each component of the superconducting order parameter. We evaluate the Gibbs free energy of the system up to second-order terms in a certain dimensionless parameter ɛ≈Lm/Lk≪1, where Lm and Lk are the magnet and kinetic inductance, respectively. We derive the complete set of exact soliton solutions. These solutions are thoroughly analyzed from the viewpoint of both local and global (thermodynamic) stability. In particular, we show that rotational-symmetry-breaking caused by the formation of solitons gives rise to a zero-frequency rotational mode. Although soliton states prove to be thermodynamically metastable, the minimal energy gap between the lowest-lying single-soliton states and thermodynamically stable zero-soliton states can be much smaller than the magnetic Gibbs free energy of the latter states, provided that intraband “penetration depths” differ substantially and interband coupling is weak. The results of our investigation may apply to a wide class of mesoscopic doubly-connected structures exhibiting two-band superconductivity.

Two-band BCS mechanism of superconductivity in a Ba(Fe0.9Co0.1)2As2 high-temperature superconductor

Terahertz and infrared spectra of the conductivity, σ(ν), and dielectric constant, ɛ(ν), of a Ba(Fe0.9Co0.1)2As2 film (Tc = 20 K) have been analyzed together with previous specific-heat and angular resolved photoelectron spectroscopy data. It has been shown that the spectra σ(ν) and ɛ(ν) of Ba(Fe0.9Co0.1)2As2 in the superconducting phase at T = 5 K, as well as the magnetic field penetration depth, can be described well using the standard Bardeen-Cooper-Schrieffer (BCS) model with an additive contribution of electron and hole bands. It has been found that the measured temperature dependence of the magnetic field penetration depth in a wide temperature range 5 K < T < Tc can be described only with the introduction of interband pairing interaction. The coupling constant of electron and hole bands, λ1, 2 = 0.1, as well as the temperature dependences of superconducting gaps in the electron and hole subsystems, has been determined using the model of two-band superconductivity developed earlier for MgB2.

Conditions for nonmonotonic vortex interaction in two-band superconductors

We describe a semi-analytic approach to the two-band Ginzburg-Landau theory, which predicts the behavior of vortices in two-band superconductors. We show that the character of the short-range vortex-vortex interaction is determined by the sign of the normal domain - superconductor interface energy, in analogy with the conventional differentiation between type-I and type-II superconductors. However, we also show that the long-range interaction is determined by a modified Ginzburg-Landau parameter $\kappa^*$, different from the standard $\kappa$ of a bulk superconductor. This opens the possibility for non-monotonic vortex-vortex interaction, which is temperature-dependent, and can be further tuned by alterations of the material on the microscopic scale.

Ginzburg–Landau theory of multi-band superconductivity and applications to Fe pnictides

We investigate multi-component superconductors, in relation to iron pnictides, by using the Ginzburg–Landau theory. We show that a three-band superconductor exhibits several significant properties that are not found in single-band or two-band superconductors. The frustrating pairing interaction among Fermi surfaces may lead to a time-reversal symmetry broken pairing state. In fact, we have a solution with time-reversal symmetry breaking, that is, a chiral solution when there is such a frustration. The Ginzburg–Landau equation for three-component superconductors leads to a double sine-Gordon equation. A kink solution exists to this equation that results in the existence of fractional-quantum flux vortices on the domain wall.

The critical magnetic field of anisotropic two-band magnetic superconductors

The upper and lower critical fields, and the critical field ratio of an anisotropic two-band magnetic superconductor in the Ginzburg–Landau (GL) scenario is derived analytically. The temperature-dependent upper critical field is investigated and applied to Fe-based superconductors. We find that a very high value of zero-temperature upper critical field in Fe-based superconductors can be found in the negative differential susceptibility region. The temperature-dependent upper critical field is presented in two formulas, in the empirical view and in the GL two-band view, which agrees with the experimental results.

Quasiclassical description of a superconductor with a spin density wave

We derive equations for the quasiclassical Green's functions $\mathrm{g\ifmmode \check{}\else \v{}\fi{}}$ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix $\mathrm{g\ifmmode \check{}\else \v{}\fi{}}$ are the retarded, advanced, and Keldysh functions, each of which is an $8\ifmmode\times\else\texttimes\fi{}8$ matrix in the Gor'kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an ${S}_{\text{SDW}}/N/{S}_{\text{SDW}}$ junction is also calculated as a function of the phase difference $\ensuremath{\varphi}$. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors ${S}_{\text{SDW}}$ and is proportional to $\mathrm{sin}\ensuremath{\varphi}$. The dissipationless spin current ${j}_{\text{sp}}$ depends on the angle $\ensuremath{\alpha}$ between the magnetization vectors in the same way (${j}_{\text{sp}}~\mathrm{sin}\ensuremath{\alpha}$) and is not zero above the superconducting transition temperature.

Influence of linear-energy-dependent density of states on two-band superconductors: Three-square-well model approach

We have derived the expressions for the transition temperature and the isotope effect exponent within the framework of Bogoliubov–Valatin two-band formalism using a linear-energy-dependent electronic density of states assuming a three-square-well potentials model. Our results show that the approach could be used to account for a wide range of values of the transition temperature and isotope effect exponent. The relevance of the present calculations to MgB2 is analyzed.

Electron transport across the interface of a normal metal and a two-band superconductor with interband pairing

A consistent scheme taking into account both intra- and interband pairings has been proposed for diagonalizing the Hamiltonian of a superconductor. The temperature dependence of the order parameter of the superconductor with interband pairing has been calculated. The electron transport across the interface of a normal metal and the two-band superconductor with interband pairing has been analyzed.

Thermal valve of superconductor heterostructures with different pairing types

Electron heat transport across the interface between a two-band superconductor with the inter- and intra- band pairing types and a normal metal, and a ferromagnet formed by domains with different magnetization directions is analyzed. The possibility of controlling the heat flow by varying the magnetization direction of one of the ferromagnetic domains is considered. The microrefrigerating applications of these structures are discussed.

Critical current density of a YNi2B2C superconductor in the two-band Ginzburg-Landau model

An analytical formula is obtained for the temperature dependence of the critical current density of a two-band superconductor. In deriving the formula, linearized equations of the two-band Ginzburg-Landau theory are used and the results are compared with the experimental data for YNi2B2C.

Thermal conductivity in the mixed state of a superconductor at low magnetic fields

We evaluate accurate low-field/low-temperature asymptotics of the thermal conductivity perpendicular to magnetic field for one-band and two-band s-wave superconductors using Keldysh-Usadel formalism. We show that heat transport in this regime is limited by tunneling of quasiparticles between adjacent vortices across a number of local points and therefore widely-used approximation of averaging over circular unit cell is not valid. In the single-band case, we obtain parameter-free analytical solution which provides theoretical lower limit for heat transport in the mixed state. In the two-band case, we show that heat transport is controlled by the ratio of gaps and diffusion constants in different bands. Presence of a weaker second band strongly enhances the thermal conductivity at low fields

Ginzburg-Landau theory of two-band superconductors: Absence of type-1.5 superconductivity

It is shown that within the Ginzburg-Landau (GL) approximation the order parameters ${\ensuremath{\Delta}}_{1}(\mathbf{r},T)$ and ${\ensuremath{\Delta}}_{2}(\mathbf{r},T)$ in two-band superconductors vary on the same length scale, the difference in zero-$T$ coherence lengths ${\ensuremath{\xi}}_{0\ensuremath{\nu}}~\ensuremath{\hbar}{v}_{F\ensuremath{\nu}}/{\ensuremath{\Delta}}_{\ensuremath{\nu}}(0)$, $\ensuremath{\nu}=1,2$ notwithstanding. This amounts to a single physical GL parameter $\ensuremath{\kappa}$ and the classic GL dichotomy: $\ensuremath{\kappa}&lt;1/\sqrt{2}$ for type I and $\ensuremath{\kappa}&gt;1/\sqrt{2}$ for type II.

Radiation damages under irradiation of the BCS superconductor MgB2 by high-energy electrons

This paper reports on the results of investigations of the influence of irradiation of the two-band BCS superconductor MgB2 by electrons with an average energy \( \bar {\rm E} \) ∼ 10 MeV at high doses (0 ≤ ϕt ≤ ∼2.5 × 1018 cm−2) on the temperature and width of the transition to the superconducting state, the temperature dependence of the electrical resistivity in the normal state, the crystal lattice parameters, and the diffraction line intensity. An increase in the electron irradiation dose ϕt leads to the following effects: a decrease in the critical temperature Tc; an increase in the width of the superconducting transition ΔTc; and a decrease in the “residual electrical resistivity” ρ273 K/ρ40 K, in the parameters a and c of the hexagonal crystal lattice, and in the ratio between the diffraction line intensities I110/I100. From analyzing the results obtained, it has been established that the main type of radiation damages under irradiation of the BCS superconductor MgB2 by high-energy electrons is the formation of vacancies in the B sublattice, which leads to a narrowing of the large band gap Δσ on the Fermi surface.

Extended Ginzburg-Landau Formalism for Two-Band Superconductors

Recent observation of unusual vortex patterns in MgB(2) single crystals raised speculations about possible "type-1.5" superconductivity in two-band materials, mixing the properties of both type-I and type-II superconductors. However, the strict application of the standard two-band Ginzburg-Landau (GL) theory results in simply proportional order parameters of the two bands-and does not support the "type-1.5" behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small τ=1-T/T(c) parameter) for a two-band clean s-wave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T→T(c). The extended version of the two-band GL formalism improves the validity of GL theory below T(c) and suggests revisiting the earlier calculations based on the standard model.

Numerical study of vortex pattern in framework of two-band Ginzburg-Landau theory

Numerical modeling of vortex nucleation in external magnetic field in two-band superconductor using modified Ginzburg-Landau theory is conducted. Results of simulation experiments for a two-band superconducting films MgB 2 near the critical temperature in perpendicular magnetic field is presented. Obtained results seems interesting from the point of investigation of pecularities of vortex dynamics in systems with complex order parameter and another possible applications.

The two-band Ginzburg-Landau theory analysis of the surface critical field of the two-band superconductor Lu2Fe3Si5

Two-band Ginzburg-Landau (GL) theory is adopted to analyze the surface critical field Hc3 of Lu2Fe3Si5 . When the surface of a superconductor coincides with any of crystallographic planes and is parallel to the external magnetic field H, the ratio Hc3/Hc2 (where Hc2 is the upper critical field of Lu2Fe3Si5) is strongly dependent on temperature. When the surface of a superconductor coincides with the bc plane and is parallel to H, the ratio depends not only on temperature, but also on the angle between the c axis and H. However, the ratio is constant for single-band superconductors.

Two-Bands Superconductivity with Intra- and Interband Pairing for Synthetic Superlattices

We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like fermi surface. In this pairing scenario, driven by the interplay between interband $V_{i,j}$ and intraband $V_{i,i}$ pairing terms, we have solved the two gap equations at the critical temperature $T = T_c$ and calculate $T_c$ and the chemical potential $\mu$ as a function of the number of carriers $n$ for various values of pairing interactions, $V_{1,1}$, $V_{2,2}$, and $V_{1,2}$. The results show the complexity of the physics of condensates with multiple order parameters with the chemical potential near band edges.

Thermal Fluctuations of Order Parameters in Two-Gap Superconductors

The thermodynamics of a finite two-band superconductor has been studied by means of the Hubbard–Stratonovich representation of partition function in the static approximation. The temperature behavior of heat capacity depends substantially on interband interaction and volume. Interband coupling controls the distribution of thermal gap fluctuations on the temperature scale according to the changes in superconducting ordering.

Electron-phonon coupling and two-band superconductivity of Al- and C-dopedMgB2

We have studied the electron-phonon and superconducting properties of the Mg{1-x}AlxB2 and MgB{2(1-y)}C{2y} alloys within the framework of density functional theory using the self-consistent virtual-crystal approximation. For both alloys, the Eliashberg spectral functions and the electron-phonon coupling constants have been calculated in the two-band model for several concentrations up to x(Al)=0.55 and y(C)=0.175. We solved numerically the two-band Eliashberg gap equations without considering interband scattering. Using a single parameter for the Coulomb pseudopotential, which was determined for the undoped compound, we were able to reproduce the experimental doping dependence of Delta_sigma, Delta_pi, and T_c for both alloys on a quantitative level. In particular, the observed differences in the doping range of superconductivity between Al and C doping indicate a pronounced influence of the doping site, which can be explained naturally in the present approach without the need to invoke interband scattering, suggesting that this factor plays only a minor role.

Highly anisotropic energy gap in superconductingBa(Fe0.9Co0.1)2As2from optical conductivity measurements

We have measured the complex dynamical conductivity, $\sigma = \sigma_{1} + i\sigma_{2}$, of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ ($T_{c} = 22$ K) at terahertz frequencies and temperatures 2 - 30 K. In the frequency dependence of $\sigma_{1}$ below $T_{c}$, we observe clear signatures of the superconducting energy gap opening. The temperature dependence of $\sigma_{1}$ demonstrates a pronounced coherence peak at frequencies below 15 cm$^{-1}$ (1.8 meV). The temperature dependence of the penetration depth, calculated from $\sigma_{2}$, shows power-law behavior at the lowest temperatures. Analysis of the conductivity data with a two-gap model, gives the smaller isotropic s-wave gap of $\Delta_{A} = 3$ meV, while the larger gap is highly anisotropic with possible nodes and its rms amplitude is $\Delta_{0} = 8$ meV. Overall, our results are consistent with a two-band superconductor with an $s_{\pm}$ gap symmetry.