We present a microscopic study of the behavior of the order parameters near boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite non-zero interband Josephson coupling.
In this paper we study the effect of non-magnetic impurities on two-band $s_{\pm}$ superconductors by deriving the corresponding Ginzburg-Landau (GL) equation. Depending on the strength of (impurity-induced) inter-band scattering we find that there are two distinctive regions where the superconductors behave very differently. In the strong impurity induced inter-band scattering regime $T_c<<τ^{-1}_t$, where $τ_t\sim$ mean-life time an electron stays in one band the two-band superconductor behaves as an effective one-band dirty superconductor. In the other limit $T_c\geqτ^{-1}_t$, the dirty two…
We calculate the s- and d-wave superconductor order parameter in the vicinity of a tilt grain boundary. We do this self-consistently within the Bogoliubov de Gennes equations, using a realistic microscopic model of the grain boundary. We present the first self-consistent calculations of supercurrent flows in such boundaries, obtaining the current-phase characteristics of grain boundaries in both s-wave and d-wave superconductors.
Green function techniques for studying nonequilibrium processes in dirty two-band superconductors are discussed. Perturbation expansions and Green function equations are developed. A time dependent modification of the Usadel equation is given.
Green's function techniques for studying nonequilibrium processes in two-band superconductor are discussed. Perturbation expansions and Green's function equations are developed. A time dependent modification of the Ginsburg-Landau equation is given.
For many applications of polycrystalline high-Tc superconductors the small critical currents of the grain boundaries pose a severe problem. To solve this problem we derive novel designs for the microstructure of coated conductors.
The anisotropy of the London penetration depth is evaluated for two-band superconductors with arbitrary inter- and intra-band scattering times. If one of the bands is clean and the other is dirty in the absence of inter-band scattering, the anisotropy is dominated by the Fermi surface of the clean band and is weakly temperature dependent. The inter-band scattering also suppress the temperature dependence of the anisotropy.
In superconductors with three or more bands, time-reversal symmetry (TRS) may be broken in the presence of repulsive interband couplings, resulting in a pair of degenerate states characterized by opposite chiralities. We consider a Josephson junction between a three-band superconductor with broken TRS and a single-band superconductor. Phenomena such as asymmetric critical currents, subharmonic Shapiro steps and symmetric Fraunhhofer patterns are revealed theoretically. Existing experimental results are discussed in terms of the present work.
It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role - such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg-Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate m…
Electronic band structure of boron-rich low-temperature superconductors UB12-like dodecaboride YB12 and CaB6-like hexaboride YB6 are investigated using the first-principle FLMTO calculations and compared with one for layered YB2 and the new "medium-Tc" superconductor MgB2 diborides.
We study the spin-lattice relaxation rate of nuclear magnetic resonance in a two-band superconductor. Both conventional and unconventional pairing symmetries for an arbitrary band structure in the clean limit are considered. The importance of the inter-band interference effects is emphasized. The calculations in the conventional case with two isotropic gaps are performed using a two-band generalization of Eliashberg theory.
Within the formalism of Usadel equations the Josephson effect in dirty point contacts between single-band and three-band superconductors is investigated. The general expression for the Josephson current, which is valid for arbitrary temperatures, is obtained. We calculate current-phase relations for very low temperature and in the vicinity of the critical temperature. For three-band superconductors with broken time-reversal symmetry (BTRS) point contacts undergo frustration phenomena with different current-phase relations, corresponding to ϕ-contacts. For three-band superconductors without BTR…
We apply the generalized two-band model of superconductivity to calculate the electronic contribution to the specific heat, superconducting gaps and electron-boson coupling constants of the multi-band layered superconductors MgB2 and Ba(Fe0.925Co0.075)2As2. For both compounds, the obtained temperature-behavior of the specific heat well describes the experimental data. We compare our findings with the "two-band - model" that is frequently used to calculate the electronic specific heat, and that is applicable only for superconductors with strong interband scattering ("dirty" enough superconducto…
We investigate flux penetration in a disordered type II superconductor by molecular dynamics simulations of interacting vortices. We focus on the effect of different boundary conditions on the scaling laws for flux front propagation. The numerical results can be interpreted using a coarse grained description of the system in terms of a non-linear diffusion equation. We propose a phenomenological equation for the front position that captures the essential behavior of the system and recovers the scaling exponents.
We show that an induced $s$-wave harmonic in the superconducting gap of an orthorhombic $d_{x^2-y^2}$ superconductor strongly affects the excitation spectrum near a twinning plane. In particular, it yields bound states of zero energy with areal density proportional to the relative weight of the $s$-wave component. An unusual scattering process responsible for the thermal conductivity across the twin boundary at low temperatures is also identified.
A theory of fluctuations in two-band superconductor MgB$_{2}$ is developed. Since the standard Ginzburg-Landau (GL) approach fails in description of its properties, we generalize it basing on the microscopic theory of a two-band superconductor. Calculating the microscopic fluctuation propagator, we build up the nonlocal two-band GL functional and the corresponding time-dependent GL equations. This allows us to calculate the main fluctuation observables such as fluctuation specific heat and conductivity.
We predict a complete TM-TE transformation of the polarization of terahertz electromagnetic waves reflected from a strongly anisotropic boundary of a layered superconductor. We consider the case when the wave is incident on the superconductor from a dielectric prism separated from the sample by a thin vacuum gap. The physical origin of the predicted phenomenon is similar to the Wood anomalies known in optics, and is related to the resonance excitation of the oblique surface waves. We also discuss the dispersion relation for these waves, propagating along the boundary of the superconductor at s…
Bardeen-Cooper-Schrieffer (BCS) theory describes a superconducting transition as a single critical point where the gap function or, equivalently, the order parameter vanishes uniformly in the entire system. We demonstrate that in superconductors described by standard BCS models, the superconducting gap survives near the sample boundaries at higher temperatures than superconductivity in the bulk. Therefore, conventional superconductors have multiple critical points associated with separate phase transitions at the boundary and in the bulk. We show this by revising the Caroli-De Gennes-Matricon …
We consider excitation spectrum near a twin boundary in an orthorhombic $d+s$ superconductor. The low-energy spectrum is highly sensitive to the presence of the small amount of s-wave component. Robustness of the bound states at the Fermi level with respect to impurities and an extra boundary potential is investigated. The role of Andreev transmission process for the low-temperature thermal conductivity across twin boundaries is studied for an impure superconductors. At very low temperatures the bulk part and the twin boundaries part of the thermal conductivity have similar linear-$T$ dependen…
Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we revise microscopic derivation of the superconductor-insulator boundary conditions for the Ginzburg-Landau (GL) model. We obtain a negative contribution to free energy in the form of surface integral. Boundary conditions for the conventional superconductor have the form $\textbf{n} \cdot \nabla ψ= \text{const} ψ$. These are shown to follow from considering the order parameter reflected in the boundary. The boundary conditions are also derived for more general GL models with higher-order derivatives and pair-density-wave states. It sh…
The upper and lower critical field, and the critical field ratio of an anisotropic two-band magnetic superconductors in Ginzburg-Landau(GL) scenery is derived analytically. The temperature-dependent on the upper critical field is investigated and applied to Fe-based superconductors. We find that the 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 as in the empirical view and in the GL two-band view that agrees with the…
We investigate a collective excitation (Leggett's mode) corresponding to small fluctuations of the relative phase of two condensates in two-band superconductor using the effective ``phase only'' action. We consider the possibility of observing Leggett's mode in MgB$_2$ superconductor and conclude that for the known at present values of the two-band model parameters for MgB$_2$ Leggett's mode arises above the two-particle threshold.
We consider the interface between a Bardeen-Cooper-Schrieffer superconductor and non-superconducting band insulator. We show that under certain conditions, such interfaces can have an elevated superconducting critical temperature, without increasing the strength of the pairing interaction at the interface. We identify the regimes where the interface critical temperature exceeds the critical temperature associated with a superconductor-vacuum interface.
In the comment of M.E. Palistrant (arXiv: cond-mat/0305496) the main results of the theory of superconductors with overlapping energy bands are formulated. The comment provides a list of references to the classical papers of the author of this theory, Prof. V.A.Moskalenko, and coworkers. This theory has been generalized by Prof. M.E.Palistrant and coworkers to the case of a reduced density of charge carriers. Respective references are also included in the comment. In our opinion, it would be useful to provide in addition to the above comment the references covering our research of the kinetic …
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 $κ^*$, different from the standard $κ$ of a bulk superconductor. This opens the possibility for non…
Iron-based superconductors offer an ideal platform for studying topological superconductivity and Majorana fermions. In this paper, we carry out a comprehensive study of the band topology and topological surface states of a number of iron-based superconductors using a combination of density functional theory (DFT) and dynamical mean field theory. We find that the strong electronic correlation of Fe 3d electrons plays a crucial role in determining the band topology and topological surface states of iron-based superconductors. Electronic correlation not only strongly renormalizes the bandwidth o…
We calculate the effect of nonmagnetic impurity scattering on the spin-lattice relaxation rate in two-band superconductors with the s-wave pairing symmetry. It is found that for the interaction parameters appropriate for MgB2 the Hebel-Slichter peak is suppressed by disorder in the limit of small interband impurity scattering rate. In the limit of strong impurity scattering, when the gap functions in the two bands become nearly equal, the single-band behavior is recovered with a well-defined coherence peak just below the transition temperature.
We point out that essentially all multi-band superconductors have an odd-frequency pairing component, as follows from a general symmetry analysis of even- and odd-frequency pairing states. We show that odd-frequency superconducting pairing requires only a finite band hybridization, or scattering, and non-identical intraband order parameters, of which only one band needs to be superconducting. Under these conditions odd-frequency odd-interband pairing is always present. From a symmetry analysis we establish a complete reciprocity between parity in band-index and frequency.
Topological defects, such as magnetic-flux-carrying quantum vortices determine the magnetic response of superconductors and hence are of fundamental importance. Here, we show that stable $\mathbb{C}P^2$ skyrmions exist in three-band $s+\rm{i} s$ superconductors as fully self-consistent solutions to a microscopic Bogoluibov-de Gennes model. This allows us to calculate microscopically the magnetic signatures of $\mathbb{C}P^2$ skyrmions and their footprint in the local density of states.
We investigate several important properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken time-reversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a …
The relaxation iterative method is used to minimize Ginzburg-Landau model for the two-band superconductor with Josephson-coupling. A stable spontaneous vortex-antivortex pair with long range order has been revealed. Our result appears due to the Josephson-coupling effect, which leads to a linearly-dependence of total free energy on the distance between vortex-antivortex pair, hence accounts for this phenomenon.
Understanding the nature of grain boundary (GB) characteristics in combination with creating low-energy GBs by modifying the processing conditions, so-called GB engineering, is of great importance for controlling and reducing the defect density, leading to improved functionalities of polycrystalline metals and ceramics. For superconductors particularly, including both low- and high-temperature superconductors, GB engineering has been developed to improve especially the critical current densities, Jc, across these GBs. The intrinsic physical properties of a given superconductor such as the cohe…
We study collective excitations in three- and four-band superconductors with inter-band frustration, which causes neither 0 nor $π$ inter-band phases in the superconducting state. Using a low-energy spin-Hamiltonian originating from a multi-band tight-binding model, we find that a massless Leggett mode occurs in a wide parameter region of this four-band system. This massless mode is related to the fact that the mean-field energy does not depend on a continuous superconducting phase. In other words, we find a link of the massless mode with a degeneracy between a time-reversal-symmetry-breaking …
We analyze the paradigmatic competition between intra-band and cross-band Cooper-pair formation in two-band superconductors, neglected in most works to date. We derive the phase-sensitive gap equations and describe the crossover between the intraband-dominated and the crossband-dominated regimes, delimited by a ``gapless'' state. Experimental signatures of crosspairing comprise notable gap-splitting in the excitation spectrum, non-BCS behavior of gaps versus temperature, as well as changes in the pairing symmetry as a function of temperature. The consequences of these findings are illustrated …
The two-band $s^{\pm}$-wave state is currently considered to be the most promising candidate for newly discovered iron-based high-$T_c$ superconductors. In this work we study theoretically the ultrasound attenuation in $s^{\pm}$-wave two-band superconductors. The impurity effect is calculated within the $\mathcal{T}$-matrix approximation. In particular, our theory predict that, when the sizes of two order parameter are comparable, a Hebel-Slichter peak may show up in the ultrasound attenuation versus temperature curves. Our calculations also confirmed the presence of the resonant impurity scat…
The effect of anisotropic order parameter to specific heat of anisotropic two-band superconductors in BCS weak-coupling limit are investigated. An analytical specific heat jump and the numerical specific heat are shown by using anisotropic order parameters, and the electron-phonon interaction and non-electron-phonon interaction. The two model of anisotropic order parameters are used for numerical calculation that we find little effect to the numerical results . The specific heat jump of, and superconductors can fit well with the both of them. By comparing to experimental data overall range of …
We investigate the effects of magnetic impurities in a superconducting state with $s_\pm$ pairing symmetry. Within a two-band model, we find that the intra-band magnetic scattering serves as a pair breaker while the inter-band magnetic scattering preserves pairing and hardly affects transition temperature in the Born limit. We also show that the same physics can persist beyond the weak scattering region. Our results coincide with recent experimental measurements in iron-based superconductors and thus provides an indirect evidence of the possible $s_\pm$ pairing symmetry in these materials.
Multi-phase physics is a new physics of multi-gap superconductors. Multi-band superconductors exhibit many interesting and novel properties. We investigate the dynamics of the phase-difference mode and show that this mode yields a new excitation mode. The phase-difference mode is represented as an abelian vector field. There are massless modes when the number of gaps is greater than three and the Josephson term is frustrated. The fluctuation of phase-difference modes with non-trivial topology leads to the existence of a fractional-quantum flux vortex in a magnetic field. A superconductor with …
By numerically solving the Bogoliubov-de Gennes equations for the single vortex state in a two-band superconductor, we demonstrate that the disparity between the healing lengths of two contributing condensates is strongly affected by the band Fermi velocities, even in the presence of the magnetic field and far beyond the regime of nearly zero Josephson-like coupling between bands. Changing the ratio of the band Fermi velocities alters the temperature dependence of the condensate lengths and significantly shifts parameters of the ``length-scales locking" regime at which the two characteristic l…
The full-potential linearized augmented plane wave method with the generalized gradient approximation for the exchange and correlation potential (LAPW-GGA) is used to understand the electronic band structure of fluorine-arsenide SrFeAsF as a possible parent material for a new group of oxygen-free FeAs superconductors. The electronic bands, density of states, Fermi surface and atomic charges have been evaluated and discussed for high-temperature tetragonal and low-temperature orthorhombic SrFeAsF phases.
Superconductors like other solids cannot relax instantaneously from thermally excited (disturbed) states to thermodynamic equilibrium. In this paper, relaxation of a multi-filamentary and of a thin film superconductor from thermal excitations is simulated. Absorption of radiation or, under conductor movement, release and transformation of mechanical tension to thermal energy are examples. The paper applies numerical simulations of superconductor energy states, as many-particle systems, under basic thermodynamic and standard, multi-component heat transfer principles (solid conduction plus radia…
The current-phase relation (CPR) for asymmetric 45 degree Josephson junctions between two d-wave superconductors has been predicted to exhibit an anomalous periodicity. We have used the single-junction interferometer to investigate the CPR for this kind of junctions in YBCO thin films. Half-fluxon periodicity has been experimentally found, providing a novel source of evidence for the d-wave symmetry of the pairing state of the cuprates.
A phase soliton is a topological defect peculiar to two-band superconductors, which is associated with a $2π$ winding of the relative phase of the two superconducting condensates. We study the quasiparticle spectrum in the presence of a single planar phase soliton. We show that the order parameter phase variation in each of the bands leads to the existence of subgap states bound to the soliton. Calculation of the soliton energy valid at all temperatures is presented, with the exact analytical results obtained for a simple soliton model.
We calculate the spectrum of the Andreev boundary modes in a two-dimensional superconductor formed at an interface between two different non-superconducting materials, e.g. insulating oxides. Inversion symmetry is absent in this system, and both the electron band structure and the superconducting pairing are strongly affected by the spin-orbit coupling of the Rashba type. We consider isotropic s-wave pairing states, both with and without time-reversal symmetry breaking, as well as various d-wave states. In all cases, there exist subgap Andreev boundary states, whose properties, in particular, …
Within the BCS framework a multiband model with d-wave symmetry is considered. Generalized Fermi surface topologies via band overlapping are introduced. The band overlap scale is of the order of the Debye energy. The order parameters and the pairing have d-wave symmetry. Experimental values reported for the critical temperatures $T_c(x)$ and the order parameters, $Δ_0(x)$, in terms of dopping $x$ are used. Numerical results for the coupling and the band overlapping parameters in terms of the doping are obtained for the cuprate superconductor $La_{2-x}Sr_xCuO_4$.
The superconducting sesquicarbides R2C3 have noncentrosymmetric point group symmetry Td. Spin-orbit coupling lifts the spin degeneracy of electronic bands in the most of the Brillouin zone. Nevertheless, due to high symmetry, there are a few directions along which the Fermi surfaces must touch. This leads to the two-band effects in the superconducting state.
We report observation of Leggett's collective mode in a multi-band MgB2 superconductor with T_c=39K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on the first principle computations.
A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.
We present LDA calculated electronic structure of recently discovered superconductor SrPt2As2 with Tc=5.2K. Despite its chemical composition and crystal structure are somehow similar to FeAs-based high-temperature superconductors, the electronic structure of SrPt2As2 is very much different. Crystal structure is orthorhombic (or tetragonal if idealized) and has layered nature with alternating PtAs4 and AsPt4 tetrahedra slabs sandwiched with Sr ions. The Fermi level is crossed by Pt-5d states with rather strong admixture of As-4p states. Fermi surface of SrPt2As2 is essentially three dimensional…
We address the question of how phonons of various frequencies contribute to the superconducting transition temperature $T_c$ of a multi-band superconductor by considering the functional derivatives of $T_c$ with respect to various intraband and interband electron-phonon coupling functions. A general scheme for computing such functional derivatives is developed. The proofs are given that the functional derivatives which are diagonal in band indices are linear in phonon energy $Ω$ at small $Ω$, while the functional derivatives which are off-diagonal in band indices diverge at $Ω$ = 0 as 1/$Ω$. T…
Using the Ginzburg-Landau theory for two-band superconductors, we determine the surface energy, sigma_s, between coexisting normal and superconducting states at the thermodynamic critical magnetic field. Close to the transition temperature, where the Ginzburg-Landau theory is applicable, we demonstrate that the two-band problem maps onto an effective single band problem. While the order parameters of the two bands may have different amplitudes in the homogeneous bulk, near the critical temperature the Josephson-like coupling between the bands leads to the same spatial dependence of both order …
Besides the well-known existence of Andreev bound states, the zero-energy local density of states at the boundary of a d-wave superconductor strongly depends on the boundary geometry itself. In this work, we examine the influence of both a simple wedge-shaped boundary geometry and a more complicated polygonal or faceted boundary structure on the local density of states. For a wedge-shaped boundary geometry, we find oscillations of the zero-energy density of states in the corner of the wedge, depending on the opening angle of the wedge. Furthermore, we study the influence of a single Abrikosov …
Magnetic response is a fundamental property of superconducting materials, which helps to distinguish two superconductivity types: the ideally diamagnetic type I and type II, which can develop the mixed state with Abrikosov vortices. We demonstrate that multi-band superconductors with one shallow band, that have recently attracted much attention for their high critical temperatures and unusual properties, often stay apart of this simple classification. In a wide range of microscopic parameters such systems fall into the inter-type or transitional interval in between the standard types and displ…
We discuss bound states appearing at the interface between two different superconductors characterized by different nontrivial topological numbers such as one-dimensional winding numbers and Chern numbers. The one-dimensional winding number characterizes d_{xy} and p_x wave superconductors. The Chern number characterizes chiral-p, chiral-d, and chiral-f wave superconductors. The interfacial bound state appears at the zero-energy when the topological numbers of the two superconductors are different from each other. When the two superconductors are characterized by the Chern numbers n and m, for…
In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$…
We study the structure of Abrikosov vortices in two-band superconductors for different external magnetic fields and different parameters of the bands. The vortex core size determined by the coherence lengths are found to have qualitatively different behaviour from that determined by the quasiparticle density of states spatial variation. These different vortex core length scales coincide near the upper critical field, while the discrepancy between them becomes quite significant at lower fields. Within the diffusive approximation we demonstrate several generic regimes in the field dependence of …
