We consider the amplitude (Higgs) mode in a superconductor with a condensate flow (supercurrent). We demonstrate that, in this case, the amplitude mode corresponding to oscillations δ|Δ|_{Ω}exp(iΩt) of the superconducting gap is excited by an external ac electric field E_{Ω}exp(iΩt) already in the first order in |E_{Ω}|, so that δ|Δ|_{Ω}∝(v_{0}E_{Ω}), where v_{0} is the velocity of the condensate. The frequency dependence δ|Δ|_{Ω} has a resonance shape with a maximum at Ω=2Δ. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude δ|Δ(t)| contribute to the admittance Y_{Ω}. We provide a formula for admittance of a superconductor with a supercurrent. The predicted effect opens new ways of experimental investigation of the amplitude mode in superconductors and materials with superconductivity competing with other states.
We consider a simple model of a quasi-one-dimensional conductor in which two order parameters (OP) may coexist, i.e., the superconducting OP ∆ and the OP W that characterizes the amplitude of a chargedensity wave (CDW). In the mean field approximation we present equations for the matrix Green's functions G i k , where the first subscript i relates to the one of the two Fermi sheets and the other, k, operates in the Gor'kov-Nambu space. Using the solutions of these equations, we find stationary states for different values of the parameter describing the curvature of the Fermi surface, µ, which can be varied, e.g., by doping. It is established, in particular, that in the interval µ 1 < µ < µ 2 the self-consistency equations have a solution for coexisting OPs ∆ and W . However, this solution corresponds to a saddle point in the energy functional Φ(∆,W ), i.e., it is unstable. Stable states are: 1) the W-state, i.e., the state with the CDW (W = 0, ∆ = 0) at µ < µ 2 ; and 2) the S-state, i.e., the purely superconducting state (∆ = 0, W = 0) at µ 1 < µ. These states correspond to minima of Φ. At µ < µ 0 = (µ 1 + µ 2 )/2, the state 1) corresponds to a global minimum, and at µ 0 < µ, the state 2) has a lower energy, i.e., only the superconducting state survives at large µ. We study the dynamics of the variations δ∆ and δW from these states in the collisionless limit. It is characterized by two modes of oscillations, the fast and the slow one. The fast mode is analogous to damped oscillations in conventional superconductors. The frequency of slow modes depends on the curvature µ and is much smaller than 2∆/ħ if the coupling constants for superconductivity and CDW are close to each other. The considered model can be applied to high-T c superconductors where the parts of the Fermi surface near the "hot" spots may be regarded as the considered two Fermi sheets. We also discuss relation of the considered model to the simplest model for Fe-based pnictides.
We consider two types of magnetic Josephson junctions (JJ). They are formed by two singlet superconductors S and magnetic layers between them so that the JJ is a heterostructure of the S m /n/S m type, where S m includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one-the spin filter-is either conducting strong ferromagnet (nematic or N-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n wire and provides the Josephson coupling between the superconductors S. Although both filters let to pass triplet Cooper pairs with total spin S parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents, I Q and I sp , do not depend on mutual orientation of the filter axes, both currents vanish in magnetic JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for I Q and I sp show clearly a duality between the superconducting phase ϕ and the angle α between the exchange fields in the weak magnetic layers. PACS numbers: 74.78.Fk, 85.25.Cp, 74.45.+c Triplet Cooper pairing is known to exist in superfluid 3 He [1, 2]. As concerns superconductors, the situation is less clear. Although some indication for the triplet superconductors has been found in a number of completely different classes of materials [3][4][5], a general consensus about the existence of the triplet superconductivity in the organic metals, heavy fermions and other interesting materials investigated from this point of view has not been achieved [6,7]. In principle, the fact that the spins of the fermions of the Cooper pairs are equal to each other does not contradict the Pauli principle because the condensate wave function f (p) and the order parameter ∆ tr (p) in these triplet superconductors are odd functions of the momentum p. In contrast to the conventional BCS superconductivity, the triplet superconductivity with such a symmetry of the order parameter is sensitive to impurity scattering [8] and, therefore, it is usually strongly suppressed by disorder.However, the triplet Cooper pairs can appear already in conventional singlet superconductors provided an external magnetic (H) or an internal exchange (h) field acts on the spins of electrons. [8][9][10][11] A triplet component inevitably arises also in magnetic superconductors [12].The triplet condensate function arising from the singlet superconductivity in the presence of the magnetic or exchange field acting on spins is odd in frequency and therefore may still have an s-wave space symmetry without violating the Pauli principle. It has a component with the 0-spin projection f tr,0 ∝ 〈ĉ ↑ĉ↓ (t ) +ĉ ↓ĉ↑ (t )〉 on the direction of the field h or H but also the components with spin projection ±1. The zero projection component f tr,0 of the condensate functio...
We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current I J in a multiterminal Josephson contact of the S m /n/S ′ m type with "magnetic" superconductors S m that generate fully polarized triplet components. The superconductors S m are attached to magnetic insulators (filters) which let to pass electrons with a fixed spin direction only. The filter axes are assumed to be oriented antiparallel to each other. The Josephson current is zero in two-terminal Josephson junction, i.e., in S/n/S m or in S m /n/S ′ m contact. But in the three-terminal Josephson junction, with another S superconductor attached to the normal wire, the finite current I J appears flowing from the S superconductor to S m superconductors. The currents through the right (left) superconductors S m are opposite in sign, I R ≡ I J = I c sin(χ R + χ L − 2χ) = −I L , where χ L/R and χ are the phases of superconductors S m , S ′ m , and S, respectively. We discuss possibilities of experimental observation of the effect.
Interfacial superconductivity is observed in a variety of heterostructures composed of different materials including superconducting and nonsuperconducting (at appropriate doping and temperatures) cuprates and iron-based pnictides. The origin of this superconductivity remains in many cases unclear. Here, we propose a general mechanism of interfacial superconductivity for systems with competing order parameters. We assume that parameters characterizing the material allow formation of another order like chargeor spin-density wave competing and prevailing superconductivity in the bulk (hidden superconductivity). Diffusive electron scattering on the interface results in a suppression of this order and releasing the superconductivity. Our theory is based on the use of Ginzburg-Landau equations applicable to a broad class of systems. We demonstrate that the local superconductivity appears in the vicinity of the interface and the spatial dependence of the superconducting order parameter ∆(x) is described by the Gross-Pitaevskii equation. Solving this equation we obtain quantized values of temperature and doping levels at which ∆(x) appears. Remarkably, the local superconductivity shows up even in the case when the rival order is only slightly suppressed and may arise also on the surface of the sample (surface superconductivity).
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