Domains in multiband superconductors

Multiband superconductors can have several types of domains that are inhibited in conventional single-band superconductors. These domains are phase domains and chiral domains and their domain wall are an interband phase difference soliton. In a superconductor with an odd number of electronic bands (five or more) and with positive interband Josephson interactions, we find other types of domains with different interband phase differences. We call these domains configuration domains because pseudo-order parameters for each band are dispersed in the complex plain and several configurations, which have several local minima. Fractional vortices serve as hubs for phase difference solitons (configuration domain walls). The divergence of the number of configurations with local minima would pose a serious problem for the stability of superconductivity.     

AC susceptibility of thin Pb films in intermediate and mixed state

Thin films of type I superconductors of a thickness comparable or less than a flux penetration length behave like type II superconductors in a mixed state. With decreasing film thickness normal domains carrying a magnetic flux get smaller with smaller number of flux quanta per domain and finally transform into single quantum flux lines, i.e. quantum vortices similar to those found in type II superconductors. We give an evidence of this behavior from the measurements of the nonlinear response of a total magnetic moment to an applied AC magnetic field, directly from the temperature dependence of an AC susceptibility.     

On the electrodynamics of the type II superconductors

Using the two fluid model, modified Londons equations have been obtained for the type II superconductors in the Schubnikov state (H _c1<H<H _c2). The effect of the normal electrons which form the cores of the flux vortices have been included. These equations can be reduced to the Londons equations under suitable assumptions. The electric field inside the superconductor and the field equations have also been obtained.     

Aspect on vortex structure in noncentrosymmetric superconductors

Helicity of vortices is studied in a single order parameter Ginzburg-Landau model with n × B term. This unusual term changes the superconductor current, but does not change the quantum of magnetic flux, and the cross helicity of the probability density current in noncentrosymmetric superconductors. In this paper I compute the kinetic helicity and magnetic helicity of a superconductor and introduce a new helicity, i.e. a new topological invariant, to describe vortex phase.     

Vortices with fractional flux in two-gap superconductors and in extended faddeev model

We discuss linear topological defects allowed in two-gap superconductors and equivalent extended Faddeev model. We show that, in these systems, there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that, we discuss topological defects which do not carry magnetic flux and describe features of ordinary one-magnetic-flux-quantum vortices in the two-gap system. The results could be relevant for the newly discovered two-band superconductor MgB2.     

Topological Majorana and Dirac zero modes in superconducting vortex cores

We provide an argument based on flux insertion to show that certain superconductors with a nontrivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two-dimensional index theorem and applies to disordered systems as well. It also provides a new way of understanding the zero modes in the vortex cores of a spinless px+ipy superconductor. Applying this approach to superconductors with and without time-reversal and spin-rotational symmetry, we predict the necessary and sufficient conditions for protected zero modes to exist in their vortices.     

Two-step flux penetration in classic antiferromagnetic superconductor

The influence of antiferromagnetic order on the mixed state of a superconductor may result in creation of spin-flop domains along vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments in the vortex core from their ground state configuration. The formation of domain structure causes modification of the surface energy barrier, and creation of the new state in which magnetic flux density is independent of the applied field. The modified surface energy barrier has been calculated for parameters of the antiferromagnetic superconductor DyMo₆S₈. The prediction of two-step flux penetration process has been verified by precise magnetization measurements performed on the single crystal of DyMo₆S₈ at milikelvin temperatures. A characteristic plateau on the virgin curve B(H ₀) has been found and attributed to the modified surface energy barrier. The end of the plateau determines the critical field, which we call the second critical field for flux penetration. Received 16 August 2002 / Received in final form 22 October 2002 Published online 29 November 2002     

Topological vortices in a two-gap superconductor

Based on the ϕ-mapping theory, we derive a new rigorous equation describing the distribution of the magnetic field for vortices in a two-gap superconductor, of which the so-called modified London equation is just a special case in a one-flavor limit. We explicitly investigate the London penetration depth, the Meissner and mixed states and Josephson effect. A magnetic flux quantization condition for vortices in a two-gap superconductor is also derived, from which it follows that in a two-gap superconductor there exist vortices which carry an arbitrary fraction of magnetic flux quantum. The branch processes during the evolution of the vortices in a two-gap superconductor are discussed.     

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.     

Observation of vortex coalescence in the anisotropic spin-triplet superconductor Sr2RuO4

We present direct imaging of magnetic flux structures over the ab face of the anisotropic, spin-triplet superconductor Sr2RuO4 using a scanning microSQUID force microscope. Individual vortices with a single flux quantum were observed at low magnetic fields applied along the out-of-pane direction. At intermediate fields, the direct imaging revealed coalescing of vortices and the formation of flux domains. Our observations imply the existence of a mechanism in this material for bringing vortices together overcoming the conventional repulsive vortex-vortex interaction.     

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor(Li_(0.84)Fe_(0.16))OHFeSe

The Major ana zero mode(MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in(Li_(0.84)Fe_(0.16))OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Major ana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state,and consequently, the conductance at zero bias is quantized as 2e~2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.     

Magnetic vortices and thermoelectric effect in a hollow superconducting cylinder

The question of a surface barrier which determines the behavior of a vortex in a hollow superconducting cylinder of finite thickness in an external magnetic field is discussed, taking into account magnetic flux quantization in the cavity. The behavior of magnetic vortices in a hollow superconductor in the presence of a thermoelectric current is also considered. Pairs of magnetic vortices with opposite magnetic field orientations (vortex-antivortex pairs) are generated by this current near T _c. The thermoelectric current drives the antivortex (the vortex with oppositely directed field) out of the cylinder, whereas the vortex is ejected into the cavity and remains on the inside cylinder surface as a current. The number of magnetic flux quanta trapped inside the cylinder increases by one. The relation of this mechanism to the “giant” thermoelectric effect in hollow superconductors is discussed. Zh. éksp. Teor. Fiz. 111, 2175–2193 (June 1997)     

Features of magnetization reversal in LCMO/YBCO heterostructures

The change in the magnetic domain structure due to the proximity of a superconductor has been experimentally investigated for the first time. The complex character of magnetization reversal at temperatures below critical, caused by the mutual long-range effect of a superconductor and a magnet, has been shown. In particular, it is found that even magnetization reversal of the heterostructure by an in-plane field leads to the formation of Abrikosov vortices in the superconductor, carrying a flux perpendicularly to the film plane. It is shown that this is a consequence of the transformation of narrow domain walls into wide stripes due to the interaction with scattering fields from the superconductor. In turn, after penetration of the magnetic flux into the superconductor at some depth, the scattering fields cause backward magnetization reversal of the external film edge, as a result of which vortices with oppositely directed fluxes enter the crystal and propagate in the superconductor bulk in the form of chains along twins, as in the case of magnetization by a perpendicular magnetic field. Thus, at longitudinal magnetization, the flux enters the superconducting film in the form of wide stripes with alternating perpendicular induction, which is explained by the long-range interaction of the scattering fields of the superconductor with the manganite magnetization.     

Instability of the magnetization reversal front in superconductors with a nonlinear anisotropic current-voltage characteristic

The instability of a magnetic flux flow in a system of vortices and antivortices in superconductors with a power (exponent m) anisotropic current-voltage characteristic was studied theoretically. It was shown that instability arose even at a comparatively weak anisotropy of the current-carrying properties of a superconductor if m?1. The dispersion equation determining the dependence of the increment of instability growth on the wave number was derived and analyzed.     

Superconductivity with broken time-reversal symmetry

This presentation gives an overview over phenomena occurring in unconventional superconductors with broken time-reversal symmetry. The best-known effect related with broken time-reversal symmetry is intrinsic magnetism observable by μSR. In many cases this magnetism is connected to the appearance of chiral quasiparticle edge states which originate from topological properties of the superconducting order parameter. Time-reversal symmetry can also be broken only locally and has then strong influence of the local quasiparticle spectrum. The existence of vortices with fractional flux pinned strongly on domain walls in time-reversal symmetry breaking superconductors leads to unusual flux flow behavior.     

Quantum creep in layered antiferromagnetic superconductor

In the mixed state of layered superconductor, the antiferromagnetic order of magnetic ions can create the spin-flop domains along the phase cores of the Josephson vortices, and this property impact upon the creep rate in the antiferromagnetic superconductor. The activation of the creep at constant temperature can be either thermal or quantum, depending on the intensity, or direction of the applied magnetic field. It is also shown that the action, and hence the activation energy, is rendered temperature dependent, when the damping and inertial mass of the vortex are included, so that the quantum tunnelling rate becomes temperature dependent below the crossover temperature.     

Intervortex quasiparticle tunneling and the electronic structure of multivortex configurations in type-II superconductors

The electronic spectrum of multivortex configurations in type-II superconductors is studied taking into account the effect of quasiparticle tunneling between the vortex cores. The tunneling is responsible for the formation of strongly coupled quasiparticle states for intervortex distances a < a _cc , where the critical distance a _c is of the order of several coherence lengths ξ. When analyzing the resulting spectra of vortex clusters bonded by quasiparticle tunneling, we find a transition from a set of degenerate Caroli-de Gennes-Matricon branches to anomalous branches similar to the ones in multiquantum giant vortices. This spectrum transformation results in the oscillatory behavior of the density of states at the Fermi level as a function of a and could be observed in mesoscopic superconductors and disordered flux line arrays in bulk systems. The text was submitted by the authors in English.     

Pinning of planar vortices and magnetic field penetration in a three-dimensional Josephson medium

The behavior of planar (laminar) vortices in a three-dimensional, ordered Josephson medium as a function of the parameter I, which is proportional to the critical junction current and the cell size, is investigated with allowance for pinning due to the cellular structure of the medium. The minimum possible distances between two isolated vortices are calculated. A system of vortices formed in a sample in a monotonically increasing external magnetic field is analyzed. The minimum distance from the outermost vortex to the nearest neighbor is proportional to I ^−1.1. For I⩽1.3 each vortex contains a single flux quantum Φ₀, and the distance between them does not decrease in closer proximity to the boundary but remains approximately constant, implying that the magnetic field does not depend on the coordinate in the region penetrated by vortices. These facts contradict the generally accepted Bean model. The sample magnetization curve has a form typical of type II superconductors. Allowance for pinning raises the critical field H _c and induces a sudden jump in the curve at H=H _c. Zh. Tekh. Fiz. 67, 38–46 (September 1997)     

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.