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Register a new userPhase transition of vortex states in two-dimensional superconductors under a oscillating magnetic field from the chiral helimagnet
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We have investigated vortex states in two-dimensional superconductors under a oscillating magnetic field from a chiral helimagnet. We have solved the two-dimensional Ginzburg-Landau equations with finite element method. We have found that when the magnetic field from the chiral helimagnet increases, vortices appear all at once in all periodic regions. This transition is different from that under the uniform magnetic field. Under the composite magnetic field with the oscillating and uniform fields (down-vortices), vortices antiparallel to the uniform magnetic field disappear. Then, the small uniform magnetic field easily remove down-vortices.
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We have investigated vortex structures in three-dimensional superconductors under a helical magnetic field from a chiral helimagnet numerically. In order to obtain vortex structures, we solve three-dimensional Ginzburg-Landau equations with the finite element method. The distribution of the helical magnetic field is assumed to be proportional to the distribution of the magnetic moments in the chiral helimagnet. Then, the magnetic field is the same direction in the yz-plane and helical rotation along the helical axis. Under this helical magnetic field, vortices appear to be perpendicular to the surface of the superconductor. But we have found that there are tilted vortices toward the helical axis, although there is no component of the magnetic field along the helical axis. This vortex structure depends on the chirality of the distribution of the helical magnetic field.
We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in Ref. [R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016)], under a strong magnetic field can be seen in LDOS without smeared out by non-zero-energy states. The spin-resolved LDOS further reveals that the spin of the exterior Majorana state is strongly polarized. Accordingly, the induced odd-frequency spin-triplet pairs are found to be spin-polarized as well. In order to detect the exterior Majorana states, however, the Fermi energy should be closed to the Dirac point to avoid contributions from continuum levels. We also study a different two-dimensional topological-superconducting system where a two-dimensional electron gas with the spin-orbit coupling is sandwiched between an s-wave superconductor and a ferromagnetic insulator. We show that the radius of an exterior Majorana state can be tuned by an applied magnetic field. However, on the contrary to the results at a TI surface, neither the exterior Majorana state nor the induced odd-frequency spin-triplet pairs are spin-polarized. We conclude that the spin-polarization of the Majorana state is attributed to the spin-polarized Landau level which is characteristic for systems with the Dirac-like dispersion.
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization. Regularization directly addresses the inherent instability of this inversion problem for non-exact (noisy) data. Performance of the technique is evaluated for different current distributions and for data with varying amounts of added noise. Comparisons are made to other methods, and the present method is demonstrated to achieve a better regularizing (noise filtering) effect while also employing the generalized-cross validation (GCV) method to choose the optimal regularization parameter from the data, without detailed knowledge of the true (and generally unknown) solution. It is also shown that clean, noiseless data is an ineffective test of an inversion algorithm.
Majorana fermions exist on the boundaries of two-dimensional topological superconductors (TSCs) as charge-neutral quasi-particles. The neutrality makes the detection of such states challenging from both experimental and theoretical points of view. Current methods largely rely on transport measurements in which Majorana fermions manifest themselves by inducing electron-pair tunneling at the lead-contacting point. Here we show that chiral Majorana fermions in TSCs generate {enhanced} local optical response. The features of local optical conductivity distinguish them not only from trivial superconductors or insulators but also from normal fermion edge states such as those in quantum Hall systems. Our results provide a new applicable method to detect dispersive Majorana fermions and may lead to a novel direction of this research field.
The vortices of two-dimensional chiral $p$-wave superconductors are predicted to exhibit some exotic behaviors; one of their curious features is the existence of two types of vortices (each vortex has vorticity either parallel or antiparallel to the Cooper pairs chirality) and the robustness of the antiparallel vortices against nonmagnetic Born-like impurities. In this work, we study the impurity effect on the vortex of the chiral $p$-wave superconductors through the quasiclassical Greens function formalism. We take account of impurities via the self-consistent $t$-matrix approximation so that we can deal with strong as well as Born-like (i.e., weak) scatterers. We found that the spectrum is heavily broadened when the phase shift $delta_0$ of each impurity exceeds a critical value $delta_{text{c}}$ above which the impurity band emerges at the Fermi level. We also found a quantitative difference in the impurity effects on the two types of vortex for $delta_0<delta_{text{c}}$. Part of the numerical results for $delta_0<delta_{text{c}}$ can be understood by a variant of the analytical theory of Kramer and Pesch for bound states localized within vortex cores.
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