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Register a new userThe Confinement of Vortices in Nano-Superconducting Devices
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We have investigated the confinement of 3-D vortices in specific cases of Type-II ($kappa = 2$) nano-superconducting devices. The emergent pattern of vortices greatly depends on the orientation of an applied magnetic field (transverse or longitudinal), and the size of the devices (a few coherence lengths $xi$). Herein, cylindrical geometries are examined. The surface barriers become very significant in these nano-systems, and hence the characteristics of the vortices become highly sensitive to the shape of the system and direction of an applied field. It is observed that nano-cylindrical superconductors, depending on their sizes, can display either first or second order phase transitions, under the influence of a longitudinal field. In the confined geometries, nucleation of a giant vortex state composed of a n-quanta emerges for the longitudinal magnetic field.
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We start by showing that the most generic spin-singlet pairing in a superconducting Weyl/Dirac semimetal is specified by a $U(1)$ phase $e^{iphi}$ and $two~real~numbers$ $(Delta_s,Delta_5)$ that form a representation of complex algebra. Such a complex superconducting state realizes a $Z_2times U(1)$ symmetry breaking in the matter sector where $Z_2$ is associated with the chirality. The resulting effective XY theory of the fluctuations of the $U(1)$ phase $phi$ will be now augmented by coupling to another dynamical variable, the $chiral~angle$ $chi$ that defines the polar angle of the complex number $(Delta_s,Delta_5)$. We compute this coupling by considering a Josephson set up. Our energy functional of two phase variables $phi$ and $chi$ allows for the realization of a half-vortex (or double Cooper pair) state and its BKT transition. The half-vortex state is sharply characterized by a flux quantum which is half of the ordinary superconductors. Such a $pi$-periodic Josephson effect can be easily detected as doubled ac Josephson frequency. We further show that the Josephson current $I$ is always accompanied by a $chiral~Josephson~current$ $I_5$. Strain pseudo gauge fields that couple to the $chi$, destabilize the half-vortex state. We argue that our complex superconductor realizes an extension of XY model that supports confinement transition from half-vortex to full vortex excitations.
Pancake vortices in stacks of thin superconducting films or layers are considered. It is stressed that in the absence of Josephson coupling topological restrictions upon possible configurations of vortices are removed and various examples of structures forbidden in bulk superconductors are given. In particular, it is shown that vortices may skip surface layers in samples of less than a certain size R_c which might be macroscopic. The Josephson coupling suppresses R_c estimates.
The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6 Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.
A monopole harmonic superconductor is a novel topological phase of matter with topologically protected gap nodes that result from the non-trivial Berry phase structure of Cooper pairs. In this work we propose to realize a monopole superconductor by the proximity effect between a time-reversal broken Weyl semi-metal and an $s$-wave superconductor. Furthermore, we study the zero-energy vortex bound states in this system by projection methods and by exact solutions. The zero modes exhibit a non-trivial phase winding in real space as a result of the non-trivial winding of the order parameter in momentum space. By mapping the Hamiltonian to the $(1+1)$d Dirac Hamiltonian, it is shown that the zero modes, analogous to the Jackiw-Rebbi mode, are protected by the index theorem. Finally, we propose possible experimental realizations.
We investigate the electronic properties of type-II superconducting Nb(110) in an external magnetic field. Scanning tunneling spectroscopy reveals a complex vortex shape which develops from circular via coffee bean-shaped to elliptical when decreasing the energy from the edge of the superconducting gap to the Fermi level. This anisotropy is traced back to the local density of states of Caroli-de-Gennes-Matricon states which exhibits a direction-dependent splitting. Oxidizing the Nb(110) surface triggers the transition from the clean to the dirty limit, quenches the vortex bound states, and leads to an isotropic appearance of the vortices. Density functional theory shows that the Nb(110) Fermi surface is stadium-shaped near the Gamma point. Calculations within the Bogoliubov-de-Gennes theory using these Fermi contours consistently reproduce the experimental results.
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