175 research outputs found

    Weyl states and Fermi arcs in parabolic bands

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    Weyl fermions are shown to exist inside a parabolic band, where the kinetic energy of carriers is given by the non-relativistic Schroedinger equation. There are Fermi arcs as a direct consequence of the folding of a ring shaped Fermi surface inside the first Brillouin zone. Our results stem from the decomposition of the kinetic energy into the sum of the square of the Weyl state, the coupling to the local magnetic field and the Rashba interaction. The Weyl fermions break the time and reflection symmetries present in the kinetic energy, thus allowing for the onset of a weak three-dimensional magnetic field around the layer. This field brings topological stability to the current carrying states through a Chern number. In the special limit that the Weyl state becomes gapless this magnetic interaction is shown to be purely attractive, thus suggesting the onset of a superconducting condensate of zero helicity states

    Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions

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    We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the case of a gaussian weight. Hence we obtain generalizations of the Legendre and of the Chebyshev polynomials in D dimensions that reduce to the respective well-known orthonormal polynomials in D=1 dimensions. We also obtain new D-dimensional polynomials orthonormal under other weights, such as the Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the Yukawa potential. We calculate the series expansion of an arbitrary function in terms of the new polynomials up to the fourth order and define orthonormal multipoles. The explicit orthonormalization of the polynomials up to the fifth order (N from 0 to 4) reveals an increasing number of orthonormalization equations that matches exactly the number of polynomial coefficients indication the correctness of the present procedure.Comment: 20 page

    Energy dependence of a vortex line length near a zigzag of pinning centers

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    A vortex line, shaped by a zigzag of pinning centers, is described here through a three-dimensional unit cell containing two pinning centers positioned symmetrically with respect to its center. The unit cell is a cube of side L=12ξL=12\xi, the pinning centers are insulating spheres of radius RR, taken within the range 0.2ξ0.2\xi to 3.0ξ3.0\xi, ξ\xi being the coherence length. We calculate the free energy density of these systems in the framework of the Ginzburg-Landau theory.Comment: Submitted to Braz. Jour. Phys. (http://www.sbfisica.org.br/bjp) 11 pages, 6 figures, 1 table, LaTex 2

    Plasma Waves in Anisotropic Superconducting Films Below and Above the Plasma Frequency

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    We consider wave propagation inside an anisotropic superconducting film sandwiched between two semi-infinite non-conducting bounding dieletric media such that along the c-axis, perpendicular to the surfaces, there is a plasma frequency ωp\omega_p below the superconducting gap. Propagation is assumed to be parallel to the surfaces in the dielectric medium, where amplitudes decay exponentially.Below ωp\omega_p, the amplitude also evanesces inside the film, and we retrieve the experimentally measured lower dispersion relation branch, ωβ\omega \propto \sqrt{\beta}, and the recently proposed higher frequency branch, ω1/β\omega \propto 1/\sqrt{\beta}.Above ωp\omega_p, propagation is of the guided wave type, i.e., a dispersive plane wave confined inside the film that reflects into the dielectric interfaces,and the modes are approximately described by ωωp1+(β/β0)2\omega \approx \omega_p \sqrt{ 1+ (\beta/\beta_0)^2}, where β0\beta_0 is discussed here.Comment: 26 pages,4 figures.Submitte

    Topologically stable gapped state in a layered superconductor

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    We show that a layered superconductor, described by a two-component order parameter, has a gapped state above the ground state, topologically protected from decay, containing flow and counter flow in the absence of an applied magnetic field. This state is made of skyrmions, breaks time reversal symmetry and produces a weak local magnetic field below the present threshold of detection by μ\muSR and NMR/NQR. We estimate the density of carriers that condense into the pseudogap.Comment: 6 pages, 4 figure

    Is the pseudogap a topological state?

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    We conjecture that the pseudogap is an inhomogeneous condensate above the homogeneous state whose existence is granted by topological stability. We consider the simplest possible order parameter theory that provides this interpretation of the pseudogap and study its angular momentum states. The normal state gap density, the breaking of the time reversal symmetry and the checkerboard pattern are naturally explained under this view. The pseudogap is a lattice of skyrmions and the inner weak local magnetic field falls below the experimental threshold of observation given by NMR/NQR and μ\muSR experiments.Comment: 12 pages, six figures, one tabl

    Effect of the boundary condition on the vortex patterns in mesoscopic three-dimensional superconductors - disk and sphere

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    The vortex state of mesoscopic three-dimensional superconductors is determined using a minimization procedure of the Ginzburg-Landau free energy. We obtain the vortex pattern for a mesoscopic superconducting sphere and find that vortex lines are naturally bent and are closest to each other at the equatorial plane. For a superconducting disk with finite height, and under an applied magnetic field perpendicular to its major surface, we find that our method gives results consistent with previous calculations. The matching fields, the magnetization and Hc3H_{c3}, are obtained for models that differ according to their boundary properties. A change of the Ginzburg-Landau parameters near the surface can substantially enhance Hc3H_{c3} as shown here.Comment: 7 pages, 4 figures (low resolution

    The Average Kinetic Energy of the Superconducting State

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    Isothermal magnetization curves are plotted as the magnetization times the magnetic induction, 4πMB4 \pi M \cdot B, versus the applied field, H. We show here that this new curve is the average kinetic energy of the superconducting state versus the applied field, for type-II superconductors with a high Ginzburg-Landau parameter κ\kappa. The maximum of 4πMB4 \pi M \cdot B occurs at a field, HH^{*}, directly related to the upper critical field, Hc2H_{c2}, suggesting that Hc2(T)H_{c2}(T) may be extracted from such plots even in cases when it is too high for direct measurement. We obtain these plots both theoretically, from the Ginzburg-Landau theory, and experimentally, using a Niobium sample with Tc=8.5KT_c = 8.5 K, and compare them.Comment: 11 pages, 9 postscript figure
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