175 research outputs found

### Weyl states and Fermi arcs in parabolic bands

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

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

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
$L=12\xi$, the pinning centers are insulating spheres of radius $R$, taken
within the range $0.2\xi$ to $3.0\xi$, $\xi$ 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

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 $\omega_p$ below the superconducting gap. Propagation is assumed to
be parallel to the surfaces in the dielectric medium, where amplitudes decay
exponentially.Below $\omega_p$, the amplitude also evanesces inside the film,
and we retrieve the experimentally measured lower dispersion relation branch,
$\omega \propto \sqrt{\beta}$, and the recently proposed higher frequency
branch, $\omega \propto 1/\sqrt{\beta}$.Above $\omega_p$, 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 $\omega \approx \omega_p \sqrt{ 1+ (\beta/\beta_0)^2}$, where
$\beta_0$ is discussed here.Comment: 26 pages,4 figures.Submitte

### Topologically stable gapped state in a layered superconductor

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 $\mu$SR 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?

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 $\mu$SR 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

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 $H_{c3}$, are obtained for models that differ
according to their boundary properties. A change of the Ginzburg-Landau
parameters near the surface can substantially enhance $H_{c3}$ as shown here.Comment: 7 pages, 4 figures (low resolution

### The Average Kinetic Energy of the Superconducting State

Isothermal magnetization curves are plotted as the magnetization times the
magnetic induction, $4 \pi M \cdot B$, 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 $\kappa$. The maximum of $4 \pi M \cdot B$ occurs at
a field, $H^{*}$, directly related to the upper critical field, $H_{c2}$,
suggesting that $H_{c2}(T)$ 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 $T_c = 8.5 K$, and compare them.Comment: 11 pages, 9 postscript figure

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