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Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors
The possibility of inducing topological superconductivity with cuprate
high-temperature superconductors (HTSC) is studied for various
heterostructures. We first consider a ballistic planar junction between a HTSC
and a metallic ferromagnet. We assume that inversion symmetry breaking at the
tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and
allows equal-spin triplet superconductivity to exist in the ferromagnet.
Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier,
and taking account of the transport anisotropy in the HTSC. By making use of
the self-consistent boundary conditions and solutions for the barrier and HTSC
regions, an effective equation of motion for the ferromagnet is obtained where
Andreev scattering at the barrier is incorporated as a boundary condition for
the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of
the HTSC, triplet p-wave superconductivity is induced. For the layer deposited
on a (110) facet, the induced gap does not have the p-wave orbital character,
but has an even orbital symmetry and an odd dependence on energy. For the layer
on the (001) facet, an exotic f-wave superconductivity is induced. We also
consider the induced triplet gap in a one-dimensional half-metallic nanowire
deposited on a (001) facet of a HTSC. We find that for a wire axis along the
a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees
away from the a-axis the induced triplet p-wave gap vanishes. For the
appropriately oriented wire, the induced p-wave gap should give rise to
Majorana fermions at the ends of the half-metallic wire. Based on our result,
topological superconductivity in a semi-conductor nanowire may also be possible
given that it is oriented along the a-axis of the HTSC.Comment: 14 pages, 4 figure
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
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