44,174 research outputs found
Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle
It is shown that a real symmetric [complex hermitian] positive
definite matrix is congruent to a diagonal matrix modulo a
pseudo-orthogonal [pseudo-unitary] matrix in [ ], for any
choice of partition . It is further shown that the method of proof in
this context can easily be adapted to obtain a rather simple proof of
Williamson's theorem which states that if is even then is congruent
also to a diagonal matrix modulo a symplectic matrix in
[]. Applications of these results considered include a
generalization of the Schweinler-Wigner method of `orthogonalization based on
an extremum principle' to construct pseudo-orthogonal and symplectic bases from
a given set of linearly independent vectors.Comment: 7 pages, latex, no figure
Determining the spin-orbit coupling via spin-polarized spectroscopy of magnetic impurities
We study the spin-resolved spectral properties of the impurity states
associated to the presence of magnetic impurities in two-dimensional, as well
as one-dimensional systems with Rashba spin-orbit coupling. We focus on Shiba
bound states in superconducting materials, as well as on impurity states in
metallic systems. Using a combination of a numerical T-matrix approximation and
a direct analytical calculation of the bound state wave function, we compute
the local density of states (LDOS) together with its Fourier transform (FT). We
find that the FT of the spin-polarized LDOS, a quantity accessible via
spin-polarized STM, allows to accurately extract the strength of the spin-orbit
coupling. Also we confirm that the presence of magnetic impurities is strictly
necessary for such measurement, and that non-spin-polarized experiments cannot
have access to the value of the spin-orbit coupling.Comment: 26 pages, 6 figure
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