2,202 research outputs found
An alternative construction of B-M and B-T unitals in Desarguesian planes
We present a new construction of non-classical unitals from a classical
unital in . The resulting non-classical unitals are B-M unitals.
The idea is to find a non-standard model of with the
following three properties: 1. points of are those of ; 2.
lines of are certain lines and conics of ; 3. the points in
form a non-classical B-M unital in .
Our construction also works for the B-T unital, provided that conics are
replaced by certain algebraic curves of higher degree.Comment: Keywords: unital, desarguesian plane 11 pages; ISSN: 0012-365
Cubic Curves, Finite Geometry and Cryptography
Some geometry on non-singular cubic curves, mainly over finite fields, is
surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are
classified accordingly. The group structure and the possible numbers of
rational points are also surveyed. A possible strengthening of the security of
elliptic curve cryptography is proposed using a `shared secret' related to the
group law. Cubic curves are also used in a new way to construct sets of points
having various combinatorial and geometric properties that are of particular
interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae
Mathematicae. In this version, we have corrected a sentence in the third
paragraph. The final publication is available at springerlink.com at
http://www.springerlink.com/content/xh85647871215644
Andreev states near short-ranged pairing potential impurities
We study Andreev states near atomic scale modulations in the pairing
potential in both - and d-wave superconductors with short coherence lengths.
For a moderate reduction of the local gap, the states exist only close to the
gap edge. If one allows for local sign changes of the order parameter, however,
resonances can occur at energies close to the Fermi level. The local density of
states (LDOS) around such pairing potential defects strongly resembles the
patterns observed by tunneling measurements around Zn impurities in
BiSrCaCuO (BSCCO). We discuss how this phase impurity model
of the Zn LDOS pattern can be distinguished from other proposals
experimentally.Comment: 4 pages, 4 figure
Elastic forward scattering in the cuprate superconducting state
We investigate the effect of elastic forward scattering on the ARPES spectrum
of the cuprate superconductors. In the normal state, small angle scattering
from out-of-plane impurities is thought to broaden the ARPES spectral response
with minimal effect on the resistivity or the superconducting transition
temperature . Here we explore how such forward scattering affects the
ARPES spectrum in the d-wave superconducting state. Away from the nodal
direction, the one-electron impurity scattering rate is found to be suppressed
as approaches the gap edge by a cancellation between normal and
anomalous scattering processes, leading to a square-root-like feature in the
spectral weight as approaches -\Delta_\k from below. For momenta
away from the Fermi surface, our analysis suggests that a dirty optimally or
overdoped system will still display a sharp but nondispersive peak which could
be confused with a quasiparticle spectral feature. Only in cleaner samples
should the true dispersing quasiparticle peak become visible. At the nodal
point on the Fermi surface, the contribution of the anomalous scattering
vanishes and the spectral weight exhibits a Lorentzian quasiparticle peak in
both energy and momentum.
Our analysis, including a treatment of unitary scatterers and inelastic spin
fluctuation scattering, suggests explanations for the sometimes mysterious
lineshapes and temperature dependences of the peak structures observed in the
\BSCCO system.Comment: 12 pages, 14 figure
Scattering by impurity-induced order parameter ``holes'' in d-wave superconductors
Nonmagnetic impurities in d-wave superconductors cause strong local
suppressions of the order parameter. We investigate the observable effects of
the scatterigng off such suppressions in bulk samples by treating the order
parameter "hole" as a pointlike off-diagonal scatterer treated within a
self-consistent t-matrix approximation. Strong scattering potentials lead to a
finite-energy spectral feature in the d-wave "impurity band", the observable
effects of which include enhanced low-temperature microwave power absorption
and a stronger sensitivity of the London penetration depth to disorder than
found previously in simpler ``dirty'' d-wave models.Comment: 5 pp. Revtex including 4 postscript figures, submitted to Phys. Rev.
A possible cooling effect in high temperature superconductors
We show that an adiabatic increase of the supercurrent along a superconductor
with lines of nodes of the order parameter on the Fermi surface can result in a
cooling effect. The maximum cooling occurs if the supercurrent increases up to
its critical value. The effect can also be observed in a mixed state of a bulk
sample. An estimate of the energy dissipation shows that substantial cooling
can be performed during a reasonable time even in the microkelvin regime.Comment: 5 pages, to appear in Phys. Rev.
0-pi transitions in Josephson junctions with antiferromagnetic interlayers
We show that the dc Josephson current through
superconductor-antiferromagnet-superconductor (S/AF/S) junctions manifests a
remarkable atomic scale dependence on the interlayer thickness. At low
temperatures the junction is either a 0- or pi-junction depending on whether
the AF interlayer consists of an even or odd number of atomic layers. This is
associated with different symmetries of the AF interlayers in the two cases. In
the junction with odd AF interlayers an additional pi-0 transition can take
place as a function of temperature. This originates from the interplay of
spin-split Andreev bound states. Experimental implications of these theoretical
findings are discussed.Comment: 4 pages, 2 figure
Nodal Quasiparticle Lifetimes in Cuprate Superconductors
A new generation of angular-resolved photoemission spectroscopy (ARPES)
measurements on the cuprate superconductors offer the promise of enhanced
momentum and energy resolution. In particular, the energy and temperature
dependence of the on-shell nodal (k_x=k_y) quasiparticle scattering rate can be
studied. In the superconducting state, low temperature transport measurements
suggest that one can describe nodal quasiparticles within the framework of a
BCS d-wave model by including forward elastic scattering and spin-fluctuation
inelastic scattering. Here, using this model, we calculate the temperature and
frequency dependence of the on-shell nodal quasiparticle scattering rate in the
superconducting state which determines the momentum width of the ARPES momentum
distribution curves. For a zero-energy quasiparticle at the nodal momentum k_N,
both the elastic and inelastic scattering rate show a sudden decrease as the
temperature drops below Tc, reflecting the onset of the gap amplitude. At low
temperatures the scattering rate decreases as T^3 and approaches a zero
temperature value determined by the elastic impurity scattering. For T>T_c, we
find a quasilinear dependence on T. At low reduced temperatures, the elastic
scattering rate for the nodal quasiparticles exhibits a quasilinear increase at
low energy which arises from elastic scattering processes. The inelastic
spin-fluctuation scattering leads to a low energy omega^3 dependence which, for
omega>~Delta_0, crosses over to a quasilinear behavior.Comment: 8 pages, 7 figures, minor revision
Universal zero-frequency Raman slope in a d-wave superconductor
It is known that for an unconventional superconductor with nodes in the gap,
the in-plane microwave or dc conductivity saturates at low temperatures to a
universal value independent of the impurity concentration. We demonstrate that
a similar feature can be accessed using channel-dependent Raman scattering. It
is found that, for a -wave superconductor, the slope of
low-temperature Raman intensity at zero frequency is universal in the
and channels, but not in the channel. Moreover, as opposed to
the microwave conductivity, universal Raman slopes are sensitive not only to
the existence of a node, but also to different pairing states and should allow
one to distinguish between such pairing states.Comment: 5 page
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