1,526 research outputs found
d-wave pairing symmetry in cuprate superconductors
Phase-sensitive tests of pairing symmetry have provided strong evidence for
predominantly d-wave pairing symmetry in both hole- and electron-doped high-Tc
cuprate superconductors. Temperature dependent measurements in YBCO indicate
that the d-wave pairing dominates, with little if any imaginary component, at
all temperatures from 0.5K through Tc. In this article we review some of this
evidence and discuss the implications of the universal d-wave pairing symmetry
in the cuprates.Comment: 4 pages, M2S 2000 conference proceeding
Geometric effects on T-breaking in p+ip and d+id superconductors
Superconducting order parameters that change phase around the Fermi surface
modify Josephson tunneling behavior, as in the phase-sensitive measurements
that confirmed order in the cuprates. This paper studies Josephson coupling
when the individual grains break time-reversal symmetry; the specific cases
considered are and , which may appear in SrRuO and
NaCoO(HO) respectively. -breaking order parameters
lead to frustrating phases when not all grains have the same sign of
time-reversal symmetry breaking, and the effects of these frustrating phases
depend sensitively on geometry for 2D arrays of coupled grains. These systems
can show perfect superconducting order with or without macroscopic
-breaking. The honeycomb lattice of superconducting grains has a
superconducting phase with no spontaneous breaking of but instead power-law
correlations. The superconducting transition in this case is driven by binding
of fractional vortices, and the zero-temperature criticality realizes a
generalization of Baxter's three-color model.Comment: 8 page
Topological insulators and superconductors
Topological insulators are new states of quantum matter which can not be
adiabatically connected to conventional insulators and semiconductors. They are
characterized by a full insulating gap in the bulk and gapless edge or surface
states which are protected by time-reversal symmetry. These topological
materials have been theoretically predicted and experimentally observed in a
variety of systems, including HgTe quantum wells, BiSb alloys, and BiTe
and BiSe crystals. We review theoretical models, materials properties
and experimental results on two-dimensional and three-dimensional topological
insulators, and discuss both the topological band theory and the topological
field theory. Topological superconductors have a full pairing gap in the bulk
and gapless surface states consisting of Majorana fermions. We review the
theory of topological superconductors in close analogy to the theory of
topological insulators.Comment: 55 pages, 44 figures, Review article commissioned by the Review of
Modern Physics. Please help us to improve the article by emailing us your
comments and missing reference
QED3 theory of underdoped high temperature superconductors
Low-energy theory of d-wave quasiparticles coupled to fluctuating vortex
loops that describes the loss of phase coherence in a two dimensional d-wave
superconductor at T=0 is derived. The theory has the form of 2+1 dimensional
quantum electrodynamics (QED3), and is proposed as an effective description of
the T=0 superconductor-insulator transition in underdoped cuprates. The
coupling constant ("charge") in this theory is proportional to the dual order
parameter of the XY model, which is assumed to be describing the quantum
fluctuations of the phase of the superconducting order parameter. The principal
result is that the destruction of phase coherence in d-wave superconductors
typically, and immediately, leads to antiferromagnetism. The transition can be
understood in terms of the spontaneous breaking of an approximate "chiral"
SU(2) symmetry, which may be discerned at low enough energies in the standard
d-wave superconductor. The mechanism of the symmetry breaking is analogous to
the dynamical mass generation in the QED3, with the "mass" here being
proportional to staggered magnetization. Other insulating phases that break
chiral symmetry include the translationally invariant "d+ip" and "d+is"
insulators, and various one dimensional charge-density and spin-density waves.
The theory offers an explanation for the rounded d-wave-like dispersion seen in
ARPES experiments on Ca2CuO2Cl2 (F. Ronning et. al., Science 282, 2067 (1998)).Comment: Revtex, 20 pages, 5 figures; this is a much extended follow-up to the
Phys. Rev. Lett. vol.88, 047006 (2002) (cond-mat/0110188); improved
presentation, many additional explanations, comments, and references added,
sec. IV rewritten. Final version, to appear in Phys. Rev.
Superconductivity of disordered Dirac fermions
We study the effect of disorder on massless, spinful Dirac fermions in two
spatial dimensions with attractive interactions, and show that the combination
of disorder and attractive interactions is deadly to the Dirac semimetal phase.
First, we derive the zero temperature phase diagram of a clean Dirac fermion
system with tunable doping level ({\mu}) and attraction strength (g). We show
that it contains two phases: a superconductor and a Dirac semimetal. Then, we
show that arbitrarily weak disorder destroys the Dirac semimetal, turning it
into a superconductor. We discuss the strength of the superconductivity for
both long range and short range disorder. For long range disorder, the
superconductivity is exponentially weak in the disorder strength. For short
range disorder, a uniform mean field analysis predicts that superconductivity
should be doubly exponentially weak in the disorder strength. However, a more
careful treatment of mesoscopic fluctuations suggests that locally
superconducting puddles should form at a much higher temperature, and should
establish global phase coherence at a temperature that is only exponentially
small in weak disorder. We also discuss the effect of disorder on the quantum
critical point of the clean system, building in the effect of disorder through
a replica field theory. We show that disorder is a relevant perturbation to the
supersymmetric quantum critical point. We expect that in the presence of
attractive interactions, the flow away from the critical point ends up in the
superconducting phase, although firm conclusions cannot be drawn since the
renormalization group analysis flows to strong coupling. We argue that although
we expect the quantum critical point to get buried under a superconducting
phase, signatures of the critical point may be visible in the finite
temperature quantum critical regime.Comment: Added some discussion, particularly pertaining to proximity effec
Constructing suitable ordinary pairing-friendly curves: A case of elliptic curves and genus two hyperelliptic curves
One of the challenges in the designing of pairing-based cryptographic protocols is to construct suitable pairing-friendly curves: Curves which would provide e�cient implementation without compromising the security of the protocols. These curves have small embedding degree and large prime order subgroup. Random curves are likely to have large embedding degree and hence are not practical for implementation of pairing-based protocols.
In this thesis we review some mathematical background on elliptic and hyperelliptic curves in relation to the construction of pairing-friendly hyper-elliptic curves. We also present the notion of pairing-friendly curves. Furthermore, we construct new pairing-friendly elliptic curves and Jacobians of genus two hyperelliptic curves which would facilitate an efficient implementation in pairing-based protocols. We aim for curves that have smaller values than ever before reported for di�erent embedding degrees. We also discuss optimisation of computing pairing in Tate pairing and its variants. Here we show how to e�ciently multiply a point in a subgroup de�ned on a twist curve by a large cofactor. Our approach uses the theory of addition chains. We also show a new method for implementation of the computation of the hard part of the �nal exponentiation in the calculation of the Tate pairing and its varian
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