5 research outputs found
Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schr\"odinger system
We study a nonlinear system of partial differential equations in which a
complex field (the Higgs field) evolves according to a nonlinear Schroedinger
equation, coupled to an electromagnetic field whose time evolution is
determined by a Chern-Simons term in the action. In two space dimensions, the
Chern-Simons dynamics is a Galileo invariant evolution for A, which is an
interesting alternative to the Lorentz invariant Maxwell evolution, and is
finding increasing numbers of applications in two dimensional condensed matter
field theory. The system we study, introduced by Manton, is a special case (for
constant external magnetic field, and a point interaction) of the effective
field theory of Zhang, Hansson and Kivelson arising in studies of the
fractional quantum Hall effect. From the mathematical perspective the system is
a natural gauge invariant generalization of the nonlinear Schroedinger
equation, which is also Galileo invariant and admits a self-dual structure with
a resulting large space of topological solitons (the moduli space of self-dual
Ginzburg-Landau vortices). We prove a theorem describing the adiabatic
approximation of this system by a Hamiltonian system on the moduli space. The
approximation holds for values of the Higgs self-coupling constant close to the
self-dual (Bogomolny) value of 1. The viability of the approximation scheme
depends upon the fact that self-dual vortices form a symplectic submanifold of
the phase space (modulo gauge invariance). The theorem provides a rigorous
description of slow vortex dynamics in the near self-dual limit.Comment: Minor typos corrected, one reference added and DOI give
Doping dependence of the superconducting gap in Bi2Sr2CaCu2O{8 + delta}
Bi2Sr2CaCu2O{8 + \delta} crystals with varying hole concentrations (0.12 < p
< 0.23) were studied to investigate the effects of doping on the symmetry and
magnitude of the superconducting gap. Electronic Raman scattering experiments
that sample regions of the Fermi surface near the diagonal (B_{2g}) and
principal axes (B_{1g}) of the Brillouin Zone have been utilized. The frequency
dependence of the Raman response function at low energies is found to be linear
for B_{2g} and cubic for B_{1g} (T< T_c). The latter observations have led us
to conclude that the doping dependence of the superconducting gap is consistent
with d_{x^2-y^2} symmetry, for slightly underdoped and overdoped crystals.
Studies of the pair-breaking peak found in the B_{1g} spectra demonstrate that
the magnitude of the maximum gap decreases monotonically with increasing hole
doping, for p > 0.12. Based on the magnitude of the B_{1g} renormalization, it
is found that the number of quasiparticles participating in pairing increases
monotonically with increased doping. On the other hand, the B_{2g} spectra show
a weak "pair-breaking peak" that follows a parabolic-like dependence on hole
concentration, for 0.12 < p < 0.23.Comment: 9 pages REvTex document including 8 eps figures; new table II;
changes to Fig. 5 and tex