117 research outputs found
Vortex Lattice Structural Transitions: a Ginzburg-Landau Model Approach
We analyze the rhombic to square vortex lattice phase transition in
anisotropic superconductors using a variant of Ginzburg-Landau (GL) theory. The
mean-field phase diagram is determined to second order in the anisotropy
parameter, and shows a reorientation transition of the square vortex lattice
with respect to the crystal lattice. We then derive the long-wavelength elastic
moduli of the lattices, and use them to show that thermal fluctuations produce
a reentrant rhombic to square lattice transition line, similar to recent
studies which used a nonlocal London model.Comment: 4 pages, 3 figures, final version with various referee suggested
modifications, scheduled to appear in PR
Viscoelastic Behavior of Solid He
Over the last five years several experimental groups have reported anomalies
in the temperature dependence of the period and amplitude of a torsional
oscillator containing solid He. We model these experiments by assuming that
He is a viscoelastic solid--a solid with frequency dependent internal
friction. We find that while our model can provide a quantitative account of
the dissipation observed in the torsional oscillator experiments, it only
accounts for about 10% of the observed period shift, leaving open the
possibility that the remaining period shift is due to the onset of
superfluidity in the sample.Comment: 4 pages, 3 figure
Static and dynamic properties of crystalline phases of two-dimensional electrons in a strong magnetic field
We study the cohesive energy and elastic properties as well as normal modes
of the Wigner and bubble crystals of the two-dimensional electron system (2DES)
in higher Landau levels. Using a simple Hartree-Fock approach, we show that the
shear moduli ('s) of these electronic crystals show a non-monotonic
behavior as a function of the partial filling factor at any given
Landau level, with increasing for small values of , before
reaching a maximum at some intermediate filling factor , and
monotonically decreasing for . We also go beyond previous
treatments, and study how the phase diagram and elastic properties of electron
solids are changed by the effects of screening by electrons in lower Landau
levels, and by a finite thickness of the experimental sample. The implications
of these results on microwave resonance experiments are briefly discussed.Comment: Discussion updated - 16 pages, 10 figures; version accepted for
publication in Phys. Rev.
Anisotropic states of two-dimensional electrons in high magnetic fields
We study the collective states formed by two-dimensional electrons in Landau
levels of index near half-filling. By numerically solving the
self-consistent Hartree-Fock (HF) equations for a set of oblique
two-dimensional lattices, we find that the stripe state is an anisotropic
Wigner crystal (AWC), and determine its precise structure for varying values of
the filling factor. Calculating the elastic energy, we find that the shear
modulus of the AWC is small but finite (nonzero) within the HF approximation.
This implies, in particular, that the long-wavelength magnetophonon mode in the
stripe state vanishes like as in an ordinary Wigner crystal, and not
like as was found in previous studies where the energy of shear
deformations was neglected.Comment: minor corrections; 5 pages, 4 figures; version to be published in
Physical Review Letter
Travelling waves in a drifting flux lattice
Starting from the time-dependent Ginzburg-Landau (TDGL) equations for a type
II superconductor, we derive the equations of motion for the displacement field
of a moving vortex lattice without inertia or pinning. We show that it is
linearly stable and, surprisingly, that it supports wavelike long-wavelength
excitations arising not from inertia or elasticity but from the
strain-dependent mobility of the moving lattice. It should be possible to image
these waves, whose speeds are a few \mu m/s, using fast scanning tunnelling
microscopy.Comment: 4 pages, revtex, 2 .eps figures imbedded in paper, title shortened,
minor textual change
Bound states of edge dislocations: The quantum dipole problem in two dimensions
We investigate bound state solutions of the 2D Schr\"odinger equation with a
dipole potential originating from the elastic effects of a single edge
dislocation. The knowledge of these states could be useful for understanding a
wide variety of physical systems, including superfluid behavior along
dislocations in solid He. We present a review of the results obtained by
previous workers together with an improved variational estimate of the ground
state energy. We then numerically solve the eigenvalue problem and calculate
the energy spectrum. In our dimensionless units, we find a ground state energy
of -0.139, which is lower than any previous estimate. We also make successful
contact with the behavior of the energy spectrum as derived from semiclassical
considerations.Comment: 6 pages, 3 figures, submitted to PR
Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid
In this work we start from the assumption that normal solid to supersolid
(NS-SS) phase transition is continuous, and develop a phenomenological Landau
theory of the transition in which superfluidity is coupled to the elasticity of
the crystalline He lattice. We find that the elasticity does not affect the
universal properties of the superfluid transition, so that in an unstressed
crystal the well-known -anomaly in the heat capacity of the superfluid
transition should also appear at the NS-SS transition. We also find that the
onset of supersolidity leads to anomalies in the elastic constants near the
transition; conversely, inhomogeneous strains in the lattice can induce local
variations of the superfluid transition temperature, leading to a broadened
transition.Comment: 4 page
Nucleation and Growth of the Superconducting Phase in the Presence of a Current
We study the localized stationary solutions of the one-dimensional
time-dependent Ginzburg-Landau equations in the presence of a current. These
threshold perturbations separate undercritical perturbations which return to
the normal phase from overcritical perturbations which lead to the
superconducting phase. Careful numerical work in the small-current limit shows
that the amplitude of these solutions is exponentially small in the current; we
provide an approximate analysis which captures this behavior. As the current is
increased toward the stall current J*, the width of these solutions diverges
resulting in widely separated normal-superconducting interfaces. We map out
numerically the dependence of J* on u (a parameter characterizing the material)
and use asymptotic analysis to derive the behaviors for large u (J* ~ u^-1/4)
and small u (J -> J_c, the critical deparing current), which agree with the
numerical work in these regimes. For currents other than J* the interface
moves, and in this case we study the interface velocity as a function of u and
J. We find that the velocities are bounded both as J -> 0 and as J -> J_c,
contrary to previous claims.Comment: 13 pages, 10 figures, Revte
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