10,311 research outputs found
Stability of topological superconducting qubits with number conservation
The study of topological superconductivity is largely based on the analysis
of simple mean-field models that do not conserve particle number. A major open
question in the field is whether the remarkable properties of these mean-field
models persist in more realistic models with a conserved total particle number
and long-range interactions. For applications to quantum computation, two key
properties that one would like to verify in more realistic models are (i) the
existence of a set of low-energy states (the qubit states) that are separated
from the rest of the spectrum by a finite energy gap, and (ii) an exponentially
small (in system size) bound on the splitting of the energies of the qubit
states. It is well known that these properties hold for mean-field models, but
so far only property (i) has been verified in a number-conserving model. In
this work we fill this gap by rigorously establishing both properties (i) and
(ii) for a number-conserving toy model of two topological superconducting wires
coupled to a single bulk superconductor. Our result holds in a broad region of
the parameter space of this model, suggesting that properties (i) and (ii) are
robust properties of number-conserving models, and not just artifacts of the
mean-field approximation.Comment: 9 pages, 1 figur
The bifurcation diagrams for the Ginzburg-Landau system for superconductivity
In this paper, we provide the different types of bifurcation diagrams for a
superconducting cylinder placed in a magnetic field along the direction of the
axis of the cylinder. The computation is based on the numerical solutions of
the
Ginzburg-Landau model by the finite element method. The response of the
material depends on the values of the exterior field, the Ginzburg-Landau
parameter and the size of the domain.
The solution branches in the different regions of the bifurcation diagrams
are analyzed and open mathematical problems are mentioned.Comment: 16 page
Mean Field Theory of Josephson Junction Arrays with Charge Frustration
Using the path integral approach, we provide an explicit derivation of the
equation for the phase boundary for quantum Josephson junction arrays with
offset charges and non-diagonal capacitance matrix. For the model with nearest
neighbor capacitance matrix and uniform offset charge , we determine,
in the low critical temperature expansion, the most relevant contributions to
the equation for the phase boundary. We explicitly construct the charge
distributions on the lattice corresponding to the lowest energies. We find a
reentrant behavior even with a short ranged interaction. A merit of the path
integral approach is that it allows to provide an elegant derivation of the
Ginzburg-Landau free energy for a general model with charge frustration and
non-diagonal capacitance matrix. The partition function factorizes as a product
of a topological term, depending only on a set of integers, and a
non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure
Competition between spin density wave order and superconductivity in the underdoped cuprates
We describe the interplay between d-wave superconductivity and spin density
wave (SDW) order in a theory of the hole-doped cuprates at hole densities below
optimal doping. The theory assumes local SDW order, and associated electron and
hole pocket Fermi surfaces of charge carriers in the normal state. We describe
quantum and thermal fluctuations in the orientation of the local SDW order,
which lead to d-wave superconductivity: we compute the superconducting critical
temperature and magnetic field in a `minimal' universal theory. We also
describe the back-action of the superconductivity on the SDW order, showing
that SDW order is more stable in the metal. Our results capture key aspects of
the phase diagram of Demler et al. (cond-mat/0103192) obtained in a
phenomenological quantum theory of competing orders. Finally, we propose a
finite temperature crossover phase diagram for the cuprates. In the metallic
state, these are controlled by a `hidden' quantum critical point near optimal
doping involving the onset of SDW order in a metal. However, the onset of
superconductivity results in a decrease in stability of the SDW order, and
consequently the actual SDW quantum critical point appears at a significantly
lower doping.
All our analysis is placed in the context of recent experimental results.Comment: 27 pages, 11 figures; (v2) added clarifications and refs, and
corrected numerical errors (thanks to A. Chubukov
Superconductivity in CoO Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model
Motivated by the recent discovery of superconductivity in two dimensional
CoO layers, we present some possibly useful results of the RVB mean field
theory applied to the triangular lattice. Away from half filling, the order
parameter is found to be complex, and yields a fully gapped quasiparticle
spectrum. The sign of the hopping plays a crucial role in the analysis, and we
find that superconductivity is as fragile for one sign as it is robust for the
other. NaCoOHO is argued to belong to the robust case, by
comparing the LDA Fermi surface with an effective tight binding model. The high
frequency Hall constant in this system is potentially interesting, since it is
pointed out to increase linearly with temperature without saturation for T
T.Comment: Published in Physical Review B, total 1 tex + 9 eps files. Erratum
added as separate tex file on November 7, 2003, a numerical factor corrected
in the erratum on Dec 3, 200
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