482 research outputs found
Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials
We theoretically investigate how the Berry curvature, which arises in
multi-band structures when the electrons can be described by an effective
single-band Hamiltonian, affects the superconducting properties of
two-dimensional electronic systems. Generically the Berry curvature is coupled
to electric fields beyond those created by the periodic crystal potential. A
potential source of such electric fields, which vary slowly on the lattice
scale, is the mutual interaction between the electrons. We show that the Berry
curvature provides additional terms in the Hamiltonian describing interacting
electrons within a single band. When these terms are taken into account in the
framework of the usual BCS weak-coupling treatment of a generic attractive
interaction that allows for the formation of Cooper pairs, the coupling
constant is modified. In pure singlet and triplet superconductors, we find that
the Berry curvature generally lowers the coupling constant and thus the
superconducting gap and the critical temperature as a function of doping. From
an experimental point of view, a measured deviation from the expected BCS
critical temperature upon doping, e.g. in doped two-dimensional
transition-metal dichalcogenides, may unveil the strength of the Berry
curvature.Comment: 14 pages, 3 figure
Magnetism, spin texture and in-gap states: Atomic specialization at the surface of oxygen-deficient SrTiO
Motivated by recent spin- and angular-resolved photoemission (SARPES)
measurements performed on the two-dimensional electronic states confined near
the (001) surface of SrTiO in the presence of oxygen vacancies, we explore
their spin structure by means of ab initio density functional theory (DFT)
calculations of slabs. Relativistic nonmagnetic DFT calculations display
Rashba-like spin winding with a splitting of a few meV and when surface
magnetism on the Ti ions is in- cluded, bands become spin-split with an energy
difference ~100 meV at the point, consistent with SARPES findings.
While magnetism tends to suppress the effects of the relativistic Rashba
interaction, signatures of it are still clearly visible in terms of complex
spin textures. Furthermore, we observe an atomic specialization phenomenon,
namely, two types of electronic contributions: one is from Ti atoms neighboring
the oxygen vacancies that acquire rather large magnetic moments and mostly
create in-gap states; another comes from the partly polarized t
itinerant electrons of Ti atoms lying further away from the oxygen vacancy,
which form the two-dimensional electron system and are responsible for the
Rashba spin winding and the spin splitting at the Fermi surface.Comment: 6 pages, 4 figures, for Suppl. Mat. please contact first autho
Exact Hybrid Covariance Thresholding for Joint Graphical Lasso
This paper considers the problem of estimating multiple related Gaussian
graphical models from a -dimensional dataset consisting of different
classes. Our work is based upon the formulation of this problem as group
graphical lasso. This paper proposes a novel hybrid covariance thresholding
algorithm that can effectively identify zero entries in the precision matrices
and split a large joint graphical lasso problem into small subproblems. Our
hybrid covariance thresholding method is superior to existing uniform
thresholding methods in that our method can split the precision matrix of each
individual class using different partition schemes and thus split group
graphical lasso into much smaller subproblems, each of which can be solved very
fast. In addition, this paper establishes necessary and sufficient conditions
for our hybrid covariance thresholding algorithm. The superior performance of
our thresholding method is thoroughly analyzed and illustrated by a few
experiments on simulated data and real gene expression data
A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds
The Newton iteration is a popular method for minimising a cost function on
Euclidean space. Various generalisations to cost functions defined on manifolds
appear in the literature. In each case, the convergence rate of the generalised
Newton iteration needed establishing from first principles. The present paper
presents a framework for generalising iterative methods from Euclidean space to
manifolds that ensures local convergence rates are preserved. It applies to any
(memoryless) iterative method computing a coordinate independent property of a
function (such as a zero or a local minimum). All possible Newton methods on
manifolds are believed to come under this framework. Changes of coordinates,
and not any Riemannian structure, are shown to play a natural role in lifting
the Newton method to a manifold. The framework also gives new insight into the
design of Newton methods in general.Comment: 36 page
Two 'transitions': the political economy of Joyce Banda's rise to power and the related role of civil society organisations in Malawi
This is an Accepted Manuscript of an article published by Taylor & Francis in Review of African Political Economy on 21/07/2014, available online: http://www.tandfonline.com/doi/abs/10.1080/03056244.2014.90194
Spin Liquid Phases in 2D Frustrated XY Model
In this paper we consider the classical and quantum 2D XY
model. Spin wave calculations show that a spin liquid phase still exists in the
quantum case as for Heisenberg models. We formulate a semiclassical approach of
these models based on spin wave action and use a variational method to study
the role played by vortices. Liquid and crystal phases of vortex could emerge
in this description. These phases seem to be directly correlated with the spin
liquid one and to its crystalline interpretation.Comment: 16 pages, Latex, 4 figures. To be published in Phys. Rev.
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