35,878 research outputs found
Accelerated Stochastic ADMM with Variance Reduction
Alternating Direction Method of Multipliers (ADMM) is a popular method in
solving Machine Learning problems. Stochastic ADMM was firstly proposed in
order to reduce the per iteration computational complexity, which is more
suitable for big data problems. Recently, variance reduction techniques have
been integrated with stochastic ADMM in order to get a fast convergence rate,
such as SAG-ADMM and SVRG-ADMM,but the convergence is still suboptimal w.r.t
the smoothness constant. In this paper, we propose a new accelerated stochastic
ADMM algorithm with variance reduction, which enjoys a faster convergence than
all the other stochastic ADMM algorithms. We theoretically analyze its
convergence rate and show its dependence on the smoothness constant is optimal.
We also empirically validate its effectiveness and show its priority over other
stochastic ADMM algorithms
Theory of magnetoelectric photocurrent generated by direct interband transitions in semiconductor quantum well
A linearly polarized light normally incident on a semiconductor quantum well
with spin-orbit coupling may generate pure spin current via direct interband
optical transition. An electric photocurrent can be extracted from the pure
spin current when an in-plane magnetic field is applied, which has been
recently observed in the InGaAs/InAlAs quantum well [Dai et al., Phys. Rev.
Lett. 104, 246601 (2010)]. Here we present a theoretical study of this
magnetoelectric photocurrent effect associated with the interband transition.
By employing the density matrix formalism, we show that the photoexcited
carrier density has an anisotropic distribution in k space, strongly dependent
on the orientation of the electron wavevector and the polarization of the
light. This anisotropy provides an intuitive picture of the observed dependence
of the photocurrent on the magnetic field and the polarization of the light. We
also show that the ratio of the pure spin photocurrent to the magnetoelectric
photocurrent is approximately equal to the ratio of the kinetic energy to the
Zeeman energy, which enables us to estimate the magnitude of the pure spin
photocurrent. The photocurrent density calculated with the help of an
anisotropic Rashba model and the Kohn-Luttinger model can produce all three
terms in the fitting formula for measured current, with comparable order of
magnitude, but discrepancies are still present and further investigation is
needed.Comment: 13 pages, 9 figures, 2 table
Linear magnetoconductivity in an intrinsic topological Weyl semimetal
Searching for the signature of the violation of chiral charge conservation in
solids has inspired a growing passion on the magneto-transport in topological
semimetals. One of the open questions is how the conductivity depends on
magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl
nodes. Here, we study both the longitudinal and transverse magnetoconductivity
of a topological Weyl semimetal near the Weyl nodes with the help of a two-node
model that includes all the topological semimetal properties. In the semimetal
phase, the Fermi energy crosses only the 0th Landau bands in magnetic fields.
For a finite potential range of impurities, it is found that both the
longitudinal and transverse magnetoconductivity are positive and linear at the
Weyl nodes, leading to an anisotropic and negative magnetoresistivity. The
longitudinal magnetoconductivity depends on the potential range of impurities.
The longitudinal conductivity remains finite at zero field, even though the
density of states vanishes at the Weyl nodes. This work establishes a relation
between the linear magnetoconductivity and the intrinsic topological Weyl
semimetal phase.Comment: An extended version accepted by New. J. Phys. with 15 pages and 3
figure
High-field magnetoconductivity of topological semimetals with short-range potential
Weyl semimetals are three-dimensional topological states of matter, in a
sense that they host paired monopoles and antimonopoles of Berry curvature in
momentum space, leading to the chiral anomaly. The chiral anomaly has long been
believed to give a positive magnetoconductivity or negative magnetoresistivity
in strong and parallel fields. However, several recent experiments on both Weyl
and Dirac topological semimetals show a negative magnetoconductivity in high
fields. Here, we study the magnetoconductivity of Weyl and Dirac semimetals in
the presence of short-range scattering potentials. In a strong magnetic field
applied along the direction that connects two Weyl nodes, we find that the
conductivity along the field direction is determined by the Fermi velocity,
instead of by the Landau degeneracy. We identify three scenarios in which the
high-field magnetoconductivity is negative. Our findings show that the
high-field positive magnetoconductivity may not be a compelling signature of
the chiral anomaly and will be helpful for interpreting the inconsistency in
the recent experiments and earlier theories.Comment: An extended version accepted by Phys. Rev. B, with 11 pages and 4
figure
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