3,644 research outputs found
Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
Majorana fermion (MF) whose antiparticle is itself has been predicted in
condensed matter systems. Signatures of the MFs have been reported as zero
energy modes in various systems. More definitive evidences are highly desired
to verify the existence of the MF. Very recently, theory has predicted MFs to
induce spin selective Andreev reflection (SSAR), a novel magnetic property
which can be used to detect the MFs. Here we report the first observation of
the SSAR from MFs inside vortices in Bi2Te3/NbSe2 hetero-structure, in which
topological superconductivity was previously established. By using
spin-polarized scanning tunneling microscopy/spectroscopy (STM/STS), we show
that the zero-bias peak of the tunneling differential conductance at the vortex
center is substantially higher when the tip polarization and the external
magnetic field are parallel than anti-parallel to each other. Such strong spin
dependence of the tunneling is absent away from the vortex center, or in a
conventional superconductor. The observed spin dependent tunneling effect is a
direct evidence for the SSAR from MFs, fully consistent with theoretical
analyses. Our work provides definitive evidences of MFs and will stimulate the
MFs research on their novel physical properties, hence a step towards their
statistics and application in quantum computing.Comment: 4 figures 15 page
On Investigating the Conservative Property of Score-Based Generative Models
Existing Score-based Generative Models (SGMs) can be categorized into
constrained SGMs (CSGMs) or unconstrained SGMs (USGMs) according to their
parameterization approaches. CSGMs model probability density functions as
Boltzmann distributions, and assign their predictions as the negative gradients
of some scalar-valued energy functions. On the other hand, USGMs employ
flexible architectures capable of directly estimating scores without the need
to explicitly model energy functions. In this paper, we demonstrate that the
architectural constraints of CSGMs may limit their modeling ability. In
addition, we show that USGMs' inability to preserve the property of
conservativeness may lead to degraded sampling performance in practice. To
address the above issues, we propose Quasi-Conservative Score-based Generative
Models (QCSGMs) for keeping the advantages of both CSGMs and USGMs. Our
theoretical derivations demonstrate that the training objective of QCSGMs can
be efficiently integrated into the training processes by leveraging the
Hutchinson trace estimator. In addition, our experimental results on the
CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets validate the effectiveness of
QCSGMs. Finally, we justify the advantage of QCSGMs using an example of a
one-layered autoencoder
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