94 research outputs found
Optimal rates of convergence for covariance matrix estimation
Covariance matrix plays a central role in multivariate statistical analysis.
Significant advances have been made recently on developing both theory and
methodology for estimating large covariance matrices. However, a minimax theory
has yet been developed. In this paper we establish the optimal rates of
convergence for estimating the covariance matrix under both the operator norm
and Frobenius norm. It is shown that optimal procedures under the two norms are
different and consequently matrix estimation under the operator norm is
fundamentally different from vector estimation. The minimax upper bound is
obtained by constructing a special class of tapering estimators and by studying
their risk properties. A key step in obtaining the optimal rate of convergence
is the derivation of the minimax lower bound. The technical analysis requires
new ideas that are quite different from those used in the more conventional
function/sequence estimation problems.Comment: Published in at http://dx.doi.org/10.1214/09-AOS752 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quasiparticle interference of C2-symmetric surface states in LaOFeAs parent compound
We present scanning tunneling microscopy studies of the LaOFeAs parent
compound of iron pnictide superconductors. Topographic imaging reveals two
types of atomically flat surfaces, corresponding to the exposed LaO layer and
FeAs layer respectively. On one type of surface, we observe strong standing
wave patterns induced by quasiparticle interference of two-dimensional surface
states. The distribution of scattering wavevectors exhibits pronounced two-fold
symmetry, consistent with the nematic electronic structure found in the
Ca(Fe1-xCox)2As2 parent state.Comment: 13 pages, 4 figure
Evolution from unconventional spin density wave to superconductivity and a novel gap-like phase in NaFe1-xCoxAs
Similar to the cuprate high TC superconductors, the iron pnictide
superconductors also lie in close proximity to a magnetically ordered phase. A
central debate concerning the superconducting mechanism is whether the local
magnetic moments play an indispensable role or the itinerant electron
description is sufficient. A key step for resolving this issue is to acquire a
comprehensive picture regarding the nature of various phases and interactions
in the iron compounds. Here we report the doping, temperature, and spatial
evolutions of the electronic structure of NaFe1-xCoxAs studied by scanning
tunneling microscopy. The spin density wave gap in the parent state is observed
for the first time, which shows a strongly asymmetric lineshape that is
incompatible with the conventional Fermi surface nesting scenario. The
optimally doped sample exhibits a single, symmetric energy gap, but in the
overdoped regime another asymmetric gap-like feature emerges near the Fermi
level. This novel gap-like phase coexists with superconductivity in the ground
state, persists deep into the normal state, and shows strong spatial
variations. The characteristics of the three distinct low energy states, in
conjunction with the peculiar high energy spectra, suggest that the coupling
between the local moments and itinerant electrons is the fundamental driving
force for the phases and phase transitions in the iron pnictides.Comment: 4 figures + supplementary informatio
Broad and colossal edge supercurrent in Dirac semimetal Cd<sub>3</sub>As<sub>2</sub> Josephson junctions
Tunable domino effect of thermomagnetic instabilities in superconducting films with multiply-connected topological structures
peer reviewedAbstract
Topology is a crucial ingredient for understanding the physical properties of superconductors. Magnetic field crowds to adopt the form of topologically-protected quantum flux lines which can lose this property when moving at high velocities. These extreme conditions can be realized when superconductors undergo a thermomagnetic instability for which the sample topology come also into play. In this work, utilizing the magneto-optical imaging technique, we experimentally study magnetic flux avalanches in superconducting films with multiply-connected geometries, including single and double rings. We observe a domino effect in which avalanches triggered at the outer ring, stimulate avalanches at the inner ring thus impairing the expected magnetic shielding resulting from the outer ring and gap. We implement numerical simulations in order to gain more insight into the underlying physical mechanism and demonstrate that such event is not caused by the heat conduction, but mainly attributed to the local current distribution variation near the preceding flux avalanche in the outer ring, which in turn has a ripple effect on the local magnetic field profile in the gap. Furthermore, we find that the domino effect of thermomagnetic instabilities can be switched on/off by the environmental temperature and the gap width between the concentric rings. These findings provide new insights on the thermomagnetic instability in superconducting devices with complex topological structures, such as the superconductor–insulator–superconductor multilayer structures of superconducting radio-frequency cavities
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