990 research outputs found
On the Phase-Space Distribution of Bloch Eigenmodes for Periodic Point Scatterers
Consider the 3-dimensional Laplacian with a potential described by point
scatterers placed on the integer lattice. We prove that for Floquet-Bloch modes
with fixed quasi-momentum satisfying a certain Diophantine condition, there is
a subsequence of eigenvalues of positive density whose eigenfunctions exhibit
equidistribution in position space and localisation in momentum space. This
result complements the result of Uebersch\"{a}r and Kurlberg who show momentum
localisation for zero quasi-momentum in 2-dimensions, and is the first result
in this direction in 3-dimensions.Comment: 16 pages, 2 figure
Surface Structure of In Situ Cleaved Single Crystal Bi2Se3 Measured by Low Energy Ion Scattering
Bismuth Selenide is a two-dimensional topological insulator material composed
of stacked quintuple layers (QL). The layers are held together by a weak van
der Waals force that enables surface preparation by cleaving. Low energy ion
scattering experiments (LEIS) show that Bi2Se3 cleaved under ultra-high vacuum
(UHV) has a Se-terminated structure that is consistent with cleaving between
QLs. Comparison of experimental data to molecular dynamics simulations confirms
the Se-termination and provides an estimate of the surface relaxation.Comment: 23 pages, 6 figures, 1 tabl
Termination of Single Crystal Bi2Se3 Surfaces Prepared by Various Methods
Bismuth Selenide (Bi2Se3) is a topological insulator with a two-dimensional
layered structure that enables clean and well-ordered surfaces to be prepared
by cleaving. Although some studies have demonstrated that the cleaved surface
is terminated with Se, as expected from the bulk crystal structure, other
reports have indicated either a Bi- or mixed-termination. Low energy ion
scattering (LEIS), low energy electron diffraction (LEED) and x-ray
photoelectron spectroscopy (XPS) are used here to compare surfaces prepared by
ex situ cleaving, in situ cleaving, and ion bombardment and annealing (IBA) in
ultra-high vacuum (UHV). Surfaces prepared by in situ cleaving and IBA are well
ordered and Se-terminated. Ex situ cleaved samples could be either
Se-terminated or Bi-rich, are less well ordered and have adsorbed contaminants.
This suggests that a chemical reaction involving atmospheric contaminants,
which may preferentially adsorb at surface defects, could contribute to the
non-reproducibility of the termination.Comment: 31 pages, 10 figures, 1 tabl
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