55,793 research outputs found
Mixed Statistics on 01-Fillings of Moon Polyominoes
We establish a stronger symmetry between the numbers of northeast and
southeast chains in the context of 01-fillings of moon polyominoes. Let \M be
a moon polyomino with rows and columns. Consider all the 01-fillings of
\M in which every row has at most one 1. We introduce four mixed statistics
with respect to a bipartition of rows or columns of \M. More precisely, let
and be the union of rows whose
indices are in . For any filling , the top-mixed (resp. bottom-mixed)
statistic (resp. ) is the sum of the number of
northeast chains whose top (resp. bottom) cell is in , together
with the number of southeast chains whose top (resp. bottom) cell is in the
complement of . Similarly, we define the left-mixed and
right-mixed statistics and , where is a subset
of the column index set . Let be any of these
four statistics , , and , we show that the joint distribution of the pair is symmetric and independent of the subsets . In
particular, the pair of statistics is
equidistributed with (\se(M),\ne(M)), where \se(M) and are the
numbers of southeast chains and northeast chains of , respectively.Comment: 20 pages, 6 figure
Two-Dimensional Inversion Asymmetric Topological Insulators in Functionalized III-Bi Bilayers
The search for inversion asymmetric topological insulators (IATIs) persists
as an effect for realizing new topological phenomena. However, so for only a
few IATIs have been discovered and there is no IATI exhibiting a large band gap
exceeding 0.6 eV. Using first-principles calculations, we predict a series of
new IATIs in saturated Group III-Bi bilayers. We show that all these IATIs
preserve extraordinary large bulk band gaps which are well above
room-temperature, allowing for viable applications in room-temperature
spintronic devices. More importantly, most of these systems display large bulk
band gaps that far exceed 0.6 eV and, part of them even are up to ~1 eV, which
are larger than any IATIs ever reported. The nontrivial topological situation
in these systems is confirmed by the identified band inversion of the band
structures and an explicit demonstration of the topological edge states.
Interestingly, the nontrivial band order characteristics are intrinsic to most
of these materials and are not subject to spin-orbit coupling. Owning to their
asymmetric structures, remarkable Rashba spin splitting is produced in both the
valence and conduction bands of these systems. These predictions strongly
revive these new systems as excellent candidates for IATI-based novel
applications.Comment: 17 pages,5figure
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