32,455 research outputs found
Numerical Methods for Quasicrystals
Quasicrystals are one kind of space-filling structures. The traditional
crystalline approximant method utilizes periodic structures to approximate
quasicrystals. The errors of this approach come from two parts: the numerical
discretization, and the approximate error of Simultaneous Diophantine
Approximation which also determines the size of the domain necessary for
accurate solution. As the approximate error decreases, the computational
complexity grows rapidly, and moreover, the approximate error always exits
unless the computational region is the full space. In this work we focus on the
development of numerical method to compute quasicrystals with high accuracy.
With the help of higher-dimensional reciprocal space, a new projection method
is developed to compute quasicrystals. The approach enables us to calculate
quasicrystals rather than crystalline approximants. Compared with the
crystalline approximant method, the projection method overcomes the
restrictions of the Simultaneous Diophantine Approximation, and can also use
periodic boundary conditions conveniently. Meanwhile, the proposed method
efficiently reduces the computational complexity through implementing in a unit
cell and using pseudospectral method. For illustrative purpose we work with the
Lifshitz-Petrich model, though our present algorithm will apply to more general
systems including quasicrystals. We find that the projection method can
maintain the rotational symmetry accurately. More significantly, the algorithm
can calculate the free energy density to high precision.Comment: 27 pages, 8 figures, 6 table
Grain Boundary Loops in Graphene
Topological defects can affect the physical properties of graphene in
unexpected ways. Harnessing their influence may lead to enhanced control of
both material strength and electrical properties. Here we present a new class
of topological defects in graphene composed of a rotating sequence of
dislocations that close on themselves, forming grain boundary loops that either
conserve the number of atoms in the hexagonal lattice or accommodate
vacancy/interstitial reconstruction, while leaving no unsatisfied bonds. One
grain boundary loop is observed as a "flower" pattern in scanning tunneling
microscopy (STM) studies of epitaxial graphene grown on SiC(0001). We show that
the flower defect has the lowest energy per dislocation core of any known
topological defect in graphene, providing a natural explanation for its growth
via the coalescence of mobile dislocations.Comment: 23 pages, 7 figures. Revised title; expanded; updated reference
Rotational Symmetry Breaking in Sodium Doped Cuprates
For reasonable parameters a hole bound to a Na^{+} acceptor in
Ca_{2-x}Na_{x}CuO_{2}Cl_{2} has a doubly degenerate ground state whose
components can be represented as states with even (odd) reflection symmetry
around the x(y) -axes. The conductance pattern for one state is anisotropic as
the tip of a tunneling microscope scans above the Cu-O-Cu bonds along the
x(y)-axes. This anisotropy is pronounced at lower voltages but is reduced at
higher voltages. Qualitative agreement with recent experiments leads us to
propose this effect as an explanation of the broken local rotational symmetry.Comment: 10 pages, 4 figure
- …