7,070 research outputs found
Melting and Rippling Phenomenan in Two Dimensional Crystals with localized bonding
We calculate Root Mean Square (RMS) deviations from equilibrium for atoms in
a two dimensional crystal with local (e.g. covalent) bonding between close
neighbors. Large scale Monte Carlo calculations are in good agreement with
analytical results obtained in the harmonic approximation. When motion is
restricted to the plane, we find a slow (logarithmic) increase in fluctuations
of the atoms about their equilibrium positions as the crystals are made larger
and larger. We take into account fluctuations perpendicular to the lattice
plane, manifest as undulating ripples, by examining dual layer systems with
coupling between the layers to impart local rigidly (i.e. as in sheets of
graphene made stiff by their finite thickness). Surprisingly, we find a rapid
divergence with increasing system size in the vertical mean square deviations,
independent of the strength of the interplanar coupling. We consider an
attractive coupling to a flat substrate, finding that even a weak attraction
significantly limits the amplitude and average wavelength of the ripples. We
verify our results are generic by examining a variety of distinct geometries,
obtaining the same phenomena in each case.Comment: 17 pages, 28 figure
Generating derivative structures: Algorithm and applications
We present an algorithm for generating all derivative superstructures--for
arbitrary parent structures and for any number of atom types. This algorithm
enumerates superlattices and atomic configurations in a geometry-independent
way. The key concept is to use the quotient group associated with each
superlattice to determine all unique atomic configurations. The run time of the
algorithm scales linearly with the number of unique structures found. We show
several applications demonstrating how the algorithm can be used in materials
design problems. We predict an altogether new crystal structure in Cd-Pt and
Pd-Pt, and several new ground states in Pd-rich and Pt-rich binary systems
Exact results for the star lattice chiral spin liquid
We examine the star lattice Kitaev model whose ground state is a a chiral
spin liquid. We fermionize the model such that the fermionic vacua are toric
code states on an effective Kagome lattice. This implies that the Abelian phase
of the system is inherited from the fermionic vacua and that time reversal
symmetry is spontaneously broken at the level of the vacuum. In terms of these
fermions we derive the Bloch-matrix Hamiltonians for the vortex free sector and
its time reversed counterpart and illuminate the relationships between the
sectors. The phase diagram for the model is shown to be a sphere in the space
of coupling parameters around the triangles of the lattices. The abelian phase
lies inside the sphere and the critical boundary between topologically distinct
Abelian and non-Abelian phases lies on the surface. Outside the sphere the
system is generically gapped except in the planes where the coupling parameters
are zero. These cases correspond to bipartite lattice structures and the
dispersion relations are similar to that of the original Kitaev honeycomb
model. In a further analysis we demonstrate the three-fold non-Abelian
groundstate degeneracy on a torus by explicit calculation.Comment: 7 pages, 8 figure
Melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices
When the constituent spins have an energetic preference to lie along an
easy-axis, triangular and Kagome lattice antiferromagnets often develop
long-range order that distinguishes the three sublattices of the underlying
triangular Bravais lattice. In zero magnetic field, this three-sublattice order
melts {\em either} in a two-step manner, {\em i.e.} via an intermediate phase
with power-law three-sublattice order controlled by a temperature dependent
exponent , {\em or} via a transition in
the three-state Potts universality class. Here, I predict that the uniform
susceptibility to a small easy-axis field diverges as in a large part of the intermediate
power-law ordered phase (corresponding to ), providing an easy-to-measure thermodynamic
signature of two-step melting. I also show that these two melting scenarios can
be generically connected via an intervening multicritical point, and obtain
numerical estimates of multicritical exponents.Comment: Revised version (under review at Phys. Rev. Lett.
- …