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The assembly of colloidal cubic diamond is a challenging process since the shape and interaction parameters and the thermodynamic conditions where this structure is stable are elusive. The simultaneous use of shape-anisotropic particles and…
Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here, we consider how such alignment can be achieved using a periodic square lattice of circular…
We study a system of ultra-cold atoms possessing long range interaction (e.g. dipole-dipole interaction) in a one dimensional optical lattice in the presence of a confining harmonic trap. We have shown that for large enough on-site and…
We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc…
Colloidal crystals are used to understand fundamentals of atomic rearrangements in condensed matter and build complex metamaterials with unique functionalities. Simulations predict a multitude of self-assembled crystal structures from…
Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent…
Monte Carlo simulations are performed in classical phase space for a one-dimensional quantum harmonic crystal. Symmetrization effects for spinless bosons and fermions are quantified. The algorithm is tested for a range of parameters against…
We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical…
We investigate the driven states of a two-dimensional crystal whose ground state can be tuned through a square-triangular transition. The depinning of such a system from a quenched random background potential occurs via a complex sequence…
We demonstrate a supersolid-like spatially-periodic square- and honeycomb-lattice crystallization of droplets, in addition to the commonly-studied triangular-lattice crystallization, in a cylindrically-symmetric quasi-two-dimensional…
The optimal "twisted" geometry of a crystalline layer on a crystal is long known, but that on a quasicrystal is still unknown and open. We predict analytically that the layer equilibrium configuration will generally exhibit a nonzero misfit…
We investigate the stability of the skyrmion crystal phase in a tetragonal polar system with the Dzyaloshinskii-Moriya interaction by focusing on the symmetry of ordering wave vectors forming the skyrmion crystal. Our analysis is based on…
Antiferromagnetic and ferro/ferrimagnetic orders are typically exclusive in nature, thus, their co-existence in atomic-scale proximity is expected only in heterostructures. Breaking this paradigm and broadening the range of unconventional…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
The minimal ingredient to generate a biaxial liquid crystalline ordering is usually considered to be the strongly biaxial interactions breaking the cylindrical symmetry of the uniaxial molecules. Although there is no fundamental reason to…
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…
Multiple intriguing phenomena have recently been discovered in tetragonal Heusler compounds, where $D_{2d}$ symmetry sets a unique interplay between Dzyaloshinskii-Moriya (DM) and magnetic dipolar interactions. In the prototype $D_{2d}$…
The singular potential method in the Q tensor order parameter representation is used to determine the ground state configuration of an elastically anisotropic nematic liquid crystal when confined to a cylindrical geometry with homeotropic…
We report the design of a diamond-based honeycomb phononic network, in which a mechanical resonator couples to three distinct phononic crystal waveguides. This two-dimensional (2D) phononic network extends an earlier study on…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…