Novel Ground-State Crystals with Controlled Vacancy Concentrations: From Kagom\'{e} to Honeycomb to Stripes

We introduce a one-parameter family, $0 \leq H \leq 1$, of pair potential functions with a single relative energy minimum that stabilize a range of vacancy-riddled crystals as ground states. The "quintic potential" is a short-ranged, nonnegative pair potential with a single local minimum of height $H$ at unit distance and vanishes cubically at a distance of \rt. We have developed this potential to produce ground states with the symmetry of the triangular lattice while favoring the presence of vacancies. After an exhaustive search using various optimization and simulation methods, we believe that we have determined the ground states for all pressures, densities, and $0 \leq H \leq 1$. For specific areas below 3\rt/2, the ground states of the "quintic potential" include high-density and low-density triangular lattices, kagom\'{e} and honeycomb crystals, and stripes. We find that these ground states are mechanically stable but are difficult to self-assemble in computer simulations without defects. For specific areas above 3\rt/2, these systems have a ground-state phase diagram that corresponds to hard disks with radius \rt. For the special case of H=0, a broad range of ground states is available. Analysis of this case suggests that among many ground states, a high-density triangular lattice, low-density triangular lattice, and striped phases have the highest entropy for certain densities. The simplicity of this potential makes it an attractive candidate for experimental realization with application to the development of novel colloidal crystals or photonic materials.Comment: 25 pages, 11 figure

Negative thermal expansion in single-component systems with isotropic interactions

We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.Comment: 21 pages, 13 figure

Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport

We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system's perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological "minigaps," manifesting an entirely new phenomenon: fractal topological systems. These topological minigaps form only when the system size is sufficiently large because their gapless edge states penetrate deep into the bulk. Hence, the topological structure emerges as a function of the system size, contrary to periodic systems where the topological phase can be completely characterized by the unit cell. We demonstrate the existence of this topological phase both by using a topological index (Bott index) and by studying the unidirectional transport of the gapless edge states and its robustness in the presence of defects. Our specific model is a Penrose lattice of helical optical waveguides - a photonic Floquet quasicrystal; however, we expect this new topological quasicrystal phase to be universal.Comment: 12 pages, 8 figure

Topological crystalline protection in a photonic system

Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in SnTe. In this work, we propose a mechanism to realize photonic boundary states topologically protected by crystalline symmetry. We map this one-dimensional system to a two-dimensional lattice model with opposite magnetic fields, as well as opposite Chern numbers in its even and odd mirror parity subspaces, thus corresponding to a topological mirror insulator. Furthermore, we test how sensitive and robust edge modes depend on their mirror parity by performing time dependent evolution simulation of edge modes in a photonic setting with realistic experimental parameters.Comment: 10 pages, 7 figure