Tunable Honeycomb Research Articles

Spatiotemporally controllable honeycomb superlattice plasma photonic crystals in dielectric barrier discharge

We present the experimental realization of tunable honeycomb superlattice plasma photonic crystals (PPCs) in dielectric barrier discharge by utilizing mesh-liquid electrodes. Fast reconfiguration among the simple honeycomb lattice, honeycomb superlattice, and honeycomb-snowflake superlattice is achieved. A dynamic control on the sizes of center scattering elements in the honeycomb superlattice has been realized. A phenomenological activator-inhibitor reaction diffusion model is established to demonstrate the formation and reconstruction of the honeycomb superlattice. The simulations reproduce well the experimental observations. The photonic band diagrams of different honeycomb PPCs are studied by using the finite element method. The addition of large center elements in honeycomb superlattice yields remarkable omnidirectional band gaps that are about 2.5 times larger than in the simple honeycomb lattice. We propose an effective scheme to fabricate spatiotemporally controllable honeycomb lattices that enable great improvement in band gap size and dynamic control of microwave radiations for wide applications.

SEM analysis of the tunable honeycomb structure of irradiated poly(vinyl chloride) films doped with polyphosphate

The fabrication of tunable poly(vinyl chloride) porous films containing polyphosphate as an additive was successful. Irradiation of poly(vinyl chloride) films containing polyphosphate at a low concentration (0.5% by weight) with an ultraviolet light (λmax = 313 nm) for 300 h leads to the formation of a honeycomb like structure. The scanning electron microscopy images, at different magnification power, confirmed the production of the PVC honeycomb-like structure. The morphological images of the polymeric film showed a rough surface and a large number of regularly distributed hexagonal pores. The number of pores increased upon irradiation time and it was maximum after 300 h. The honeycomb structure formation could be due to the regular aggregation of polyphosphate among the polymeric chains, the increase in solution intrinsic viscosity and evaluation of hydrogen chloride gas through dehydrochlorination process.

Supramolecular star polymer films with tunable honeycomb structures templated by breath figures

Microporous films with tunable honeycomb structures were fabricated based on the self-assembly of a series of clusto-supramolecular star polymers (CSPs) guided by breath figure templates. The CSPs consist of a hydrophilic polyoxometalate cluster core and several hydrophobic polystyrene arms that are electrostatically connected to the core, in which three Keggin-type polyoxometalate clusters [CoW12O40]6-, [SiW12O40]4- and [PW12O40]3- were used as the cores. The dynamic bonding character endows CSPs a rearrangeable amphiphilic conformation that facilities them to accumulate at the oil/water interface to stabilize water droplets. By precisely adjusting the arm number and arm length of CSPs, we revealed the relationship between the structure and the film-forming behavior of CSPs. Regular pores with a small diameter as low as 260 nm were obtained by optimizing the structure of CSPs. Moreover, the CSPs could act as morphological modifiers to efficiently improve the microporous regularity of polystyrene films, even at a low CSP content of 0.8 wt%. To the best of our knowledge, this is the first work using supramolecular star polymers to fabricate microporous films by the breath figure method, which not only introduces a new film-formation material, but also provides a facile way to incorporate inorganic functional components into microporous polymer films.

Effect of water on the supramolecular assembly and functionality of a naphthalimide derivative: tunable honeycomb structure with mechanochromic properties

This work demonstrated that the honeycomb structure self-assembled by a gelator can be facilely tuned by solvent in both gel and gel emulsions. The corresponding xerogel performs grinding chromism.

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients---one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum---are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between $s$ and $p$ orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.

Zitterbewegungfor ultracold atoms in the merging of Dirac points

We investigate Zitterbewegung (ZB) of the ultracold atoms in a tunable honeycomb optical lattice. By tuning the parameters of the lattice one can realize the merging of two Dirac points. The process of two Dirac points merging into a hybrid point implies a topological phase transition from a semimetallic to a band insulator phase. After merging, it presents a linear-quadratic dispersion relation which is linear in one direction and quadric in the other orthogonal direction. We show that ZB occurs isotropically before merging but occurs only in the direction of the linear dispersion after merging. Furthermore, we obtain that ZB is exponentially damping for a negative energy gap but is a stable oscillation for a positive energy gap. The frequency and amplitude of ZB can be controlled in a detectable range, so the phenomena can be observable in the ultracold atomic experiments.

Self-consistent tight-binding description of Dirac points moving and merging in two-dimensional optical lattices

We present an accurate ab initio tight-binding model, capable of describing the dynamics of Dirac points in tunable honeycomb optical lattices following a recent experimental realization [Tarruell et al., Nature (London) 483, 302 (2012)]. Our scheme is based on first-principle maximally localized Wannier functions for composite bands. The tunneling coefficients are calculated for different lattice configurations, and the spectrum properties are well reproduced with high accuracy. In particular, we show which tight-binding description is needed in order to accurately reproduce the position of Dirac points and the dispersion law close to their merging, for different laser intensities.

Double transfer through Dirac points in a tunable honeycomb optical lattice

We report on Bloch-Zener oscillations of an ultracold Fermi gas in a tunable honeycomb lattice. The quasi-momentum distribution of the atoms is measured after sequentially passing through two Dirac points. We observe a double-peak feature in the transferred fraction to the second band, both as a function of the band gap at the Dirac points and the quasi-momentum of the trajectory. Our results are in good agreement with a simple analytical model based on two successive Landau-Zener transitions. Owing to the variation of the potential gradient over the cloud size, coherent St\"uckelberg oscillations are not visible in our measurements. This effect of the harmonic confinement is confirmed by a numerical simulation of the dynamics of a trapped 2D system.

Superfluidity of Dirac fermions in a tunable honeycomb lattice: Cooper pairing, collective modes, and critical currents

Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak coupling, we find that the maximum mean-field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean-field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripelike density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry-breaking charge-ordered state on the honeycomb lattice. The latter provides a nontrivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice