Bloch oscillations in complex crystals with PT symmetry

Bloch oscillations (BO) in complex lattices with PT symmetry are theoretically investigated with specific reference to optical BO in photonic lattices with gain/loss regions. Novel dynamical phenomena with no counterpart in ordinary lattices, such as non-reciprocal BO related to violation of the Friedel's law of Bragg scattering in complex potentials, are highlighted.Comment: 4 pages, 3 figure

Band gap opening by two-dimensional manifestation of Peierls instability in graphene

Using first-principles calculations of graphene having high-symmetry distortion or defects, we investigate band gap opening by chiral symmetry breaking, or intervalley mixing, in graphene and show an intuitive picture of understanding the gap opening in terms of local bonding and antibonding hybridizations. We identify that the gap opening by chiral symmetry breaking in honeycomb lattices is an ideal two-dimensional (2D) extension of the Peierls metal-insulator transition in 1D linear lattices. We show that the spontaneous Kekule distortion, a 2D version of the Peierls distortion, takes place in biaxially strained graphene, leading to structural failure. We also show that the gap opening in graphene antidots and armchair nanoribbons, which has been attributed usually to quantum confinement effects, can be understood with the chiral symmetry breaking

Rigid unit modes in tetrahedral crystals

The 'rigid unit mode' (RUM) model requires unit blocks, in our case tetrahedra of SiO_4 groups, to be rigid within first order of the displacements of the O-ions. The wave-vectors of the lattice vibrations, which obey this rigidity, are determined analytically. Lattices with inversion symmetry yield generically surfaces of RUMs in reciprocal space, whereas lattices without this symmetry yield generically lines of RUMs. Only in exceptional cases as in beta-quartz a surface of RUMs appears, if inversion symmetry is lacking. The occurence of planes and bending surfaces, straight and bent lines is discussed. Explicit calculations are performed for five modifications of SiO_2 crystals.Comment: 18 pages, 6 figures, improved notatio

Percolation on dual lattices with k-fold symmetry

Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an infinite open cluster when it exists; this argument requires some symmetry. Here we show that a simple modification of Zhang's argument requires only 2-fold (or 3-fold) symmetry, proving that the critical probabilities for percolation on dual planar lattices with such symmetry sum to 1. Like Zhang's argument, our extension applies in many contexts; in particular, it enables us to answer a question of Grimmett concerning the anisotropic random cluster model on the triangular lattice.Comment: 11 pages, 1 figure. Revised with applications added; to appear in Random Structures and Algorithm

Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices

We report the effect of symmetry-broken contacts on quantum transport in quasi-one-dimensional lattices. In contrast to 1D chains, transport in quasi-one-dimensional lattices, which are made up of a finite number of 1D chain layers, is strongly influenced by contacts. Contact symmetry depends on whether the contacts maintain or break the parity symmetry between the layers. With balanced on-site potential, a flat band can be detected by asymmetric contacts, but not by symmetric contacts. In the case of asymmetric contacts with imbalanced on-site potential, transmission is suppressed at certain energies. We elucidate these energies of transmission suppression related to antiresonance using reduced lattice models and Feynman paths. These results provide a nondestructive measurement of flat band energy which it is difficult to detect.Comment: 8 pages, 5 figure

Rotating states for trapped bosons in an optical lattice

Rotational states for trapped bosons in an optical lattice are studied in the framework of the Hubbard model. Critical frequencies are calculated and the main parameter regimes are identified. Transitions are observed from edge superfluids to vortex lattices with Mott insulating cores, and subsequently to lattices of interstitial vortices. The former transition coincides with the Mott transition. Changes in symmetry of the vortex lattices are observed as a function of lattice depth. Predictions for experimental signatures are presented.Comment: 6 pages, 6 figures, accepted for publication in EP