Gauge fields, quantized fluxes and monopole confinement of the honeycomb lattice

Electron hopping models on the honeycomb lattice are studied. The lattice consists of two triangular sublattices, and it is non-Bravais. The dual space has non-trivial topology. The gauge fields of Bloch electrons have the U(1) symmetry and thus represent superconducting states in the dual space. Two quantized Abrikosov fluxes exist at the Dirac points and have fluxes $2pi$ and $-2pi$, respectively. We define the non-Abelian SO(3) gauge theory in the extended 3$d$ dual space and it is shown that a monopole and anti-monoplole solution is stable. The SO(3) gauge group is broken down to U(1) at the 2$d$ boundary.The Abrikosov fluxes are related to quantized Hall conductance by the topological expression. Based on this, monopole confinement and deconfinement are discussed in relation to time reversal symmetry and QHE. The Jahn-Teller effect is briefly discussed.Comment: 10 pages, 11 figure

Variational wave functions of a vortex in cyclotron motion

In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational states of a vortex in a cylinder and the cyclotron states of an electron in the central gauge is found. Like the Landau levels of an electron, the energy levels of a vortex are highly degenerate. However, the gap between two adjacent energy levels does not only depend on the quantized circulation, but also increases with the energy, and scales with the size of the vortex.Comment: LaTeX, 4 pages, 2 EPS figures, To appear in ``Series on Advances in Quantum Many-Body Theory'' ed. by R.F. Bishop, C.E. Campbell, J.W. Clark and S. Fantoni (World Scientific, 2000

Resonant atom-field interaction in large-size coupled-cavity arrays

We consider an array of coupled cavities with staggered inter-cavity couplings, where each cavity mode interacts with an atom. In contrast to large-size arrays with uniform-hopping rates where the atomic dynamics is known to be frozen in the strong-hopping regime, we show that resonant atom-field dynamics with significant energy exchange can occur in the case of staggered hopping rates even in the thermodynamic limit. This effect arises from the joint emergence of an energy gap in the free photonic dispersion relation and a discrete frequency at the gap's center. The latter corresponds to a bound normal mode stemming solely from the finiteness of the array length. Depending on which cavity is excited, either the atomic dynamics is frozen or a Jaynes-Cummings-like energy exchange is triggered between the bound photonic mode and its atomic analogue. As these phenomena are effective with any number of cavities, they are prone to be experimentally observed even in small-size arrays.Comment: 12 pages, 4 figures. Added 5 mathematical appendice

Holstein model and Peierls instability in 1D boson-fermion lattice gases

We study an ultracold bose-fermi mixture in a one dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A Bosonic density wave with a wavenumber of twice the Fermi wavenumber will appear in the quasi one-dimensional system.Comment: 5 pages, 4 figure

Possible Lattice Distortions in the Hubbard Model for Graphene

The Hubbard model on the honeycomb lattice is a well known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most six atoms per unit cell as compared to two atoms for the undistorted lattice.Comment: 5 pages, 3 figure

Dark-field transmission electron microscopy and the Debye-Waller factor of graphene

Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multi-layer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.Comment: 10 pages, 4 figure

Graphyne: Hexagonal network of carbon with versatile Dirac cones

We study alpha, beta, and gamma graphyne, a class of graphene allotropes with carbon triple bonds, using a first-principles density-functional method and tight-binding calculation. We find that graphyne has versatile Dirac cones and it is due to remarkable roles of the carbon triple bonds in electronic and atomic structures. The carbon triple bonds modulate effective hopping matrix elements and reverse their signs, resulting in Dirac cones with reversed chirality in alpha graphyne, momentum shift of the Dirac point in beta graphyne, and switch of the energy gap in gamma graphyne. Furthermore, the triple bonds provide chemisorption sites of adatoms which can break sublattice symmetry while preserving planar sp2-bonding networks. These features of graphyne open new possibilities for electronic applications of carbon-based two-dimensional materials and derived nanostructures.Comment: 5 pages, 5 figures, 1 tabl

Symmetry breaking in the self-consistent Kohn-Sham equations

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.Comment: a few typos eliminate

Nonlinear thermal control in an N-terminal junction

We demonstrate control over heat flow in an N-terminal molecular junction. Using simple model Hamiltonians we show that the heat current through two terminals can be tuned, switched, and amplified, by the temperature and coupling parameters of external gating reservoirs. We discuss two models: A fully harmonic system, and a model incorporating anharmonic interactions. For both models the control reservoirs induce thermal fluctuations of the transition elements between molecular vibrational states. We find that a fully harmonic model does not show any controllability, while for an anharmonic system the conduction properties of the junction strongly depend on the parameters of the gates. Realizations of the model system within nanodevices and macromolecules are discussed

Phonon-phonon interactions in transition metals

In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be reasonable for bcc and fcc metals. For hcp metals we show that the Raman active mode decays into a pair of acoustic phonons, their wave vector being located on a surface defined by conservation laws.Comment: 14 pages, 3 figure