Impact of disorder on dynamics and ordering in the honeycomb-lattice iridate Na2IrO3

Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as α-RuCl3, Li2IrO3, and Na2IrO3 continue to present open questions about how the dynamics of a spin liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use Na23 nuclear magnetic resonance to probe both static and dynamical magnetic properties in single-crystal Na2IrO3. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below TN the spectra show a broad distribution of internal magnetic fields. Both of these results provide evidence for inequivalent magnetic sites at low temperature, suggesting inhomogeneities are important for the magnetism. The spin-lattice relaxation rate is isotropic and diverges at TN, suggesting that the Kitaev cubic axes may control the critical quantum spin fluctuations. In the ordered state, we observe gapless excitations, which may arise from site substitution, emergent defects from milder disorder, or possibly be associated with nearby quantum paramagnetic states distinct from the Kitaev spin liquid

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.Comment: 55 pages, Urbana Prepin

Selective oxidation of aromatic alcohols in the presence of C3N4 photocatalysts derived from the polycondensation of melamine, cyanuric and barbituric acids

A set of C3N4 samples has been prepared by using melamine, cyanuric acid and barbituric acid as the precursors. The materials were subjected both to physical and chemical characterization and were used as photocatalysts for the selective oxidation of aromatic alcohols in water suspension under UV and visible irradiation. The photoactivity of the materials versus the partial oxidation of four substituted benzyl alcohols was investigated. The type and position of the substituents in the aromatic molecule influenced conversion and selectivity to the corresponding aldehyde. The presence of barbituric and cyanuric acids in the preparation method has changed the graphitic-C3N4 structure, and therefore both the characteristics of the material and the ability of light to activate the surface of the photocatalyst. The most active material prepared in the presence of melamine and cyanuric acid showed a remarkable selectivity towards the aldehyde even under visible irradiation

Single-mode approximation and effective Chern-Simons theories for quantum Hall systems

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern-Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern-Simons theory. For single-layer systems the effective theory agrees with the standard Chern-Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.Comment: 9 pages, Revtex

A Classification of 3-Family Grand Unification in String Theory I. The SO(10) and E_6 Models

We give a classification of 3-family SO(10) and E_6 grand unification in string theory within the framework of conformal field theory and asymmetric orbifolds. We argue that the construction of such models in the heterotic string theory requires certain Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SO(10) or E_6. We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly free. There are two types of such 3-family models. The first type consists of the unique SO(10) model with SU(2) X SU(2) X SU(2) as its hidden sector (which is not asymptotically-free at the string scale). This SO(10) model has 4 left-handed and 1 right-handed 16s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and 5 left-handed and 2 right-handed families in the grand unified gauge group. One of these models is the unique E_6 model with an asymptotically-free SU(2) hidden sector. The others are SO(10) models, 8 of them with an asymptotically free hidden sector at the string scale.Comment: 35 pages, Revtex 3.0, one eps figure (to appear in Phys. Rev. D

On the solution of a supersymmetric model of correlated electrons

We consider the exact solution of a model of correlated electrons based on the superalgebra $Osp(2|2)$. The corresponding Bethe ansatz equations have an interesting form. We derive an expression for the ground state energy at half filling. We also present the eigenvalue of the transfer matrix commuting with the Hamiltonian.Comment: Palin latex , 8 page

Asymmetric Orbifolds and Grand Unification

We generalize the rules for the free fermionic string construction to include other asymmetric orbifolds with world-sheet bosons. We use these rules to construct various grand unified string models that involve level-3 current algebras. We present the explicit construction of three classes of 3-chiral-family grand unified models in the heterotic string theory. Each model has 5 left-handed, and two right-handed families, and an adjoint Higgs. Two of them are SO(10) and the third is E_6. With Wilson lines and/or varying moduli, we show how other 3-family grand unified models, such as SO(10) and SU(5), may be constructed from them.Comment: 47 pages, Revtex 3.0, minor misprints corrected (to appear in Phys. Rev. D

Compactification and Supersymmetry Breaking in M-theory

Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss the various orbifold compactifications of M-theory suggested by Horava and Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by keeping singlets under $SU(2)\times U(1)$ symmetry, then the compactification on $S^1/Z_2$. We also discuss the next to leading order K\"ahler potential, superpotential, and gauge kinetic function in the $Z_{12}$ case. In addition, we calculate the SUSY breaking soft terms and find out that the universality of the scalar masses will be violated, but the violation might be very small.Comment: 16 pages, latex, no figure

Generalised Chern-Simons Theory of Composite Fermions in Bilayer Hall Systems

We present a field theory of Jain's composite fermion model as generalised to the bilayer quantum Hall systems. We define operators which create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complexified version of the familiar Chern Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in usual Chern Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin . But unlike normal Chern Simons theories, we obtain all features of the first-quantised wavefunctions including its phase, modulus and correct gaussian factors at the mean field level. The familiar Jain relations for monolayers and the Halperin wavefunction for bilayers come out as special cases.Comment: Revtex file; 20 pages after processing; no figure