We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magneto-translation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology.

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A rapid and simple multi-residue method for determination of pesticides has been applied to drinking water and beverages. To a disposable polypropylene tube containing 10.0 g sample, 20 mL acetonitrile was added and the mixture was shaken vigorously for 1 min to extract pesticides. Then, 1 g sodium chloride and 4 g magnesium sulfate anhydrous were added, followed by vigorous shaking for 1 min and centrifugation to obtain the organic phase. The organic phase was processed with a graphite carbon black/PSA solid phase column. After concentration and reconstitution with 25 methanol containing aqueous solution, the test solution was analyzed with LC-MS/MS. Recovery tests of 91 pesticides fortified 0.02 μg/g in 35 kinds of drinking water and beverages were conducted. The decline of recoveries in alcoholic beverages is considered to be due to the increase of organic phase volume owing to ethanol included in the alcoholic beverages. A simulation study was carried out with simulated alcoholic beverages, which consisted of 50 grape juice, with various amounts of ethanol and water, to examine pesticides recoveries and volume of the organic phase. The results suggested this method would be applicable both to alcoholic beverages containing less than 10 ethanol and to alcoholic beverages containing over 10 ethanol after dilution with water to below 10 ethanol prior to the addition of acetonitrile. A sample could be processed and analyzed by LC-MS/MS within 2 h. Thus, this method should be useful for monitoring and screening pesticide residues in drinking water and various beverages.

We discuss exact plaquette-ordered ground states of the generalized Hubbard model based on the projection operator method for several corner sharing lattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exact ground states are interpreted as Néel ordered states on the plaquette-located electrons. We demonstrate that these models also have exact edge states. We also calculate the entanglement entropy exactly in these systems.