Weak Decays of Doubly-Heavy Tetraquarks bcˉqqˉ{b\bar c}{q\bar q}

We study the weak decays of exotic tetraquark states ${b\bar c}{q\bar q}$ with two heavy quarks. Under the SU(3) symmetry for light quarks, these tetraquarks can be classified into an octet plus a singlet: $3\bigotimes\bar 3=1\bigoplus8$. We will concentrate on the octet tetraquarks with $J^{P}=0^{+}$, and study their weak decays, both semileptonic and nonleptonic. Hadron-level effective Hamiltonian is constructed according to the irreducible representations of the SU(3) group. Expanding the Hamiltonian, we obtain the decay amplitudes parameterized in terms of a few irreducible quantities. Based on these amplitudes, relations for decay widths are derived, which can be tested in future. We also give a list of golden channels that can be used to look for these states at various colliders.Comment: 14 pages,3 figure

Transverse emission of isospin ratios as a probe of high-density symmetry energy in isotopic nuclear reactions

Transverse emission of preequilibrium nucleons, light clusters (complex particles) and charged pions from the isotopic $^{112,124}$Sn+$^{112,124}$Sn reactions at a beam energy of 400\emph{A} MeV, to extract the high-density behavior of nuclear symmetry energy, are investigated within an isospin and momentum dependent transport model. Specifically, the double ratios of neutron/proton, triton/helium-3 and $\pi^{-}/\pi^{+}$ in the squeeze-out domain are analyzed systematically, which have the advantage of reducing the influence of the Coulomb force and less systematic errors. It is found that the transverse momentum distribution of isospin ratios strongly depend on the stiffness of nuclear symmetry energy, which would be a nice observable to extract the high-density symmetry energy. The collision centrality and the mass splitting of neutron and proton in nuclear medium play a significant role on the distribution structure of the ratios, but does not change the influence of symmetry energy on the spectrum.Comment: 5 figures, 13 page

Designer Topological Insulators in Superlattices

Gapless Dirac surface states are protected at the interface of topological and normal band insulators. In a binary superlattice bearing such interfaces, we establish that valley-dependent dimerization of symmetry-unrelated Dirac surface states can be exploited to induce topological quantum phase transitions. This mechanism leads to a rich phase diagram that allows us to design strong, weak, and crystalline topological insulators. Our ab initio simulations further demonstrate this mechanism in [111] and [110] superlattices of calcium and tin tellurides.Comment: 5 pages, 4 figure

Giant and tunable valley degeneracy splitting in MoTe2

Monolayer transition-metal dichalcogenides possess a pair of degenerate helical valleys in the band structure that exhibit fascinating optical valley polarization. Optical valley polarization, however, is limited by carrier lifetimes of these materials. Lifting the valley degeneracy is therefore an attractive route for achieving valley polarization. It is very challenging to achieve appreciable valley degeneracy splitting with applied magnetic field. We propose a strategy to create giant splitting of the valley degeneracy by proximity-induced Zeeman effect. As a demonstration, our first principles calculations of monolayer MoTe$_2$ on a EuO substrate show that valley splitting over 300 meV can be generated. The proximity coupling also makes interband transition energies valley dependent, enabling valley selection by optical frequency tuning in addition to circular polarization. The valley splitting in the heterostructure is also continuously tunable by rotating substrate magnetization. The giant and tunable valley splitting adds a readily accessible dimension to the valley-spin physics with rich and interesting experimental consequences, and offers a practical avenue for exploring device paradigms based on the intrinsic degrees of freedom of electrons.Comment: 8 pages, 5 figures, 1 tabl

The geometric mean is a Bernstein function

In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers. From this integral representation, the geometric mean is proved to be a Bernstein function and a new proof of the well known AG inequality is provided.Comment: 10 page