Optimal entanglement witnesses based on local orthogonal observables

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. G\"uhne, M. Mechler, G. T\'oth and P. Adam, Phys. Rev. A 74, 010301 (2006)] in linear and nonlinear forms can be optimized, respectively. As applications, we calculate the optimal nonlinear witnesses of pure bipartite states and show a lower bound on the I-concurrence of bipartite higher dimensional systems with our method.Comment: 6 pages, 1 figure; minor changes, references adde

Type-II Topological Dirac Semimetals: Theory and Materials Prediction (VAl3 family)

The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. The new type-II Dirac fermions, their novel magneto-transport response, the topological tunability and the large number of compounds make VAl3 an exciting platform to explore the wide-ranging topological phenomena associated with Lorentz-violating Dirac fermions in electrical and optical transport, spectroscopic and device-based experiments.Comment: 28 pages, 7 Figure

Hybrid nature of 0846+51W1: a BL Lac object with a narrow line Seyfert 1 nucleus

We have found a NLS1 nucleus in the extensively studied eruptive BL Lac, 0846+51W1, out of a large sample of NLS1 compiled from the spectroscopic dataset of SDSS DR1. Its optical spectrum can be well decomposed into three components, a power law component from the relativistic jet, a stellar component from the host galaxy, and a component from a typical NLS1 nucleus. The emission line properties of 0846+51W1, FWHM(Hbeta) ~ 1710 km s^-1 and [OIII]5007/Hbeta ~ 0.32 when it was in faint state, fulfil the conventional definition of NLS1. Strong FeII emission is detected in the SDSS spectrum, which is also typical of NLS1s. We try to estimate its central black hole mass using various techniques and find that 0846+51W1 is very likely emitting at a few times 10% L_Edd. We speculate that Seyfert-like nuclei, including NLS1s, might be concealed in a significant fraction of BL Lacs but have not been sufficiently explored due to the fact that, by definition, the optical-UV continuum of such kind of objects are often overwhelmed by the synchrotron emission.Comment: ChJAA accepte

Mirror protected Dirac fermions on a Weyl semimetal NbP surface

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbPs (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions, and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbPs already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology