A method for constructing the low energy effective models for pairings in the generalized Bernevig-Hughes-Zhang model for materials like Bi$_{2}$Se$_{3}$ is proposed. Pairings in this two-orbital model are identified with those familiar in one-orbita
l models, enabling a unified understanding. The theory provides an easy way to understand the topological nature of the superconducting state that is not directly related to the topological order in the normal state but due to subtle coupling among the degrees of freedom. Furthermore this approach shows a simple way to characterize the anisotropic nature of surface Andreev bound states (SABSs). In particular, we have identified the conditions to have a surprising new result of having two pairs of SABSs. It also leads to a conclusion that SABSs always connect with the topological surface states if the latter are well defined at the chemical potential.
We present an analysis of the mid-infrared emission lines for a sample of 12 low metallicity Blue Compact Dwarf (BCD) galaxies based on high resolution observations obtained with Infrared Spectrograph on board the {rm Spitzer} Space Telescope. We com
pare our sample with a local sample of typical starburst galaxies and active galactic nuclei (AGNs), to study the ionization field of starbursts over a broad range of physical parameters and examine its difference from the one produced by AGN. The high-ionization line [OIV]25.89$mu$m is detected in most of the BCDs, starbursts, and AGNs in our sample. We propose a diagnostic diagram of the line ratios [OIV]25.89$mu$m/[SIII]33.48$mu$m as a function of [NeIII]15.56$mu$m/[NeII]12.81$mu$m which can be useful in identifying the principal excitation mechanism in a galaxy. Galaxies in this diagram split naturally into two branches. Classic AGNs as well as starburst galaxies with an AGN component populate the upper branch, with stronger AGNs displaying higher [NeIII]/[NeII] ratios. BCDs and pure starbursts are located in the lower branch. We find that overall the placement of galaxies on this diagram correlates well with their corresponding locations in the log([NII]/H$alpha$) vs. log([OIII]/H$beta$) diagnostic diagram, which has been widely used in the optical. The two diagrams provide consistent classifications of the excitation mechanism in a galaxy. On the other hand, the diagram of [NeIII]15.56$mu$m/[NeII]12.81$mu$m vs. [SIV]10.51$mu$m/[SIII]18.71$mu$m is not as efficient in separating AGNs from BCDs and pure starbursts. (abridged)
