Pairing State with a time-reversal symmetry breaking in FeAs based superconductors

We investigate the competition between the extended $s_{\pm}$-wave and $d_{x^2-y^2}$-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole fermi pockets, a time reversal symmetry breaking $s+id$ pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory, and explore the experimental consequences. In such a state, spatial inhomogeneity induces supercurrent near a non-magnetic impurity and the corners of a square sample. The resonance mode between the $s_{\pm}$ and $d_{x^2-y^2}$-wave order parameters can be detected through the $B_{1g}$-Raman spectroscopy.Comment: 4 pages, 4 figures, new references adde

Orbital Resonance Mode in Superconducting Iron Pnictides

We show that the fluctuations associated with ferro orbital order in the $d_{xz}$ and $d_{yz}$ orbitals can develop a sharp resonance mode in the superconducting state with a nodeless gap on the Fermi surface. This orbital resonance mode appears below the particle-hole continuum and is analogous to the magnetic resonance mode found in various unconventional superconductors. If the pairing symmetry is $s_{\pm}$, a dynamical coupling between the orbital ordering and the d-wave subdominant pairing channels is present by symmetry. Therefore the nature of the resonance mode depends on the relative strengths of the fluctuations in these two channels, which could vary significantly for different families of the iron based superconductors. The application of our theory to a recent observation of a new $\delta$-function-like peak in the B$_{1g}$ Raman spectrum of Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ is discussed.Comment: 6 pages, 3 figure

Replacement Paths via Row Minima of Concise Matrices

Matrix $M$ is {\em $k$-concise} if the finite entries of each column of $M$ consist of $k$ or less intervals of identical numbers. We give an $O(n+m)$-time algorithm to compute the row minima of any $O(1)$-concise $n\times m$ matrix. Our algorithm yields the first $O(n+m)$-time reductions from the replacement-paths problem on an $n$-node $m$-edge undirected graph (respectively, directed acyclic graph) to the single-source shortest-paths problem on an $O(n)$-node $O(m)$-edge undirected graph (respectively, directed acyclic graph). That is, we prove that the replacement-paths problem is no harder than the single-source shortest-paths problem on undirected graphs and directed acyclic graphs. Moreover, our linear-time reductions lead to the first $O(n+m)$-time algorithms for the replacement-paths problem on the following classes of $n$-node $m$-edge graphs (1) undirected graphs in the word-RAM model of computation, (2) undirected planar graphs, (3) undirected minor-closed graphs, and (4) directed acyclic graphs.Comment: 23 pages, 1 table, 9 figures, accepted to SIAM Journal on Discrete Mathematic