Electron localization and a confined electron gas in nanoporous inorganic electrides

The nanoporous main group oxide 12CaO.7Al(2)O(3) (C12A7) can be transformed from a wide-gap insulator to an electride where electrons substitute anions in cages constituting a positive frame. Our ab initio calculations of the electronic structure of this novel material give a consistent explanation of its high conductivity and optical properties. They show that the electrons confined in the inert positive frame are localized in cages and undergo hopping between neighboring cages. The results are useful for the understanding of behavior of confined electron gas of different topology and electron-phonon coupling, and for designing new transparent conductors, electron emitters, and electrides

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.Comment: 71 pages, three Wilson line

Non-Supersymmetric Stringy Attractors

In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show that, in the presence of such O(1) corrections, the D0-D4 attractors can either be stable or unstable depending on the geometry of the underlying Calabi-Yau manifold, and on the specific values of the charges they carry.Comment: corrected typos, minor modification

Some combinatorial problems

AbstractThere are many interesting and sophisticated problems posed in the IMO, Putnam and domestic Olympiads. Some of these problems have deep mathematical background, nice generalizations, and lead to new areas of research in combinatorics. We investigate several topics in this category and mention some results and open problems

Origin of critical-temperature enhancement of an iron-based high-T_c superconductor, LaFeAsO_{1-x}F_{x} : NMR study under high pressure

Nuclear magnetic resonance (NMR) measurements of an iron (Fe)-based superconductor LaFeAsO_{1-x}F_x (x = 0.08 and 0.14) were performed at ambient pressure and under pressure. The relaxation rate 1/T_1 for the overdoped samples (x = 0.14) shows T-linear behavior just above T_c, and pressure application enhances 1/T_1T similar to the behavior of T_c. This implies that 1/T_1T = constant originates from the Korringa relation, and an increase in the density of states at the Fermi energy D(E_F) leads to the enhancement of T_c. In the underdoped samples (x = 0.08), 1/T_1T measured at ambient pressure also shows T-independent behavior in a wide temperature range above T_c. However, it shows Curie-Weiss-like T dependence at 3.0 GPa accompanied by a small increase in T_c, suggesting that predominant antiferromagnetic fluctuation suppresses development of superconductivity or remarkable enhancement of T_c. The qualitatively different features between underdoped and overdoped samples are systematically explained by a band calculation with hole and electron pockets

Seiberg-Witten prepotential for E-string theory and random partitions

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.Comment: 14 page

Proximity fingerprint of s+- superconductivity

We suggest a straightforward and unambiguous test to identify possible opposite signs of superconducting order parameter in different bands proposed for iron-based superconductors (s+- state). We consider proximity effect in a weakly coupled sandwich composed of a s+- superconductor and thin layer of s-wave superconductor. In such system the s-wave order parameter is coupled differently with different s+- gaps and it typically aligns with one of these gaps. This forces the other s+- gap to be anti-aligned with the s-wave gap. In such situation the aligned band induces a peak in the s-wave density of states (DoS), while the anti-aligned band induces a dip. Observation of such contact-induced negative feature in the s-wave DoS would provide a definite proof for s+- superconductivity.Comment: 4 pages, one figur

Angle-resolved photoemission spectroscopy of Co-based boride superconductor LaCo1.73Fe0.27B2

We have performed angle-resolved photoemission spectroscopy of Co-based boride superconductor LaCo1.73Fe0.27B2 (Tc = 4.1 K), which is isostructural to the 122-type Fe-pnictide superconductor with the pnictogen atom being replaced with boron. We found that the Fermi level is located at a dip in the density of states (DOS) in contrast to Co-pnictide ferromagnets. This reduction in DOS together with the strong Co 3d-B 2p covalent bonding removes the ferromagnetic order and may cause the superconductivity. The energy bands near the Fermi level show higher three dimensionality and a weaker electron-correlation effect than those of Fe pnictides. The Fermi surface topology is considerably different from that of Fe pnictides, suggesting the difference in the superconducting mechanism between boride and pnictide superconductors.Comment: 5 pages, 4 figure