Superconductivity and Abelian Chiral Anomalies

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the $x,y$ and $z$-directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called $q$-helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.Comment: An example with a figure and discussions are supplemente

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Singular Density of States of Disordered Dirac Fermions in the Chiral Models

The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random chiral models. Two distinct structures of density of states (DoS) around zero energy, one is a power-law dependence on energy in the intermediate energy range and the other is a diverging one at zero energy, are revealed by an extensive numerical study for large systems up to $250\times 250$. For the random hopping model, our finding of the diverging DoS within very narrow energy range reconciles previous inconsistencies between the lattice and the continuum models.Comment: 4 pages, 4 figure

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.Comment: Completely rewritten. Discussions on coexistence of is- or id_{xy}-wave order parameter near edges in d_{x^{2}-y^{2}}-wave superconductors are added; 4 pages, 3 figure

Local structural disorder and superconductivity in KxFe2-ySe2

We report significantly enhanced magnetic moment in K0.69(2)Fe1.45(1)Se2.00(1) single crystals with sharp Tc and bulk superconductivity obtained by postannealing and quenching process. There are two Fe sites in the K0.69(2)Fe1.45(1)Se2.00(1) unit cell: Fe1, which has higher symmetry with longer average Fe-Se bond length, and Fe2, which has lower symmetry with shorter average Fe-Se bond length. Temperature-dependent x-ray absorption fine-structure (XAFS) analysis results on quenched and as-grown K0.69(2)Fe1.45(1)Se2.00(1) crystals show that quenched K0.69(2)Fe1.45(1)Se2.00(1) have increased average Fe-Se bond length and decreased static disorder. Our results indicate that nonzero population of Fe1 sites is the key structural parameter that governs the bulk superconductivity. We also show clear evidence that Fe1 sites carry higher magnetic moment than Fe2 sites.Comment: 3 figures, 4 page

Entanglement Entropy of One-dimensional Gapped Spin Chains

We investigate the entanglement entropy (EE) of gapped S=1 and $S=1/2$ spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to the EE. For the $S=1/2$ dimerized Heisenberg chain, the EE of the sufficiently long chain is essentially explained by the localized $S=1/2$ effective spins on the boundaries. As for S=1, the effective spins are also $S=1/2$ causing a Kennedy triplet that yields a lower bound for the EE. In this case, the residual entanglement reduces substantially by a continuous deformation of the Heisenberg model to that of the AKLT Hamiltonian.Comment: 5 pages, 6 figure

The K2-ESPRINT Project VI: K2-105 b, a Hot-Neptune around a Metal-rich G-dwarf

We report on the confirmation that the candidate transits observed for the star EPIC 211525389 are due to a short-period Neptune-sized planet. The host star, located in K2 campaign field 5, is a metal-rich ([Fe/H] = 0.26$\pm$0.05) G-dwarf (T_eff = 5430$\pm$70 K and log g = 4.48$\pm$0.09), based on observations with the High Dispersion Spectrograph (HDS) on the Subaru 8.2m telescope. High-spatial resolution AO imaging with HiCIAO on the Subaru telescope excludes faint companions near the host star, and the false positive probability of this target is found to be <$10^{-6}$ using the open source vespa code. A joint analysis of transit light curves from K2 and additional ground-based multi-color transit photometry with MuSCAT on the Okayama 1.88m telescope gives the orbital period of P = 8.266902$\pm$0.000070 days and consistent transit depths of $R_p/R_\star \sim 0.035$ or $(R_p/R_\star)^2 \sim 0.0012$. The transit depth corresponds to a planetary radius of $R_p = 3.59_{-0.39}^{+0.44} R_{\oplus}$, indicating that EPIC 211525389 b is a short-period Neptune-sized planet. Radial velocities of the host star, obtained with the Subaru HDS, lead to a 3\sigma\ upper limit of 90 $M_{\oplus} (0.00027 M_{\odot})$ on the mass of EPIC 211525389 b, confirming its planetary nature. We expect this planet, newly named K2-105 b, to be the subject of future studies to characterize its mass, atmosphere, spin-orbit (mis)alignment, as well as investigate the possibility of additional planets in the system.Comment: 11 pages, 9 figures, 4 tables, PASJ accepte

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature added in response to referee's reques

Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry

For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient features of the behavior of the transmission phase in an interferometer with a QD. The theory of this effect will be reviewed with special emphasis on the role of the interactions. New results on the dot-charging measurements and the fine structure of occupation switchings will be presented, accompanied by the unified description of the whole series of CB peaks caused by a single broad level. We then discuss the case where the system approaches the Kondo regime.Comment: 30 pages in IOP format, 11 figure