An analogue of Dubrovin's conjecture

We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call "mutation systems". Given such a Fano manifold $X$, one of the structures is given by the Stokes structure of the quantum connection of $X$, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on $X$. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.Comment: 42 pages. To appear at Annales de l'Institut Fourie

Local Lattice Distortion Caused by Short Range Charge Ordering in LiMn2_2O4_4

We have performed powder neutron diffraction on $^7$Li-enriched sample of LiMn$_2$O$_4$ at 300 K. The crystal structure determined by Rietveld analysis is a cubic spinel with space group of $Fd\bar{3}m$ in which all Mn atoms are crystallograghically equivalent, consistent with many preceding studies. However, the atomic pair distrubution function (PDF) of this compound can not be fitted by the cubic structure with space group of $Fd\bar{3}m$ satisfactorily, and it can be reproduced by the orthorhombic structure with $Fddd$. It corresponds with the structure of charge ordered phase below about 260 K, indicating a short range charge ordering. In the local structure determined by PDF analysis, two types of MnO$_6$ octahedra with long and short atomic distances between Mn and O atoms exist and their Mn-O distances are almost consistent with the distances in the charge ordered phase. From these results, valence electrons are localized at Mn sites like a glass even in the cubic phase, resulting in the non-metallic electrical conductivity.Comment: 6 pages, 4 figure

Inelastic neutron scattering study on the resonance mode in an optimally doped superconductor LaFeAsO0.92_{0.92}F0.08_{0.08}

An optimally doped iron-based superconductor LaFeAsO$_{0.92}$F$_{0.08}$ with $T_c = 29$ K has been studied by inelastic powder neutron scattering. The magnetic excitation at $Q=1.15$ \AA$^{-1}$ is enhanced below $T_c$, leading to a peak at $E_{res}\sim13$ meV as the resonance mode, in addition to the formation of a gap at low energy below the crossover energy $\Delta_{c}\sim10 meV$. The peak energy at $Q=1.15$ \AA$^{-1}$ corresponds to $5.2 k_B T_c$ in good agreement with the other values of resonance mode observed in the various iron-based superconductors, even in the high-$T_c$ cuprates. Although the phonon density of states has a peak at the same energy as the resonance mode in the present superconductor, the $Q$-dependence is consistent with the resonance being of predominately magnetic origin.Comment: 4 pages, 5 Postscript figure

Dynamical Screening and Superconducting State in Intercalated Layered Metallochloronitrides

An essential property of layered systems is the dynamical nature of the screened Coulomb interaction. Low energy collective modes appear as a consequence of the layering and provide for a superconducting-pairing channel in addition to the electron-phonon induced attractive interaction. We show that taking into account this feature allows to explain the high critical temperatures (Tc~26K) observed in recently discovered intercalated metallochloronitrides. The exchange of acoustic plasmons between carriers leads to a significant enhancement of the superconducting critical temperature that is in agreement with the experimental observations

Microwave Penetration Depth and Quasiparticle Conductivity in PrFeAsO_1-y Single Crystals : Evidence for a Full-Gap Superconductor

In-plane microwave penetration depth $\lambda_{ab}$ and quaiparticle conductivity at 28 GHz are measured in underdoped single crystals of the Fe-based superconductor PrFeAsO$_{1-y}$ ($T_c\approx 35$ K) by using a sensitive superconducting cavity resonator. $\lambda_{ab}(T)$ shows flat dependence at low temperatures, which is incompatible with the presence of nodes in the superconducting gap $\Delta({\bf k})$. The temperature dependence of the superfluid density demonstrates that the gap is non-zero ($\Delta/k_BT_c\gtrsim 1.6$) all over the Fermi surface. The microwave conductivity below $T_c$ exhibits an enhancement larger than the coherence peak, reminiscent of high-$T_c$ cuprate superconductors.Comment: 4 pages, 3 figures. Version accepted for publication in Phys. Rev. Lett. For related results of hole-doped 122 system, see arXiv:0810.350