Stable bundles as Frobenius morphism direct image

Let X be a smooth projective curve of genus $g\geq 2$ defined over an algebraically closed field k of characteristic $p>0$ and let $F:X\rightarrow X_{1}$ be the relative k-linear Frobenius map. We prove (Theorem 1.1) E is a stable bundle on $X_{1}$ with $I(E)= (p-1)(2g-2)$ if and only if E is the direct image of some stable bundle W on $X$.Comment: 4 page

Quantum Anomalous Hall Effect with Cold Atoms Trapped in a Square Lattice

We propose an experimental scheme to realize and detect the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental set-ups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.Comment: 5 pages, 3 figures, to appear in Phys. Rev.

Prediction of quantum stripe ordering in optical lattices

We predict the robust existence of a novel quantum orbital stripe order in the $p$-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.Comment: 4 pages, three figures, accepted by Phys. Rev. Let

Incommensurate superfluidity of bosons in a double-well optical lattice

We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunnelling timescales, in contrast to that of a simple single-well lattice. In addition, for sufficiently small lattice depths the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.Comment: 4 pages, 5 figures

Charge 4e superconductivity and chiral metal in the 45∘45^\circ-twisted bilayer cuprates and similar materials

The vestigial phase above the $T_c$ of a multi-component pairing state is a hot topic recently. Here we study the vestigial phases of a class of materials made through stacking a homo-bilayer with the largest twist angle, dubbed as the twist-bilayer quasi-crystal (TB-QC), exampled by the 45$^\circ$-twisted bilayer cuprates and 30$^\circ$-twisted bilayer graphene. When each mononlayer hosts a pairing state with the largest pairing angular momentum, e.g. $d$-wave for the cuprates or $f$-wave for some members in the graphene family, previous studies yield that the second-order interlayer Josephson coupling would drive chiral $d+id$ or $f+if$ topological superconductivity (TSC) in the TB-QC. Here we propose that, above the $T_c$ of the chiral TSC phase, either the total- or relative- pairing phase of the two layers can be unilateral quasi-ordered or ordered. In the form case, a Cooper pair from the top layer pairs with a Cooper pair from the bottom layer to form the charge-4e SC; in the latter case, a time-reversal symmetry breaking chiral metal phase is formed. Based on a thorough symmetry analysis, we arrive at the low-energy effective Hamiltonian describing the pairing-phase fluctuations. Our combined renormalization group and Monte-Carlo studies reveal the presence of the charge-4e SC and chiral metal phases in certain regimes in the phase diagram. These vestigial phases are characterized by various temperature-dependent quantities and spatial-dependent correlations.Comment: 4.2 pages plus Appendi

Bis[(2-pyrid­yl)(2-pyridyl­amino)­methano­lato]manganese(III) nitrate

The MnIII atom in the title complex, [Mn(C11H10N3O)2]NO3, is coordinated by the two tridentate (2-pyrid­yl)(2-pyridyl­amino)­methano­late ligands, forming a six-coordinate environment. The four pyridyl N atoms constitute the equatorial plane on which the manganese(III) ion lies; the coordination plane suffers a slight distortion as indicated by the average plane deviation of 0.058 Å. The methano­late O atoms occupy the axial positions. The coordination geometry is thus octa­hedral. In the title compound, the cations are linked by nitrate anions via N—H⋯O hydrogen bonds to form one-dimensional chains. Moreover, the one-dimensional structure is stabilized by inter­molecular edge-to-face aromatic π–π inter­actions with a center-of-inversion at a distance of ca 4.634 Å

Kondo effect in the helical edge liquid of the quantum spin Hall state

Following the recent observation of the quantum spin Hall (QSH) effect in HgTe quantum wells, an important issue is to understand the effect of impurities on transport in the QSH regime. Using linear response and renormalization group methods, we calculate the edge conductance of a QSH insulator as a function of temperature in the presence of a magnetic impurity. At high temperatures, Kondo and/or two-particle scattering give rise to a logarithmic temperature dependence. At low temperatures, for weak Coulomb interactions in the edge liquid the conductance is restored to unitarity with unusual power-laws characteristic of a `local helical liquid', while for strong interactions transport proceeds by weak tunneling through the impurity where only half an electron charge is transferred in each tunneling event.Comment: 5 pages, 2 figures; version accepted for publication in Phys. Rev. Let