Топологические моды в неэрмитовых фононных кристаллах, индуцированных оптически в массиве квантовых ям

We study theoretically propagation of acoustic waves in an array of quantum wells, where a spatially modulated amplification and attenuation of sound is realized by optical excitation with a frequency close to the exciton resonance. The dispersion of sound waves near Bragg resonances corresponding to the modulation wave vector is calculated. The appearance of "imaginary" stop bands, where the imaginary parts of the Bloch mode frequencies are split, is described. The emergence of acoustic topological modes at the edge of the structure is demonstrated.

The Modulated Structure of SrAuSn2

The ternary stannide SrAuSn2 was synthesized by induction melting of the elements under an argon atmosphere in a sealed niobium ampoule in a water-cooled sample chamber of a high-frequency furnace. The structure of SrAuSn2 was investigated by X-ray powder and single crystal diffraction. It was found to be favourable to describe as a commensurately modulated structure. The 3+1 dimensional superspace group symmetry P : Cmcm(α, 0, 0) : 0s0 with the unit cell dimensions a = 460.20(14), b = 2038.8(8), c = 460.34(19) pm and the modulation wave vector q =¼ [100]*. The Sn1 atoms were those with the strongest modulation while the rest of the atoms showed rather small deviations from the average structure. The SrAuSn2 structure is closely related to the CeNiSi2 type. Geometrically these structures are built up from distorted ThCr2Si2 and AlB2 slabs. The gold atoms are located in the ThCr2Si2 slab. They have a distorted square pyramidal tin coordination at Au-Sn distances ranging from 266 to 294 pm. These pyramids are condensed via common edges forming two-dimensional layers. The latter are condensed via the Sn1 atoms within the AlB2 slabs that form one-dimensional zigzag chains with Sn1-Sn1 distances ranging from 282 to 288 pm. These chains show the strong modulations. Together, the gold and tin atoms build up a three-dimensional [AuSn2] network, in which the strontium atoms fill distorted hexagonal channels.

The incommensurate modulation of the structure of Sr2Nb2O7

The incommensurately modulated structure of Sr_{2}Nb_{2}O_{7} at room temperature is reported, as determined by single-crystal X-ray diffraction. The crystal structure of Sr_{2}Nb_{2}O_{7} comprises slabs with a perovskite-type structure that are separated by planes of additional O atoms. The driving force for the modulation is shown to be internal strain around the Sr atoms that lie at the interface between the slabs. At room temperature, Sr_{2}Nb_{2}O_{7} crystallizes in the superspace group Cmc2_{1}(\alpha00)0s0, with lattice parameters a = 3.9544\,(7), b = 26.767\,(6) and c = 5.6961\,(8) Å. The modulation wave vector is determined as {\bf q} = 0.488\,(3)\,{\bf a}^{*}. X-ray diffraction data were collected at a synchrotron using a CCD area detector. A total of 3626 unique main reflections and 1262 unique first-order satellites with I \,\gt \,3 \sigma (I\,) were obtained. Refinements using a single harmonic modulation wave converged at R = 0.057 (R = 0.051 for the main reflections and R = 0.121 for the satellite reflections). The modulated structure is interpreted in terms of rotations of NbO_{6} octahedra and displacements of the Sr atoms.

Effect of oxygen deficiency on Charge Ordering in La0.5Ca0.5MnO3-δ

Elastically-filtered transmission electron diffraction patterns of La0.5Ca0.5MnO3-δ have been obtained between 105K to 288K using the Leo 912 Omega. On heating La0.5Ca0.5MnO3 undergoes a transition from antiferromagnetic insulator to ferromagnetic metal (TN ∼ 150K) and then to paramagnetic insulator (Tc ∼ 230K) . The q modulation wave vector along the b-axis direction arises from charge ordering of Mn3+ and Mn4+, and orbital ordering of dz22 orbitals associated with Jahn-Teller distortions in the Mn3+O6 octahedra at low temperature. Both the intensity and the position of superlattice peaks change as a function of temperature during heating. The large incommensurability we see between 105K to 260K differs from that seen previously and proposed model. Figure 1 a) shows the lattice constants a, b, c related to the simple perovskite lattice parameters ap (ap ∼ 3.9Å) by a≈b≈ap and c≈2ap, and indicates the octahedral coordination.