Lifshitz phase transitions in a one-dimensional Gamma model.

In this paper, we study quantum phase transitions and magnetic properties of a one-dimensional spin-1/2 Gamma model, which describes the off-diagonal exchange interactions between edge-shared octahedra with strong spin-orbit couplings along the sawtooth chain. The competing exchange interactions between the nearest neighbors and the second neighbors stabilize the semimetallic ground state in terms of spinless fermions, and give rise to a rich phase diagram, which consists of three gapless phases. We find distinct phases are characterized by the number of Weyl nodes in the momentum space, and such changes in the topology of the Fermi surface without symmetry breaking produce a variety of Lifshitz transitions, in which the Weyl nodes situating at k=π change from type I to type II. A coexistence of type-I and type-II Weyl nodes is found in phase II. The information measures including concurrence, entanglement entropy, and relative entropy can effectively signal the second-order transitions. The results indicate that the Gamma model can act as an exactly solvable model to describe Lifshitz phase transitions in correlated electron systems.

A three-dimensional ZnII coordination network based on 5,5'-methylenebis(2,4,6-trimethylisophthalic acid) and 2,7-bis(1H-imidazol-1-yl)fluorene: synthesis, structure and luminescence properties.

In recent years, coordination polymers constructed from multidentate carboxylate ligands and N-containing ligands have attracted much attention since these ligands can adopt a rich variety of coordination modes which can lead to crystalline products with intriguing structures and interesting properties. A new coordination polymer, namely poly[[diaqua[µ-2,7-bis(1H-imidazol-1-yl)fluorene-κ2N3:N3'][µ-5,5'-methylenebis(3-carboxy-2,4,6-trimethylbenzoato)-κ2O1:O1']zinc(II)] hemihydrate], {[Zn(C23H22O8)(C19H14N4)(H2O)2]·0.5H2O}n, 1, was prepared by the self-assembly of Zn(NO3)2·6H2O with 5,5'-methylenebis(2,4,6-trimethylisophthalic acid) (H4BTMIPA) and 2,7-bis(1H-imidazol-1-yl)fluorene (BIF) under solvothermal conditions. The structure of 1 was determined by elemental analysis, single-crystal X-ray crystallography, powder X-ray diffraction, IR spectroscopy and thermogravimetric analysis. Each ZnII ion is six-coordinated by two O atoms from two H2BTMIPA2- ligands, by two N atoms from two BIF ligands and by two water molecules, forming a distorted octahedral ZnN2O4 coordination geometry. Adjacent ZnII ions are linked by H2BTMIPA2- ligands and BIF ligands, leading to the formation of a two-dimensional (2D) (4,4)-sql network, and intermolecular hydrogen-bonding interactions connect the 2D layer structure into the three-dimensional (3D) supramolecular structure. Each 2D layer contains two kinds of helices with the same direction, which are opposite in adjacent layers. The luminescence properties of complex 1 in the solid state have also been investigated.