相关论文: Rigid unit modes in tetrahedral crystals

Using Density Functional Theory we theoretically study the orientational properties of uniform phases of hard kites -- two isosceles triangles joined by their common base. Two approximations are used: Scaled Particle Theory, and a new…

In this work we study the crystal symmetry fractionalization in chiral spin liquids with the chiral-semion topological order. We show that if such a chiral spin liquid is realized in a two-dimensional lattice model with odd number of…

We model short-period superlattices of WO$_3$ and ReO$_3$ with first-principles calculations. In fully-relaxed superlattices, we observe that octahedral tilts about an axis in the planes of the superlattices do not propagate from one…

The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…

Four sets of necessary and sufficient conditions are obtained for the first-order rigidity of a periodic bond-node framework \C in R^d which is of crystallographic type. In particular, an extremal rank characterisation is obtained which…

A theory of free spanning sets, free bases and their space group symmetric variants is developed for the first order flex spaces of infinite bar-joint frameworks. Such spanning sets and bases are computed for a range of fundamental…

Trigonal tellurium (Te) has attracted researchers' attention due to its transport and optical properties, which include electrical magneto-chiral anisotropy, spin polarization and bulk photovoltaic effect. It is the anisotropic and chiral…

Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…

This paper provides a combinatorial characterisation for generic forced symmetric rigidity of bar-joint frameworks in the Euclidean plane that are symmetric with respect to the orientation-reversing wallpaper group…

Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a Rare Earth nucleus 152Sm. We use realistic nuclear mean-field theory…

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…

Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the coordinate singularities associated with local coordinate…

At room temperature, the normal oxide spinels NiCr_2O_4 and CuCr_2O_4 are tetragonally distorted and crystallize in the I4_1/amd space group due to cooperative Jahn-Teller ordering driven by the orbital degeneracy of tetrahedral Ni$^{2+}$…

Two new transition-metal tellurium oxy-chlorides of the general formula Ni_5(TeO_3)_4X_2 (X=Cl, Br) have been isolated during the investigation of the ternary phase diagram NiO-NiCl2-TeO2. They crystallize in the monoclinic system, space…

Despite more than a quarter century of research, the nature of the second-order phase transition in the heavy-fermion metal URu$_2$Si$_2$ remains enigmatic. The key question is which symmetry is being broken below this "hidden order"…

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_1$-functor without using the corresponding result from linear $K$-theory under the…

Raman spectroscopy is employed to probe directly the soft rotation and tilting modes, which are two primary order parameters predicted in the hybrid improper ferroelectric material Ca$_3$Mn$_2$O$_7$. We observe a giant softening of the…

We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.

We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…