Group Theory Arguments Research Articles

Structural origin of spin-splitting anisotropy in janus dichalcogenides monolayers under pressure

Abstract Janus transition-metal dichalcogenides (TMDs) have drawn a great deal of attention because of their mirror plane symmetry breaking that allows the emergence of a built-in out-of-plane dipole which determine superior piezoelectric and spin-related properties. Furthermore, it has been shown in the recent literature that pressure application is capable of modulating spin-related phenomena in this class of materials. Generally, the spin-splitting presence in real systems is explored in terms of point group symmetry reduction using solely group theory arguments. However, we seek to associate the enhancement of spin-splitting in Janus TMDs monolayers by searching the most important local asymmetries responsible for the symmetry lowering that leads the monolayer larger spin-splitting energies. In this sense, we seek to unveil a possible structural descriptor that correlates with subbands splitting magnitude in Janus TMDs. To accomplish this, we performed a detailed first-principles investigation into WSSe Janus monolayers under biaxial in-plane strain to find that pressure induces a symmetry lowering from the C 3v to the C s point group. From these observations, we found that in-plane angle asymmetries between the chalcogens yield a distortion metric that can serve as a descriptor for enhanced spin-splitting in Janus WSSe since it strongly correlates with spin-splitting energies. Hence, our work establishes that, rather than solely global symmetry analysis, specific local distortions provide a key design principle to achieve strong spin-splitting in 2D Janus TMDs.

Unification of gauge and Yukawa couplings

In this talk we describe how unification of gauge and Yukawa couplings can be obtained in gauge-Higgs unification models in extra-dimensions using a toy model. It is usually considered that such unification is difficult to obtain using simple group theory arguments. We consider a toy model based on the SU(3) symmetry and show that including the renormalisation group running at one loop for the couplings improve the result. The gauge couplings unify asymptotically at high energies, and this may result from the presence of an UV fixed point. The Yukawa coupling is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved. Some other arguments and directions of study are also mentioned to tackle the problem of producing a scalar potential allowing to accommodate the measured Higgs mass at 125 GeV.

On hidden sums compatible with a given block cipher diffusion layer

Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some regular subgroups of the affine group. Mixing group theory arguments and cryptographic tools, we pass from characterizing our hidden sums to designing an efficient algorithm to perform the necessary preprocessing for the exploitation of the trapdoor.

Topologically stable gapless phases in nonsymmorphic superconductors

We study topological stability of nodes in nonsymmorphic superconductors (SCs). In particular, we demonstrate that line nodes in nonsymmirphic odd-parity SCs are protected by the interplay between topology and nonsymmorphic symmetry. As an example, it is shown that the $E_{2u}$-superconducting state of UPt$_3$ hosts the topologically stable line node at the Brillouin zone face. Our theory indicates that the existence of spin-orbit coupling is essential for protecting such a line node, complementing the Norman's group theory argument. Developing the topological arguments, we also argue generalization to point nodes and to other symmetry cases beyond the group theory arguments.

Vibrational modes of chalcopyrite CdGeAs2 crystal

The optical-phonon spectra of CdGeAs2 were investigated by low temperature polarized Raman scattering. According to vibrational modes of ZnS-type materials and selection rules of Raman scattering, all Raman active vibrational modes in the Brillouin-zone (BZ) center of CdGeAs2 predicted from group-theory arguments were identified and artificially grouped in three energy bands, including 45–94, 158–215 and around 260cm−1. Based on the Lyddane-Sachs-Teller (LST) relation and measured refractive indices, the low-frequency dielectric constant ε(0) is estimated to be 15.04 and shows good agreement with the previous tests and predictions.

Cusped Wilson lines in symmetric representations

We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\cal N} = 4$ super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\sqrt{\lambda}\gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $k\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.

Origin of Transitions between Metallic and Insulating States in Simple Metals.

Unifying principles that underlie recently discovered transitions between metallic and insulating states in elemental solids under pressure are developed. Using group theory arguments and first-principles calculations, we show that the electronic properties of the phases involved in these transitions are controlled by symmetry principles. The valence bands in these systems are described by simple and composite band representations constructed from localized Wannier functions centered on points unoccupied by atoms, and which are not necessarily all symmetrical. The character of the Wannier functions is closely related to the degree of s-p(-d) hybridization and reflects multicenter chemical bonding in these insulating states. The conditions under which an insulating state is allowed for structures having an integer number of atoms per primitive unit cell as well as reentrant (i.e., metal-insulator-metal) transition sequences are detailed, resulting in predictions of behavior such as phases having band-contact lines. The general principles developed are tested and applied to the alkali and alkaline earth metals, including elements where high-pressure insulating phases have been reported (e.g., Li, Na, and Ca).

Raman-Active Modes of Even-Numbered Cycloparaphenylenes: Comparisons between Experiments and Density Functional Theory (DFT) Calculations with Group Theory Arguments

[6]-, [8]-, [10]-, and [12]cycloparaphenylenes (CPPs), the smallest even-numbered carbon nanohoops synthesized to date, are probed by Raman spectroscopy. For the highly symmetric even [n]CPPs, group theory predicts that there are 133 Raman-active modes in total for n ≥ 8, 73 for [6]CPP, and 100 for [4]CPP. The Raman-active modes of these even-numbered CPPs are identified by comparing experimental results with theoretical Raman spectra calculated using density functional theory (DFT). Taking advantage of the symmetry arguments in these symmetric molecules allows the assignment of the observed Raman peaks, as well as the identification of their dependence on the sizes of the CPPs.

Global supersymmetry on curved spaces in various dimensions

We propose methods towards a systematic determination of d-dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hn+1 and compact spheres Sn or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S1×Sn, with n<6. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres Sd if d>5 (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.

Designing a Deep-Ultraviolet Nonlinear Optical Material with a Large Second Harmonic Generation Response

The generation of intense coherent deep-UV light from nonlinear optical materials is crucial to applications ranging from semiconductor photolithography and laser micromachining to photochemical synthesis. However, few materials with large second harmonic generation (SHG) and a short UV-cutoff edge are effective down to 200 nm. A notable exception is KBe2BO3F2, which is obtained from a solid-state reaction of highly toxic beryllium oxide powders. We designed and synthesized a benign polar material, Ba4B11O20F, that satisfies these requirements and exhibits the largest SHG response in known borates containing neither lone-pair-active anions nor second-order Jahn-Teller-active transition metals. We developed a microscopic model to explain the enhancement, which is unexpected on the basis of conventional anionic group theory arguments. Crystal engineering of atomic displacements along the polar axis, which are difficult to attribute to or identify within unique anionic moieties, and greater cation polarizabilities are critical to the design of next-generation SHG materials.

Spontaneous symmetry breaking in a non-rigid molecule approach to intrinsically disordered proteins

An analog to Longuet-Higgins' non-rigid molecular group theory arguments can be applied to the structure and reaction dynamics of intrinsically disordered proteins via a somewhat counterintuitive Morse Function treatment inspired by statistical mechanics, providing possible symmetry classifications of the molecular 'fuzzy lock-and-key'.

Tangent unit-vector fields: Nonabelian homotopy invariants and the dirichlet energy

Let O be a closed geodesic polygon in S 2. Maps from O into S 2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S 2, we compute the infimum Dirichlet energy ɛ(H) for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for ɛ(H) involves a topological invariant – the spelling length – associated with the (non-abelian) fundamental group of the n-times punctured two-sphere, π 1( S 2 − { s 1,…, s n }, *). The lower bound for ɛ(H) is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes (classes containing wholly conformal and anticonformal representatives respectively), the expression for ɛ(H) reduces to a previous result involving the degrees of a set of regular values s 1, …, s n in the target S 2 space. These degrees may be viewed as invariants associated with the abelianization of π 1( S 2 - { s 1,…, s n }, *). For nonconformal classes, however, ɛ(H) may be strictly greater than the abelian bound. This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy (one-constant Oseen-Frank energy) of reflection-symmetric tangent unit-vector fields in a rectangular prism.

Symmetry, Symmetry Breaking and Topology

The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.

Group theoretical study of nonstrange and strange mixed symmetric baryon states[Nc−1,1]in the1/Ncexpansion

Using group theory arguments we extend and complete our previous work by deriving all SU(6) exact wave functions associated with the spectrum of mixed symmetric baryon states $[{N}_{c}\ensuremath{-}1,1]$ in the $1/{N}_{c}$ expansion. The extension to SU(6) enables us to study the mass spectra of both strange and nonstrange baryons, while previous work was restricted to nonstrange baryons described by SU(4). The wave functions are specially written in a form to allow a comparison with the approximate, customarily used wave functions, where the system is separated into a ground state core and an excited quark. We show that the matrix elements of the flavor operator calculated with the exact wave functions acquire the same asymptotic form at large ${N}_{c}$, irrespective of the spin-flavor multiplet contained in $[{N}_{c}\ensuremath{-}1,1]$, while with the approximate wave function one cannot obtain a similar behavior. The isoscalar factors of the permutation group of ${N}_{c}$ particles derived here can be used in any problem where a given fermion system is described by the partition $[{N}_{c}\ensuremath{-}1,1]$, and one fermion has to be separated from the rest.

Neutron diffraction andS119nMössbauer spectroscopy study ofMn3Sn2

The temperature dependence of the magnetic structure of ${\text{Mn}}_{3}{\text{Sn}}_{2}$ has been determined down to 2 K from powder neutron diffraction and $^{119}\text{S}\text{n}$ M\"ossbauer spectroscopy experiments. The ${\text{Mn}}_{3}{\text{Sn}}_{2}$ compound crystallizes with the ${\text{Ni}}_{3}{\text{Sn}}_{2}$ type of structure $(Pnma)$ which comprises two crystallographic inequivalent positions for both the Mn atoms ($4c$ and $8d$) and the Sn atoms (Sn1 and Sn2 in $4c$ positions). Below ${T}_{\text{C}1}\ensuremath{\sim}262\text{ }\text{K}$, the $\text{Mn}\text{ }4c$ sublattice orders ferromagnetically with magnetic moments along the $b$ axis and polarizes the $\text{Mn}\text{ }8d$ atoms. The $\text{Mn}\text{ }8d$ sublattice cooperatively orders at ${T}_{\text{C}2}\ensuremath{\sim}227\text{ }\text{K}$ in a canted ferromagnetic arrangement, with the ferromagnetic component along the $b$ axis and the antiferromagnetic one along the $a$ axis, while the ferromagnetic order of the $\text{Mn}\text{ }4c$ magnetic moments along the $b$ axis is preserved. The ferromagnetic component of both $\text{Mn}\text{ }4c$ and $\text{Mn}\text{ }8d$ reorients toward the $c$ axis below ${T}_{t}\ensuremath{\sim}197\text{ }\text{K}$. The results are discussed in connection with previous magnetic, magnetocaloric, and specific-heat measurements. Group theory arguments indicate that the magnetic state realized below ${T}_{t}$ should be described by a spin Hamiltonian incorporating fourth or higher-order terms in the spins or that a very small (undetected) monoclinic distortion takes place. The spin reorientation at ${T}_{t}$ yields strong variation in the apparent quadrupolar splittings $(2\ensuremath{\epsilon})$ of the two $^{119}\text{S}\text{n}$ M\"ossbauer subspectra and allows observing anisotropic contributions to the hyperfine field. The ${V}_{ZZ}$ components of the electric field gradient tensor at the Sn1 and Sn2 nuclei are found to lie in the $ac$ plane and to be of opposite sign. The $5p$ charge and spin densities are both deduced to be more anisotropic on Sn2 atoms than on Sn1 atoms.

Odd parity and line nodes in nonsymmorphic superconductors

Group theory arguments have been invoked to argue that odd parity order parameters cannot have line nodes in the presence of spin-orbit coupling. In this paper we show that these arguments do not hold for certain non-symmorphic superconductors. Specifically, we demonstrate that when the underlying crystal has a twofold screw axis, half of the odd parity representations vanish on the Brillouin zone face perpendicular to this axis. Many unconventional superconductors have non-symmorphic space groups, and we discuss implications for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.

A group-theory method to find stationary states in nonlinear discrete symmetry systems

In the field of nonlinear optics, the self-consistency method has been applied to searching optical solitons in different media. In this paper, we generalize this method to other systems, adapting it to discrete symmetry systems by using group theory arguments. The result is a new technique that incorporates symmetry concepts into the iterative procedure of the self-consistency method, that helps the search of symmetric stationary solutions. An efficient implementation of this technique is also presented, which restricts the computational work to a reduced section of the entire domain and is able to find different types of solutions by specifying their symmetry properties. As a practical application, we develop an efficient algorithm for solving the nonlinear Schrödinger equation with a discrete symmetry potential.

Vortex Transmutation

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a "transmutation pass" determining the conditions for this phenomenon to occur and numerically analyze it in the context of two-dimensional optical lattices. An analogous approach is applicable to the problems of Bose-Einstein condensates in periodic potentials.

Vorticity Cutoff in Nonlinear Photonic Crystals

Using group-theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the nonlinearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.

Linear Carbon Dioxide in the High-Pressure High-Temperature Crystalline Phase IV

High-temperature IR absorption spectra of solid CO2 in phases II and IV were measured in a resistive heated diamond anvil cell up to 30 GPa. The spectral structures of the bending mode, observed in high quality thin crystalline samples, and of the IR lattice phonons, measured for the first time between 80 and 640 K, are discussed using group theory arguments. According to this analysis the claimed bent molecular geometry of CO2 in phase IV can be unambiguously ruled out. Furthermore, the structures of both phases II and IV have been identified, among those so far proposed, as orthorhombic.