Directions Of Symmetry Breaking Research Articles

Nano and micro-structural complexity of nematic liquid crystal configurations

Of our interest are frustration-driven pattern generating mechanisms in systems which in bulk equilibrium display spatially homogeneous long-range orientational order in absence of perturbations. As testbed material, we select thermotropic nematic liquid crystals. In bulk, they exhibit weakly discontinuous order–disorder phase transformation on varying temperature where the ordered nematic phase features spatially uniform axial order along an arbitrary symmetry breaking direction. However, due to continuous symmetry breaking (CSB) the established order is extremely susceptible to various perturbations which are in real systems in general always present. We theoretically illustrate how diverse complex patterns could be excited. Particularly intriguing configurations could appear if topological defects are present that could be generated via CSB. Our analysis is based on a relatively simple Lebwohl–Lasher-type model in which we could get analytical insight into phenomena of our interest. Using it we illustrate history dependent early stage isotropic-nematic phase evolution and final patterns in presence of “impurities” (e.g., nanoparticles). We show how characteristic effective interaction characteristics predict qualitatively different emerging patterns. Our analysis is based on CSB which is ubiquitous in nature. Consequently, demonstrated mechanisms are expected to manifest also in other condensed matter systems whose ordered phase is formed via CSB. We illustrate how kinetics and impurities could impact key structural properties of the systems of our interest.

Nanoscale decoupling of electronic nematicity and structural anisotropy in FeSe thin films

In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to spatially varying strain. We map local anisotropic strain by analyzing scanning tunneling microscopy topographs, and visualize electronic nematic domains from concomitant spectroscopic maps. While the domains form so that the energy of nemato-elastic coupling is minimized, we observe distinct regions where electronic nematic ordering fails to flip direction, even though the underlying structural anisotropy is locally reversed. The findings point towards a nanometer-scale stiffness of the nematic order parameter.

Circular photogalvanic spectroscopy of Rashba splitting in 2D hybrid organic\u2013inorganic perovskite multiple quantum wells

The two-dimensional (2D) Ruddlesden−Popper organic-inorganic halide perovskites such as (2D)-phenethylammonium lead iodide (2D-PEPI) have layered structure that resembles multiple quantum wells (MQW). The heavy atoms in 2D-PEPI contribute a large spin-orbit coupling that influences the electronic band structure. Upon breaking the inversion symmetry, a spin splitting (‘Rashba splitting’) occurs in the electronic bands. We have studied the spin splitting in 2D-PEPI single crystals using the circular photogalvanic effect (CPGE). We confirm the existence of Rashba splitting at the electronic band extrema of 35±10 meV, and identify the main inversion symmetry breaking direction perpendicular to the MQW planes. The CPGE action spectrum above the bandgap reveals spin-polarized photocurrent generated by ultrafast relaxation of excited photocarriers separated in momentum space. Whereas the helicity dependent photocurrent with below-gap excitation is due to spin-galvanic effect of the ionized spin-polarized excitons, where spin polarization occurs in the spin-split bands due to asymmetric spin-flip.

Spectral weight suppression and Fermi arc-like features with strong holographic lattices

We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. We solve the Dirac equation for a probe fermion in the associated background geometry. When the spatial modulation effect becomes sufficiently strong, we see a spectral weight suppression whenever the Fermi surface is larger than the first Brillouin zone. This leads to the gradual disappearance of the Fermi surface along the symmetry breaking direction, in all of the cases we have examined. This effect appears to be a generic consequence of strong inhomogeneities, independently of whether translational invariance is broken spontaneously or explicitly. The resulting Fermi surface is segmented and has features reminiscent of Fermi arcs.

Holographic fermions in striped phases

We examine the fermionic response in a holographic model of a low temperature striped phase, working for concreteness with the setup we studied in [1, 2], in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. We include an ionic lattice that breaks translational symmetry explicitly in the UV of the theory. Thus, this construction realizes spontaneous crystallization on top of a background lattice. We solve the Dirac equation for a probe fermion in the associated background geometry using numerical techniques, and explore the interplay between spontaneous and explicit breaking of translations. We note that in our model the breaking of the U(1) symmetry doesn’t play a role in the analysis of the fermionic spectral function. We investigate under which conditions a Fermi surface can form and focus in particular on how the ionic lattice affects its structure. When the ionic lattice becomes sufficiently strong the spectral weight peaks broaden, denoting a gradual disappearance of the Fermi surface along the symmetry breaking direction. This phenomenon occurs even in the absence of spontaneously generated stripes. The resulting Fermi surface appears to consist of detached segments reminiscent of Fermi arcs.

Direct construction of symmetry-breaking directions in bifurcation problems with spherical symmetry

We consider bifurcation problems in the presence of \begin{document}$ O(3) $\end{document} symmetry. Well known group-theoretic techniques enable the classification of all maximal isotropy subgroups of \begin{document}$ O(3) $\end{document} , with associated mode numbers \begin{document}$\ell∈\mathbb{N} $\end{document} , leading to 1-dimensional fixed-point subspaces of the \begin{document}$ (2\ell+1) $\end{document} -dimensional space of spherical harmonics. In each case the so-called equivariant branching lemma can then be used to establish the existence of a local branch of bifurcating solutions having the symmetry of the respective subgroup. To first-order, such a branch is a precise linear combination of the \begin{document}$ 2\ell+1 $\end{document} spherical harmonics, which we call the bifurcation direction. Our work here is focused on the direct construction of these bifurcation directions, complementing the above-mentioned classification. The approach is an application of a general method for constructing families of symmetric spherical harmonics, based on differentiating the fundamental solution of Laplace's equation in \begin{document}$ \mathbb{R}^3 $\end{document} .

Viscosity bound for anisotropic superfluids with dark matter sector

The shear viscosity to the entropy density ratio $\eta/s$ of the anisotropic superfluid has been calculated by means of the gauge/gravity duality in the presence of the {\it dark matter} sector. The {\it dark matter} has been described by the Yang-Mills field analogous to the one describing visible matter sector and it is assumed to interact with the visible field with coupling constant $\alpha$. Close to the superfluid transition temperature ($T_c$) the analytical solution has been given up to the leading order in a symmetry breaking parameter and the ratio of the gravitational constant and Yang-Mils coupling. The tensor element of ratio $\eta/s$ remains unaffected by the {\it dark matter} for the viscosity tensor in the plane perpendicular to the symmetry breaking direction (here $yz$). The temperature dependence and the linear correction in $(1-\alpha)$ in the plane containing this direction (here $xy$) was also revealed. The correction linearly vanishes for temperature tending to the critical one $T\rightarrow T_c$.

Numerical adiabatic potentials of orthorhombic Jahn-Teller effects retrieved from ultrasound attenuation experiments. Application to the SrF2:Cr crystal

A methodology is worked out to retrieve the numerical values of all the main parameters of the six-dimensional adiabatic potential energy surface (APES) of a polyatomic system with a quadratic T-term Jahn-Teller effect (JTE) from the ultrasound experiments. The method is based on a verified assumption that ultrasound attenuation and speed encounter anomalies when the direction of propagation and polarization of its wave of strain coincides with the characteristic directions of symmetry breaking in the JTE. For the SrF2:Cr crystal, employed as a basic example, we observed anomaly peaks in the temperature dependence of attenuation of ultrasound at frequencies of 50–160 MHz in the temperature interval of 40–60 K for the wave propagating along the [110] direction, for both the longitudinal and the shear modes, the latter with two polarizations along the [001] and [11¯0] axes, respectively. We show that these anomalies are due to the ultrasound relaxation by the system of non-interacting Cr2+ JT centers with orthorhombic local distortions. The interpretation of the experimental findings is based on the T2g⊗(eg+t2g) JTE problem including the linear and the quadratic terms of vibronic interactions in the Hamiltonian and the same-symmetry modes reduced to one interaction mode. Combining the experimental results with a theoretical analysis, we show that on the complicated six-dimensional APES of this system with three tetragonal, four trigonal, and six orthorhombic extrema points, the latter are global minima, while the former are saddle points, and we estimate numerically all the main parameters of this surface, including the linear and quadratic vibronic coupling constants, the primary force constants, the coordinates of all the extrema points and their energies, the energy barrier between the orthorhombic minima, and the tunneling splitting of the ground vibrational states. To our knowledge, such a based-on-experimental-data numerical reconstruction of the APES of a JTE problem in the five-dimensional space of all active tetragonal and trigonal displacements has not been reported before.

Signal detection in high dimension: The multispiked case

This paper applies Le Cam’s asymptotic theory of statistical experiments to the signal detection problem in high dimension. We consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the Gaussian asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. Those asymptotic powers remain valid for non-Gaussian data satisfying mild moment restrictions. They appear to lie very substantially below the Gaussian power envelope, at least for small values of the number of symmetry-breaking directions. In contrast, the asymptotic power of Gaussian likelihood ratio tests based on the eigenvalues of the sample covariance matrix are shown to be very close to the envelope. Although based on Gaussian likelihoods, those tests remain valid under non-Gaussian densities satisfying mild moment conditions. The results of this paper extend to the case of multispiked alternatives and possibly non-Gaussian densities, the findings of an earlier study [Ann. Statist. 41 (2013) 1204–1231] of the single-spiked case. The methods we are using here, however, are entirely new, as the Laplace approximation methods considered in the single-spiked context do not extend to the multispiked case.

ChemInform Abstract: The Ultrafast Pathway of Photon‐Induced Electrocyclic Ring‐Opening Reactions: the Case of 1,3‐Cyclohexadiene

AbstractReview: 74 refs.

The Ultrafast Pathway of Photon-Induced Electrocyclic Ring-Opening Reactions: The Case of 1,3-Cyclohexadiene

The photochemically induced electrocyclic ring-opening reaction of 1,3-cyclohexadiene to 1,3,5-hexatriene serves as a prototype for many important reactions in chemistry and in biological systems. Based on experimental and computational studies, a detailed picture of the reaction has now emerged: Excitation to the Franck-Condon region places the molecule on a steeply repulsive part of the 1B potential energy surface, which propels the molecule in exactly the conrotatory direction that conforms to the Woodward-Hoffmann rules of orbital symmetry. Bypassing a cusp in a symmetry-breaking direction, the wave packet enters the 2A state within 55 fs. It continues to move directly toward the 2A/1A conical intersection, where it crosses in approximately 80 fs to the ground state. This article summarizes the published experimental and theoretical work to describe the current understanding of the reaction while pointing to important questions that remain to be addressed.

Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure.

Principal component analysis (PCA) is a ubiquitous method of multivariate statistics that focuses on the eigenvalues lambda and eigenvectors of the sample covariance matrix of a data set. We consider p, N-dimensional data vectors xi drawn from a distribution with covariance matrix C. We use the replica method to evaluate the expected eigenvalue distribution rho(lambda) as N--> infinity with p=alphaN for some fixed alpha. In contrast to existing studies we consider the case where C contains a number of symmetry-breaking directions, so that the sample data set contains some definite structure. Explicitly we set C=sigma2I+sigma(2)Sigma(S)(m=1)A(m)B(m)B(T)(m), with A(m)>0 for all m. We find that the bulk of the eigenvalues are distributed as for the case when the elements of xi are independent and identically distributed. With increasing alpha a series of phase transitions are observed, at alpha=A(-2)(m), m=1,2,..., S, each time a single delta function, delta(lambda-lambda(u)(A(m))), separates from the upper edge of the bulk distribution, where lambda(u)(A)=sigma(2)[1+A][1+(alphaA)(-1)]. We confirm the results of the replica analysis by studying the Stieltjes transform of rho(lambda). This suggests that the results obtained from the replica analysis are universal, irrespective of the distribution from which xi is drawn, provided the fourth moment of each element of xi exists.

The three-dimensional, three-state Potts model in an external field

We analyze the critical behaviour of the 3-d, 3-state Potts model in the presence of an external ordering field. From a finite size scaling analysis on lattices of size up to 70 3 we determine the critical endpoint of the line of first order phase transitions as ( β c , h c )=(0.54938(2),0.000775(10)). We determine the relevant temperature like and symmetry breaking directions at this second order critical point and explicitly verify that it is in the universality class of the 3-d Ising model.

Bayesian learning versus optimal learning

We consider the optimal performance that may be reached in the problem of learning the symmetry-breaking direction of a cloud of P= αN points in a N-dimensional space. The performance is measured through the overlap R opt between the true symmetry-breaking direction and the learnt one. Depending on the problem, the learning curves R opt( α) may present discontinuities. We show that close to these, bayesian learning is not optimal.

Monte Carlo optimization applied to symmetry breaking

We present a Monte Carlo optimization algorithm to search for the boundary points of the orbit space which is important in determining the symmetry breaking directions in the Higgs potential and the Landau potential. Our algorithm is robust and generally applicable. For large problems we have also developed a parallel version. We apply the method to the Landau potential of the d-wave abnormal superconductor, He-3, and a SU(5) Higgs potential.

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.

Patterns of quark mass matrices in a class of Calabi-Yau models

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete E 6-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles. The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeros, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale, and the predicted mass matrices have no simple symmetry properties.

One-loop effective potential for SO(10) GUT theories in de Sitter space

Zeta-function regularization is applied to the evaluation of the one-loop effective potential for SO(10) grand unified theories in de Sitter cosmologies. When the Higgs scalar field belongs to the 210-dimensional irreducible representation of SO(10), attention is focused on the mass matrix relevant for the symmetry-breaking direction, to agree with the low-energy phenomenology of the standard model of particle physics. The analysis is restricted to those values of the tree-level potential parameters for which the absolute minimum of the classical potential has been evaluated. As shown in the recent literature, such minima turn out to be or invariant. Electroweak phenomenology is more naturally derived, however, from the former minima. Hence the values of the parameters leading to the alternative set of minima have been discarded. Within this framework, the flat-space limit and the general form of the one-loop effective potential are studied in detail by using analytic and numerical methods. It turns out that, as far as the absolute-minimum direction is concerned, the flat-space limit of the one-loop calculation with a de Sitter background does not change the results previously obtained in the literature, where the tree-level potential in flat spacetime was studied. Moreover, even when curvature effects are no longer negligible in the one-loop potential, it is found that the early universe can only reach the absolute minimum.

Very large intermediate scales in three-generation models

The issue of large intermediate scales is addressed in a class of three-generation models based on the best-known Calabi-Yau compactification of the heterotic string. The renormalisation group equations for this class are studied to determine the scale, μ≡ M I , at which the first “intermediate-scale” symmetry breaking occurs. Throughout most of the parameter space specifying the models, M I is found to be extremely close to the compactification scale, M c, as is required by phenomenology. This is due to the large number of fields which are massless below M c. Depending on unknown normalisation factors, different directions of symmetry breaking are possible, including the one thus far preferred on phenomenological grounds.