How single conjugated polymer molecules respond to electric fields

Conjugated polymers find applications in a range of devices such as light-emitting diodes, field-effect transistors and solar cells. The elementary electronic response of these semiconductors to electric fields is understood in terms of nanoscale perturbations of charge density. We demonstrate a general breaking of spatial charge symmetry by considering the linear Stark effect in the emission of single chromophores on individual chains. Spectral shifts of several nanometres occur due to effective dipoles exceeding 10 D. Although the electric field does not ionize the exciton, some molecules exhibit field-induced intensity modulations. This quenching illustrates the equivalence of charge symmetry breaking and polaron-pair or charge-transfer-state formation, and provides a microscopic picture of permanent charging, which leads to doping and exciton dissociation in actual devices. In addition to using this tuneable emission in single-photon electro-optic modulators, hysteresis in the Stark shift suggests a route to designing nanoscale memory elements such as molecular switches.     

Bifurcations in dynamical systems with interior symmetry

We propose a definition of interior symmetry in the context of general dynamical systems. This concept appeared originally in the theory of coupled cell networks, as a generalization of the idea of symmetry of a network. The notion of interior symmetry introduced here can be seen as a special form of forced symmetry breaking of an equivariant system of differential equations. Indeed, we show that a dynamical system with interior symmetry can be written as the sum of an equivariant system and a ‘perturbation term’ which completely breaks the symmetry. Nonetheless, the resulting dynamical system still retains an important feature common to systems with symmetry, namely, the existence of flow-invariant subspaces. We define interior symmetry breaking bifurcations in analogy with the definition of symmetry breaking bifurcation from equivariant bifurcation theory and study the codimension one steady-state and Hopf bifurcations. Our main result is the full analogues of the well-known Equivariant Branching Lemma and the Equivariant Hopf Theorem from the bifurcation theory of equivariant dynamical systems in the context of interior symmetry breaking bifurcations.     

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors

A complicating factor in unravelling the theory of high-temperature (high-T(c)) superconductivity is the presence of a 'pseudogap' in the density of states, the origin of which has been debated since its discovery. Some believe the pseudogap is a broken symmetry state distinct from superconductivity, whereas others believe it arises from short-range correlations without symmetry breaking. A number of broken symmetries have been imaged and identified with the pseudogap state, but it remains crucial to disentangle any electronic symmetry breaking from the pre-existing structural symmetry of the crystal. We use scanning tunnelling microscopy to observe an orthorhombic structural distortion across the cuprate superconducting Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4+x) (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion-symmetry-breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field and doping, that it cannot be the long-sought pseudogap state. To detect this picometre-scale variation in lattice structure, we have implemented a new algorithm that will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.     

Surface Pyroelectricity in Cubic SrTiO3

Symmetry‐imposed restrictions on the number of available pyroelectric and piezoelectric materials remain a major limitation as 22 out of 32 crystallographic material classes exhibit neither pyroelectricity nor piezoelectricity. Yet, by breaking the lattice symmetry it is possible to circumvent this limitation. Here, using a unique technique for measuring transient currents upon rapid heating, direct experimental evidence is provided that despite the fact that bulk SrTiO₃ is not pyroelectric, the (100) surface of TiO₂‐terminated SrTiO₃ is intrinsically pyroelectric at room temperature. The pyroelectric layer is found to be ≈1 nm thick and, surprisingly, its polarization is comparable with that of strongly polar materials such as BaTiO₃. The pyroelectric effect can be tuned ON/OFF by the formation or removal of a nanometric SiO₂ layer. Using density functional theory, the pyroelectricity is found to be a result of polar surface relaxation, which can be suppressed by varying the lattice symmetry breaking using a SiO₂ capping layer. The observation of pyroelectricity emerging at the SrTiO₃ surface also implies that it is intrinsically piezoelectric. These findings may pave the way for observing and tailoring piezo‐ and pyroelectricity in any material through appropriate breaking of symmetry at surfaces and artificial nanostructures such as heterointerfaces and superlattices.     

Phase transition induced symmetry breaking in granular materials

The number of particles in two connected identical compartments can vary significantly when the system is under vertical vibration. This report proposes a new scenario for breaking system symmetry through molecular dynamics simulations. Instead of clustering in gaseous regime, symmetry breaking reported here is induced by the liquid–solid transition of particles in each compartment when particle number exceeds a critical value.     

Phase transition in space: how far does a symmetry bend before it breaks?

We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the 'scar' over which the order parameter adjusts as it 'bends' interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale--the size of the scar--is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.     

Classification of a Supersolid: Trial Wavefunctions, Symmetry Breakings and Excitation Spectra

A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal U(1) symmetry. Here, we review some past and recent works in phenomenological Ginsburg-Landau theories, ground state trial wavefunctions and microscopic numerical calculations. We also write down a new effective supersolid Hamiltonian on a lattice. The eigenstates of the Hamiltonian contains both the ground state wavefunction and all the excited states (supersolidon) wavefunctions. We contrast various kinds of supersolids in both continuous systems and on lattices, both condensed matter and cold atom systems. We provide additional new insights in studying their order parameters, symmetry breaking patterns, the excitation spectra and detection methods.     

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Hänchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.     

In situ atomic force microscopy tip-induced deformations and Raman spectroscopy characterization of single-wall carbon nanotubes

In this work, an atomic force microscope (AFM) is combined with a confocal Raman spectroscopy setup to follow in situ the evolution of the G-band feature of isolated single-wall carbon nanotubes (SWNTs) under transverse deformation. The SWNTs are pressed by a gold AFM tip against the substrate where they are sitting. From eight deformed SWNTs, five exhibit an overall decrease in the Raman signal intensity, while three exhibit vibrational changes related to the circumferential symmetry breaking. Our results reveal chirality dependent effects, which are averaged out in SWNT bundle measurements, including a previously elusive mode symmetry breaking that is here explored using molecular dynamics calculations.     

Effects of Radiative Corrections on a Quantum Disordered Self-dual Josephson Junction Array

The quantum effective potential of a three-dimensional Abelian Maxwell-mixed-Chern-Simons gauge theory coupled to complex fields and massless fermions is investigated at zero temperature. The insulating phase of the related self-dual Josephson junction array is found to be stable against gauge field fluctuations since these do not induce symmetry breaking terms in the one-loop effective potential. Conversely, coupling to gapless fermions is shown to generate correction terms in the effective potential which change the symmetry of the ground state and favor transitions between the insulating and superconducting states.     

Four coupled parity-time symmetric micro-rings for single-mode laser operation

In this paper, a novel scheme is proposed to obtain the single-mode laser using parity-time symmetry breaking. Four analogue micro-rings are optically coupled in the square configuration in a way that two micro-rings on the square diameter experience gain and the other two experience loss. The coupling coefficient for horizontal and vertical coupling between micro-rings is considered to be different. According to this new scheme, the symmetry of structure is destroyed, and thus the degenerate modes that can disrupt the stability of laser, disappeared. Due to the coupling of the resonators, four super-modes, which are coupled pairwise, are generated. The Eigen-frequency and parity-time symmetry breaking of the two super-modes depend on the difference between horizontal and vertical coupling coefficient; however, these parameters depend on the summation of the coupling coefficients for the other two. Results show that the laser output is single mode in a specific condition of coupling coefficient and gains. It is concluded that the threshold of pump parameter is improved in the new scheme, relative to the two coupled micro-rings.     

Aspects of breaking of symmetry through vibrational motions

Varied aspects of breaking of symmetry in crystalline and molecular conditions are considered. Distributions of electronic density about atomic centres of Li and H in crystalline LiH and isolated diatomic molecules of that compound en route to dissociation are discussed in relation to symmetry.     

Study on the breaking strength of jute fibres using modified Weibull distribution

The two-parameter Weibull distribution does not always adequately describe the experimental bast fibre strength at different gauge lengths. For this reason, it was modified by incorporating the diameter variation of jute fibres in this paper. The fibre diameter was measured with an optical microscope. The three-parameter Weibull model was also used to compare with the modified model. It was found that as the fibre diameter variation increased the tensile strength of the jute fibre decreased. The strength predicted by modified Weibull distribution was more accurate than that of the two conventional models. In addition, the breaking strength of jute fibre was less sensitive to gauge length than that of cotton fibre because the breaking of jute filament involves ultimate cells breaking repeatedly and matrix cracking.     

Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-Dimensional Subspace

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane–anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called ‘tachyon condensation’, where the existence of tachyons is attributable to the instability of the brane–anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose–Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a two-dimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a ‘vorton’ when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems.     

Kant vs. Legendre on Symmetry: Mirror Images in Philosophy and Mathematics

Abstract.   In 1768, Kant published a short essay in which he inquired into the possibility of determining the directionality of space. Kant's central argument invokes the strategy that if one were to demonstrate directionality, then the relational view of space that Leibniz propounded would be refuted. This paper has been considered a major turning point in Kant's philosophical development towards his critical philosophy of transcendental idealism. I demonstrate that in this study, Kant came very close to the modern concept of symmetry . His novel construction of incongruent counterpart ( inkongruentes Gegenstück ) contains elements essential to the modern notion of symmetry . However, Kant does not consider the incongruent counterparts, which he designates as 'Right' and 'Left', symmetric; rather, he holds the French encyclopaedist view that symmetry is a kind of balance. This study convinced Kant that the solution to the problem of the nature of space lies not in mathematics but in metaphysics. He was wrong in this conclusion, at least with respect to symmetry. The solution was found within the framework of mathematics, that is, solid geometry. In 1794, Legendre recast the traditional encyclopaedist concept of symmetry by calling a certain property of polyhedra symmetrical. The view of Kant is contrasted with that of Legendre by comparing their usages of mirror image as an aid for understanding. While in both cases mirror images are not considered illusions—perhaps for the first time in the history of mirror reflections—the differences are substantial, highlighting the limitation of Kant's position and the great potential of Legendre's new concept of symmetry.     

Aligned short-fibre reinforced thermosets: Experiments and analysis lend little support for established theory

Experiments with epoxy resins reinforced with aligned short carbon fibres give results which disagree sharply with traditional fibre reinforcement theory based on interface yielding and slip and the concept of the critical fibre aspect ratio. Earlier results and evidence from interface studies are therefore reviewed, and it is shown that, as the carbon/polymer interface is brittle, the progressive interface failure process previously envisaged almost certainly does not take place. Furthermore, a careful reading of the sources of data relating to the yielding and slip theory indicates that the evidence in support of it is very weak. Thus, the idea of the critical fibre aspect ratio, borrowed from the metallurgists, may not be appropriate for short-fibre reinforced plastics. Instead, a process involving brittle fibre debonds should be considered. These debonds could trigger matrix cracking and hence explain the anomalously low composite breaking strains observed when the breaking strain of the fibre is greater than that of the polymer, and other properties of aligned short-fibre composites.     

Anharmonic Lattice Vibrations in Small-Molecule Organic Semiconductors

The intermolecular lattice vibrations in small-molecule organic semiconductors have a strong impact on their functional properties. Existing models treat the lattice vibrations within the harmonic approximation. In this work, polarization-orientation (PO) Raman measurements are used to monitor the temperature-evolution of the symmetry of lattice vibrations in anthracene and pentacene single crystals. Combined with first-principles calculations, it is shown that at 10 K, the lattice dynamics of the crystals are indeed harmonic. However, as the temperature is increased, specific lattice modes gradually lose their PO dependence and become more liquid-like. This finding is indicative of a dynamic symmetry breaking of the crystal structure and shows clear evidence of the strongly anharmonic nature of these vibrations. Pentacene also shows an apparent phase transition between 80 and 150 K, indicated by a change in the vibrational symmetry of one of the lattice modes. These findings lay the groundwork for accurate predictions of the electronic properties of high-mobility organic semiconductors at room temperature.     

Quantized Massive Gauge Fields and Hole-Induced Spin Glass Mechanism in Underdoped Cuprates

We have discussed the restoration mechanism of the spontaneous symmetry breaking, C ₂ spatial symmetry breaking mechanism, and spin glass-like mechanism in high- T _c cuprates from the standpoint of field-theoretical formula. It is suggested strongly that quantized massive gauge fields, which contain effects of spin fluctuations, charge fluctuations, and phonons, might be mediating Cooper pairing in high- T _c cuprates.     

Evidence for Skyrmions in the High-Temperature Superconductors

We claim that the charge density wave recently found by resonant soft X-ray scattering in layered copper oxides is the tetragonal symmetry defined by the distance between neighboring Cu³⁺ ions in the CuO₂ layer that determines the critical temperature. We find evidence that this tetragonal symmetry is a skyrmionic state, which is responsible for an unusual magnetic order and charge flow in the layers that leads to the breaking of the time reversal symmetry below the pseudogap line. The core of the skyrmions form pockets of local magnetic field piercing the superconducting layers in opposite direction to the rest of the unit cell.     

The speed of interfacial waves polarized in a symmetry plane

The surface-impedance matrix method is used to study interfacial waves polarized in a plane of symmetry of anisotropic elastic materials. Although the corresponding Stroh polynomial is a quartic, it turns out to be analytically solvable in quite a simple manner. A specific application of the result concerns the calculation of the speed of a Stoneley wave, polarized in the common symmetry plane of two rigidly bonded anisotropic solids. The corresponding algorithm is robust, easy to implement, and gives directly the speed (when the wave exists) for any orientation of the interface plane, normal to the common symmetry plane. Through the examples of the couples (Aluminum)–(Tungsten) and (Carbon/epoxy)–(Douglas pine), some general features of a Stoneley wave speed are verified: the wave does not always exist; it is faster than the slowest Rayleigh wave associated with the separated half-spaces.