Group-theoretical description of domain and phase boundaries in crystalline solids

The theory is reviewed of domains and domain boundaries arising in phase transitions accompanied by symmetry breaking. Conclusions concerning the number, the crystallographic type and the spatial orientation of coherent interfaces between crystals of the same structure (domain boundaries) and between different structures of the same material (interphase boundaries) are presented in terms of the space group theory and of the Landau theory of phase transitions. The application of the two-dimensional space groups and the diperiodic groups in three dimensions to the discussed objects is described. The conditions for the coexistence of domains and phases without macroscopic stress are given. An example of the group-theoretical analysis of domain structure is given for a real material: NaO₂.     

Translational symmetry changes in second-order phase transitions on clean crystal surfaces

The group theory approach, within the Landau-Lifshitz theory of phase transitions, is presented to predict the possible translational symmetry changes (possible surface superstructures) in second-order phase transitions on clean crystal surfaces. 80 diperiodic groups in three dimensions are used to describe the symmetry of the surface layer. A comparison of the theoretical results with experimental data is given.     

Unit-cell vibrational spectra of chromium trichoride and chromium tribromide

Raman spectra (at temperatures down to 4.2°K) and infrared spectra (at room temperature) of chromium trichloride and chromium tribromide have been obtained. Based on a factor group analysis and on the insensitivity of the CrCl₃ Raman spectrum to the monoclinic ā rhombohedral structural transformation, it is concluded that the spectra are characteristic of the unit cell of the diperiodic halogen-metal-halogen “sandwich” and not of the unit cell of the true triperiodic crystallographic space group.     

Metastable states of hydrogen: their geometric phases and flux densities

We discuss the geometric phases and flux densities for the metastable states of hydrogen with principal quantum number n = 2 being subjected to adiabatically varying external electric and magnetic fields. Convenient representations of the flux densities as complex integrals are derived. Both, parity conserving (PC) and parity violating (PV) flux densities and phases are identified. General expressions for the flux densities following from rotational invariance are derived. Specific cases of external fields are discussed. In a pure magnetic field the phases are given by the geometry of the path in magnetic field space. But for electric fields in presence of a constant magnetic field and for electric plus magnetic fields the geometric phases carry information on the atomic parameters, in particular, on the PV atomic interaction. We show that for our metastable states also the decay rates can be influenced by the geometric phases and we give a concrete example for this effect. Finally we emphasise that the general relations derived here for geometric phases and flux densities are also valid for other atomic systems having stable or metastable states, for instance, for He with n = 2. Thus, a measurement of geometric phases may give important experimental information on the mass matrix and the electric and magnetic dipole matrices for such systems. This could be used as a check of corresponding theoretical calculations of wave functions and matrix elements.     

Effect of space discretization on phase diagrams in ionic systems: a field-theoretic approach

Using Landau-Ginzburg-Wilson field-theoretic methods we determine for what kind of space discretization the transition between charge-disordered and charge-ordered phases in the restricted primitive model is fluctuation-induced first order. We identify this transition with ionic-crystal formation. We predict four types of generic phase diagrams in ionic systems for various kinds of space discretization for low and intermediate densities of ions. Our results also shed light on the simulation results obtained for an off-lattice ionic system over a wide range of densities, including the fcc crystal.     

Dirty, skewed, and backwards: the smectic A-C phase transition in aerogel

We study the smectic A-C transition in anisotropic and uniaxial disordered environments, e.g., uniaxially stretched aerogel. We find very strange behavior of translational correlations: the low-temperature, lower-symmetry smectic C phase is less translationally ordered than the high-temperature, higher-symmetry smectic A phase, with short ranged and algebraic translational correlations, respectively. Specifically, the A and C phases belong to the quasi-long-ranged translationally ordered "XY Bragg glass" and short ranged translationally ordered "m=1 Bragg glass" phase, respectively. The A-C phase transition itself belongs to a new universality class, whose fixed points and exponents we find in a d=5-epsilon expansion.     

Far-infrared optical properties of CrCl3 and CrBr3

We measured the far-infrared transmittance and reflectance spectra of the layered compounds CrBr₃ and CrCl₃ at normal and oblique incidences and at room temperature. The results are compared with the spectra from previous Raman measurements and are analyzed on the basis of the unit cell group method applied to the diperiodic crystalline structure of a single layer. A fit of the CrBr₃ reflectivity spectrum with damped Lorentzian oscillators is made which also allows us to evaluate the static dielectric constant ?₀.     

The high density properties of lithium hydride

The zero temperature phases of LiH are discussed for densities ranging from zero pressure equilibrium up to the region of extreme densities for which the electrons become relativistic. Estimates are made for the critical densities and pressures for the lower pressure insulator-metal transition, the high density pressure ionization transition and the phase separation at extreme densities. Structural modifications are discussed and lattice dynamics in the pressure ionized regime is considered.     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.     

Broken relativistic symmetry groups,toroidal moments and superconductivity in magnetoelectric crystals

Summary A connection between the creation of toroidal moments and the breaking of the relativistic crystalline group associated to a given crystal is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, a Goldstone boson responsible for the production of toroidal moments is created and, consequently toroidal phases arise in the crystal. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.     

Nature of the transition from two- to three-dimensional ordering in a confined colloidal suspension

We report the results of extensive molecular dynamics simulations of solid-to-solid transitions in two- to six-layer colloidal suspensions confined between two smooth parallel walls. The studies are designed to elucidate the ordered particle packings that interpolate between the structures of two- and three-dimensional crystals in a confined space. At a fixed density per layer, as the wall separation increases we find a sequence of stable phases, each characterized by uniform amplitude buckling along the normal to the layer planes. The buckling is coupled to an in-plane ordering transition. The buckled phases alternate with phases whose structures contain only parallel planes of particles. The relative densities of the positively and negatively displaced particles in a buckled layer, the in-plane structures, and the behavior with respect to increasing wall separation of the split density distribution that characterizes a buckled layer, clearly identify these layers as intermediates in the reconstructive transformations ntriangle up-->(n+1) square that occur when the character of the constrained space evolves from being two dimensional to being three dimensional (triangle up denotes layers with hexagonal packing symmetry, while square denotes layers with square packing symmetry). The two transitions, ntriangle up-->n-buckled-->(n+1) square, are found to be first order.     

Doubly charged Higgs from e–γ scattering in the 3-3-1 Model

The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models.     

Transport in two dimensional electronic micro-emulsions

In two dimensional electron systems with Coulomb or dipolar interactions, a direct transition, whether first or second order, from a liquid to a crystalline state is forbidden. As a result, between these phases there must be other (micro-emulsion) phases which can be viewed as a meso-scale mixture of the liquid and crystalline phases. We investigate the transport properties of these new electronic phases and present arguments that they are responsible for the various transport anomalies that have been seen in experiments on the strongly correlated 2DEG in high mobility semiconductor devices with low electron densities.     

Magnetic-field-induced insulating phases at large r s

Exploring a two-dimensional hole system in the large r(s) regime we found a surprisingly rich phase diagram. At the highest densities, beside the nu =1/3, 2/3, and 2/5 fractional quantum Hall states, we observe both of the previously reported high field insulating and reentrant insulating phases. As the density is lowered, the reentrant insulating phase initially strengthens, then it unexpectedly starts weakening until it completely disappears. The intricate behavior of the insulating phases can be explained by a nonmonotonic melting line in the nu-r(s) phase space.     

Travelling with/against the Flow. Deterministic Diffusive Driven Systems

We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars moving in opposite directions along a narrow road. Our main results concern the Fundamental diagram of the system describing the dependence of average particle velocities on their densities and the Phase diagram describing the partition of the space of particle configurations into regions having different qualitative properties, which we identify with free, jammed and hysteresis phases. This research has been partially supported by Russian Foundation for Fundamental Research, CRDF and French Ministry of Education grants.     

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter S?1. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity, which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.     

Classification and structure of silicon carbide phases

Molecular-mechanical and semiempirical quantum-mechanical methods have been applied to simulate and calculate a geometrically optimized structure of clusters of polymorphic types of silicon carbide, and their structural parameters and some properties (densities, sublimation energies) have been determined. A classification of silicon carbide phases has been proposed, which shows the possible existence of twenty one SiC phases whose atoms are at crystallographically equivalent sites. The structures of seventeen proposed silicon carbide phases have been described and studied for silicon carbide for the first time.     

Polarization fields and phase space densities in storage rings: Stroboscopic averaging and the ergodic theorem

A class of orbital motions with volume preserving flows and with vector fields periodic in the “time” parameter θ is defined. Spin motion coupled to the orbital dynamics is then defined, resulting in a class of spin-orbit motions which are important for storage rings. Phase space densities and polarization fields are introduced. It is important, in the context of storage rings, to understand the behavior of periodic polarization fields and phase space densities. Due to the 2π time periodicity of the spin-orbit equations of motion the polarization field, taken at a sequence of increasing time values θ,θ+2π,θ+4π,…, gives a sequence of polarization fields, called the stroboscopic sequence. We show, by using the Birkhoff ergodic theorem, that under very general conditions the Cesàro averages of that sequence converge almost everywhere on phase space to a polarization field which is 2π-periodic in time. This fulfills the main aim of this paper in that it demonstrates that the tracking algorithm for stroboscopic averaging, encoded in the program SPRINT and used in the study of spin motion in storage rings, is mathematically well-founded. The machinery developed is also shown to work for the stroboscopic average of phase space densities associated with the orbital dynamics. This yields a large family of periodic phase space densities and, as an example, a quite detailed analysis of the so-called betatron motion in a storage ring is presented.     

Boundary Effects on Microwave Propagation in a Large Waveguide Containing a Magnetoplasma

Solution of Maxwell's equations for a cold, uniform magnetoplasma bounded by conducting walls shows (i) how plane waves evolve in the space of (?/?c,?p/?c) with (kc/?c) as parameter, and (ii) the range of parameters in which whistler mode propagation without Wieder's fine structure can be expected. In this space, the whistler evolves from an electrostatic mode at low densities, the whistler characteristic appears in a range of densities where the static approximation is invalid, and at still higher densities, residual effects of boundaries show up in the fine structure, as accounted for by J. C. Lee. The asymptotic form of the solution when lateral dimensions are large shows the existence of classes of solutions which are inadmissible because none can be reached along a continuous locus in this space. Effects of finite boundaries on the dispersion characteristic and the interpretation of experimental data are discussed.