Engineering of Pyroelectric Crystals Decoupled from Piezoelectricity as Illustrated by Doped α-Glycine.

Design of pyroelectric crystals decoupled from piezoelectricity is not only a topic of scientific curiosity but also demonstrates effects in principle that have the potential to be technologically advantageous. Here we report a new method for the design of such materials. Thus, the co-doping of centrosymmetric crystals with tailor-made guest molecules, as illustrated by the doping of α-glycine with different amino acids (Threonine, Alanine and Serine). The polarization of those crystals displays two distinct contributions, one arising from the difference in dipole moments between guest and host and the other from the displacement of host molecules from their symmetry-related positions. These contributions exhibit different temperature dependences and response to mechanical deformation. Thus, providing a proof of concept for the ability to design pyroelectric materials with reduced piezoelectric coefficient (d22 ) to a minimal value, below the resolution limit of the method (<0.005 pm/V).

Symmetry-Reduction Enhanced Polarization-Sensitive Photodetection in Core-Shell SbI3 /Sb2 O3 van der Waals Heterostructure.

Structural symmetry is a simple way to quantify the anisotropic properties of materials toward unique device applications including anisotropic transportation and polarization-sensitive photodetection. The enhancement of anisotropy can be achieved by artificial symmetry-reduction design. A core-shell SbI3 /Sb2 O3 nanowire, a heterostructure bonded by van der Waals forces, is introduced as an example of enhancing the performance of polarization-sensitive photodetectors via symmetry reduction. The structural, vibrational, and optical anisotropies of such core-shell nanostructures are systematically investigated. It is found that the anisotropic absorbance of a core-shell nanowire is obviously higher than that of two single compounds from both theoretical and experimental investigations. Anisotropic photocurrents of the polarization-sensitive photodetectors based on these core-shell SbI3 /Sb2 O3 van der Waals nanowires are measured ranging from ultraviolet (UV) to visible light (360-532 nm). Compared with other van der Waals 1D materials, low anisotropy ratio (Imax /Imin ) is measured based on SbI3 but a device based on this core-shell nanowire possesses a relatively high anisotropy ratio of ≈3.14 under 450 nm polarized light. This work shows that the low-symmetrical core-shell van der Waals heterostructure has large potential to be applied in wide range polarization-sensitive photodetectors.

Conditional Lie-Bäcklund Symmetries and Differential Constraints of Radially Symmetric Nonlinear Convection-Diffusion Equations with Source.

A conditional Lie-Bäcklund symmetry method and differential constraint method are developed to study the radially symmetric nonlinear convection-diffusion equations with source. The equations and the admitted conditional Lie-Bäcklund symmetries (differential constraints) are identified. As a consequence, symmetry reductions to two-dimensional dynamical systems of the resulting equations are derived due to the compatibility of the original equation and the additional differential constraint corresponding to the invariant surface equation of the admitted conditional Lie-Bäcklund symmetry.

Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants.

We review a modern differential geometric description of fluid isentropic motion and features of it including diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. We study the differential-geometric structure of isentropic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and related invariant theory. In particular, we construct an infinite hierarchy of different kinds of integral magneto-hydrodynamic invariants, generalizing those previously constructed in the literature, and analyzing their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, and some generalizations of the canonical Lie-Poisson type bracket is presented.

Reduction of quantum systems and the local Gauss law.

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).

Symmetry-Reduction Enhanced Polarization-Sensitive Photoresponse Based on One-Dimensional van der Waals Materials.

Designing high-performance polarization-sensitive photodetectors is essential for photonic device applications. Anisotropic one-dimensional (1D) van der Waals (vdW) materials have provided a promising platform to that end. Despite significant advances in 1D vdW photonic devices, their performance is still far from delivering practical potential. Herein, we propose the design of high-performance polarization-sensitive photodetectors using unique 1D vdW materials. By leveraging the chemical vapor transport technique, we successfully fabricate high-quality 1D vdW Nb2Pd1-xSe5 (x = 0.29) nanowires. The 1D vdW Nb2Pd1-xSe5 photodetector exhibits a high mobility of ∼56 cm2/(V s) and superior photoresponse performance, including a high responsivity of 1A/W and an ultrafast response time of ∼8 µs under 638 nm illumination. Moreover, the 1D vdW Nb2Pd1-xSe5 photodetector demonstrates excellent polarization-sensitive photoresponse with a degree of linear polarization (DOLP) up to 0.85 and can be modulated by adjusting the gate voltage, laser power density, and wavelength. Those exceptional performance are believed to be relevant to the symmetry-reduction induced by the partial occupation of Pd sites. This study offers feasible approaches to enhance the anisotropy of 1D vdW materials and the modulation of their polarization-sensitive photoresponse, which may provide deep insights into the physical origin of anisotropic properties of 1D vdW materials.

On reducing and finding solutions of nonlinear evolutionary equations via generalized symmetry of ordinary differential equations.

We study symmetry reductions of nonlinear partial differential equations that can be used for describing diffusion processes in heterogeneous medium. We find ansatzes reducing these equations to systems of ordinary differential equations. The ansatzes are constructed using generalized symmetries of second-order ordinary differential equations. The method applied gives the possibility to find exact solutions which cannot be obtained by virtue of the classical Lie method. Such solutions are constructed for nonlinear diffusion equations that are invariant with respect to one-parameter and two-parameter Lie groups of point transformations. We prove a theorem relating the property of invariance of a found solution to the dimension of the Lie algebra admitted by the corresponding equation. We also show that the method is applicable to non-evolutionary partial differential equations and ordinary differential equations.

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12.

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Optimality, reduction and collective motion.

The planar self-steering particle model of agents in a collective gives rise to dynamics on the N-fold direct product of SE(2), the rigid motion group in the plane. Assuming a connected, undirected graph of interaction between agents, we pose a family of symmetric optimal control problems with a coupling parameter capturing the strength of interactions. The Hamiltonian system associated with the necessary conditions for optimality is reducible to a Lie-Poisson dynamical system possessing interesting structure. In particular, the strong coupling limit reveals additional (hidden) symmetry, beyond the manifest one used in reduction: this enables explicit integration of the dynamics, and demonstrates the presence of a 'master clock' that governs all agents to steer identically. For finite coupling strength, we show that special solutions exist with steering controls proportional across the collective. These results suggest that optimality principles may provide a framework for understanding imitative behaviours observed in certain animal aggregations.