Local Symmetry Breaking Research Articles

B-P codopant effects on Raman spectra of Si nanocrystals using real space pseudopotentials

We calculate vibrational and Raman spectra for B-doped, P-doped, and B-P codoped Si nanocrystals using real-space pseudopotentials constructed within density functional theory. An experimental extrinsic peak in the Raman spectra near 650 cm−1 is observed in codoped nanocrystals. We analyze the origin of this peak and find that it can be best explained by the presence of B-P bonds, which are located near the surface of the nanocrystal. We propose that the spectral details of this peak are related to quantum confinement and the breaking of local symmetry associated with the phonon modes involving dopant bonds.

Atomic-scale measurement of polar entropy

Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly mind boggling length scales - from nanoparticles to galaxies. However, quantitative measurements of entropy change using calorimetry are predominantly macroscopic, with direct atomic scale measurements being exceedingly rare. Here for the first time, we experimentally quantify the polar configurational entropy (in meV/K) using sub-\r{a}ngstr\"{o}m resolution aberration corrected scanning transmission electron microscopy. This is performed in a single crystal of the prototypical ferroelectric $\mathsf{LiNbO_3}$ through the quantification of the niobium and oxygen atom column deviations from their paraelectric positions. Significant excursions of the niobium - oxygen polar displacement away from its symmetry constrained direction is seen in single domain regions which increases in the proximity of domain walls. Combined with first principles theory plus mean field effective Hamiltonian methods, we demonstrate the variability in the polar order parameter, which is stabilized by an increase in the magnitude of the configurational entropy. This study presents a powerful tool to quantify entropy from atomic displacements and demonstrates its dominant role in local symmetry breaking at finite temperatures in classic, nominally Ising ferroelectrics.

Energy-weighted sum rule for nuclear density functional theory

The expressions for the energy-weighted sum rule of the isoscalar and isovector coordinate operators are derived based on the second-order fluctuation of the local densities. Conventional derivation of the Thouless theorem for the energy-weighted sum rule is based on the double commutator of the Hamiltonian, while the present derivation does not assume a Hamiltonian operator and is applicable to nuclear energy density functionals. The expressions include the contribution of the local gauge symmetry breaking of the energy density functional. It is shown that the local gauge invariance of the kinetic and current densities and kinetic pair density is important, while all the other local densities do not contribute to the energy-weighted sum rule of the coordinate operators. The finite-amplitude method calculations are performed and the expressions for the energy-weighted sum rule are numerically examined for the isoscalar and isovector multipole operators up to $L=3$ for selected spherical and axially deformed nuclei.

Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking

A novel phenomenon is observed in the meta-atoms composed of a complementary rectangular double split-ring resonator (SRR). An intrinsic Fano-resonance collapses with the outer SRR deformed asymmetrically. Alternatively, a trapped mode emerges at an adjacent frequency region, of which its strength grows up with increasing the asymmetric deviation. However, the asymmetric deformation in the inner SRR has influence neither on the evolution of this intrinsic Fano-resonance nor on the excitation of the aforementioned trapped mode. The results of electromagnetic field simulation indicate that an interference of two magnetic dipoles leads to the intrinsic Fano-resonance on the outer SRR. The asymmetric deviation destructs coherent interference so that the Fano-resonance collapses. To the trapped mode, the surface current passes through the metal gap of the outer SRR, leading to a couple of antiparallel currents, which results in a couple of magnetic dipole oscillations. The intrinsic modes are kept constant, even though the inner SRR is asymmetrically deformed. The outer SRR plays the role of a Faraday cage, which electromagnetically shields the trapped mode on the inner SRR.

Pressure-induced local symmetry breaking upon liquid-liquid transition of GeI4 and SnI4.

SnI4 and GeI4 have been confirmed to have another liquid state appearing on compression. To identify the microscopic pathway from the low- to high-pressure liquid states, the structure of these liquids in the appropriate thermodynamic regions was analyzed using a reverse Monte Carlo method. The occurrence of pressure-induced symmetry lowering of molecules, from regular tetrahedral to ammonia-like pyramidal symmetry, was then recognizable in these systems. This symmetry lowering is reflected in the change in shape of the molecular form factor. The latter change occurs abruptly near the expected transition pressure in liquid SnI4, whereas it proceeds gradually in GeI4. This is consistent with our observation that SnI4 seems to undergo a first-order liquid-liquid transition, whereas the transition seems to end up with a crossover in liquid GeI4. Interestingly, when the molecular density becomes high, it is possible for the two-body intermolecular interaction to have a double-minimum character, which offers two characteristic length scales corresponding to two liquid states with different densities. However, quantum chemical calculations show that molecular deformation for this type of symmetry lowering results in an increase in electronic energy, which leaves the problem of the physical origin for this anisotropic deformation. We speculate that this symmetry lowering occurs as a precursor to the whole change in the liquid structure.

Complete determination of elastic stiffness coefficients and local symmetry breaking in the paraelectric barium titanate

The temperature dependence of all independent elastic stiffness coefficients of cubic BaTiO3 was determined over a wide temperature range from 400 °C to the Curie point (Tc ∼ 131 °C) by using Brillouin light scattering spectroscopy. Among the two elastic eigen-modes corresponding to the two measured transverse acoustic waves, (C11-C12)/2 showed a large softening in the paraelectric phase, while the change in C44 was very small. This result caused the elastic anisotropy A, defined as 2C44/(C11-C12), to increase from ∼2.1 to ∼2.7 upon cooling toward the phase transition temperature. The large elastic anisotropy was attributed to the tetragonal instability and the associated anisotropic polarization fluctuations of precursor polar clusters formed by the correlated Ti motions. The elastic anisotropy was fitted by using the Curie-Weiss law resulting in a significant deviation in a certain temperature range between Tc and ∼Tc + 50 °C, similar to the dielectric permittivity.

Haldane phases with ultracold fermionic atoms in double-well optical lattices

We propose to realize one-dimensional topological phases protected by SU($N$) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of $N$, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters of the model. For even $N$, the celebrated spin-1 Haldane phase and its generalization to SU($N$) are obtained with no local symmetry breaking. In stark contrast, at least for $N=3$, a new class of SPT phases, dubbed chiral Haldane phases, that spontaneously break inversion symmetry, emerge with a two-fold ground-state degeneracy. The latter ground states with open-boundary conditions are characterized by different left and right boundary spins which are related by conjugation. Our results show that topological phases are within close reach of the latest experiments on cold fermions in optical lattices.

Microstructural-defect-induced Dzyaloshinskii-Moriya interaction

The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) plays a decisive role for the stabilization and control of chirality of skyrmion textures in various magnetic systems exhibiting a noncentrosymmetric crystal structure. A less studied aspect of the DMI is that this interaction is believed to be operative in the vicinity of lattice imperfections in crystalline magnetic materials, due to the local structural inversion symmetry breaking. If this scenario leads to an effect of sizable magnitude, it implies that the DMI introduces chirality into a very large class of magnetic materials---defect-rich systems such as polycrystalline magnets. Here, we show experimentally that the microstructural-defect-induced DMI gives rise to a polarization-dependent asymmetric term in the small-angle neutron scattering (SANS) cross section of polycrystalline ferromagnets with a centrosymmetric crystal structure. The results are supported by theoretical predictions using the continuum theory of micromagnetics. This effect, conjectured already by Arrott in 1963, is demonstrated for nanocrystalline terbium and holmium (with a large grain-boundary density), and for mechanically-deformed microcrystalline cobalt (with a large dislocation density). Analysis of the scattering asymmetry allows one to determine the defect-induced DMI constant, $D = 0.45 \pm 0.07 \, \mathrm{mJ/m^2}$ for Tb at $100 \, \mathrm{K}$. Our study proves the generic relevance of the DMI for the magnetic microstructure of defect-rich ferromagnets with vanishing intrinsic DMI. Polarized SANS is decisive for disclosing the signature of the defect-induced DMI, which is related to the unique dependence of the polarized SANS cross section on the chiral interactions. The findings open up the way to study defect-induced skyrmionic magnetization textures in disordered materials.

Suppression of the spectral weight of topological surface states on the nanoscale via local symmetry breaking

In topological crystalline insulators the topological conducting surface states are protected by crystal symmetry, in principle making it possible to pattern nanoscale insulating and conductive motifs solely by breaking local symmetries on an otherwise homogenous, single-phase material. We show using scanning tunneling microscopy/spectroscopy that defects that break local symmetry of SnTe suppress electron tunneling over an energy range as large as the bulk band gap, an order of magnitude larger than that produced globally via magnetic fields or uniform structural perturbations. Complementary ab initio calculations show how local symmetry breaking obstructs topological surface states as shown by a threefold reduction of the spectral weight of the topological surface states. The finding highlights the potential benefits of manipulating the surface morphology to create devices that take advantage of the unique properties of topological surface states and can operate at practical temperatures.

The Noether current in Maxwell's equations and radiation under symmetry breaking

Symmetries in physical systems are defined in terms of conserved Noether Currents of the associated Lagrangian. In electrodynamic systems, global symmetry is defined through conservation of charges, which is reflected in gauge symmetry; however, loss of charges from a radiating system can be interpreted as localized loss of the Noether current which implies that electrodynamic symmetry has been locally broken. Thus, we propose that global symmetries and localized symmetry breaking are interwoven into the framework of Maxwell's equations which appear as globally conserved and locally non-conserved charges in an electrodynamic system and define the geometric topology of the electromagnetic field. We apply the ideas in the context of explaining radiation from dielectric materials with low physical dimensions. We also briefly look at the nature of reversibility in electromagnetic wave generation which was initially proposed by Planck, but opposed by Einstein and in recent years by Zoh.This article is part of the theme issue 'Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory''.

Enabling nanoscale flexoelectricity at extreme temperature by tuning cation diffusion

Any dielectric material under a strain gradient presents flexoelectricity. Here, we synthesized 0.75 sodium bismuth titanate −0.25 strontium titanate (NBT-25ST) core–shell nanoparticles via a solid-state chemical reaction directly inside a transmission electron microscope (TEM) and observed domain-like nanoregions (DLNRs) up to an extreme temperature of 800 °C. We attribute this abnormal phenomenon to a chemically induced lattice strain gradient present in the core–shell nanoparticle. The strain gradient was generated by controlling the diffusion of strontium cations. By combining electrical biasing and temperature-dependent in situ TEM with phase field simulations, we analyzed the resulting strain gradient and local polarization distribution within a single nanoparticle. The analysis confirms that a local symmetry breaking, occurring due to a strain gradient (i.e. flexoelectricity), accounts for switchable polarization beyond the conventional temperature range of existing polar materials. We demonstrate that polar nanomaterials can be obtained through flexoelectricity at extreme temperature by tuning the cation diffusion.

Vibrational dynamics of ferroelectric K(Ta1−xNbx)O3 studied by far-infrared spectroscopic ellipsometry and Raman scattering

KTa1−xNbxO3 (KTN) with the perovskite structure has attracted much attention owing to the application of its huge second-order electro-optic effect just above the Curie temperature (TC). We studied the vibrational properties by far-infrared spectroscopic ellipsometry (FIRSP) and Raman scattering of infrared and Raman active modes, respectively. In a cubic paraelectric phase with , three T1u modes are Raman inactive but infrared active. The result of FIRSP shows only the small softening of the lowest-frequency TO1 mode on cooling. In a ferroelectric tetragonal phase with P4mm, no TO1 mode was observed clearly in the present Raman scattering studies because of low intensity. However, between TC and the intermediate temperature (T*), TO2 and TO4 modes were observed owing to local symmetry breaking caused by polar nanoregions. On the basis of FIRSP and Raman scattering study results, it is concluded that the ferroelectric instability of KTN32 (x = 0.32) is essentially of the order–disorder type.

Spin-orbital-lattice entangled states in cubic d1 double perovskites

The interplay of spin-orbit coupling and vibronic coupling on the heavy ${d}^{1}$ site of cubic double perovskites is investigated by ab initio calculations. The stabilization energy of spin-orbital-lattice entangled states is found to be comparable to or larger than the exchange interactions, suggesting the presence of Jahn-Teller dynamics in the systems. In ${\mathrm{Ba}}_{2}{\mathrm{YMoO}}_{6}$, the pseudo-Jahn-Teller coupling enhances the mixing of the ground and excited spin-orbit multiplet states, which results in strong temperature dependence of effective magnetic moments. The entanglement of the spin and lattice degrees of freedom induces a strong magnetoelastic response. This multiferroic effect is at the origin of the recently reported breaking of local point symmetry accompanying the development of magnetic ordering in ${\mathrm{Ba}}_{2}{\mathrm{NaOsO}}_{6}$.

Correlated local dipoles in PbTe

We present a combined single-crystal x-ray diffuse scattering and ab-initio molecular dynamics study of lead telluride, PbTe. Well-known for its thermoelectric and narrow-gap semiconducting properties, PbTe recently achieved further notoriety following the report of an unusual off-centering of the lead atoms, accompanied by a local symmetry breaking, on heating. This observation, which was named emphanisis, ignited considerable controversy regarding the details of the underlying local structure and the appropriate interpretation of the total scattering experiments. In this study, we demonstrate close agreement between our diffuse scattering measurements and our calculations, which allows us to analyze features such as higher-order correlations that are accessible in the simulations but not experimentally. This allowed us to discover an unusual correlated local dipole formation extending over several unit cells with an associated local reduction of the cubic symmetry in both our x-ray diffuse scattering measurements and our molecular dynamics simulations. Importantly, when averaged spatially or temporally, the most probable positions for the ions are at the centers of their coordination polyhedra. Our results therefore clarify the nature of the local symmetry breaking, and reveal the source of the earlier controversy regarding the existence or absence of off-centering. Finally, we provide an interpretation of the behavior in terms of coupled soft optical and acoustic modes, which is linked also to the high thermoelectric performance of PbTe.

Qualitative Views on the Polyradical Character of Long Acenes.

Spin-symmetry breaking appears in the DFT treatment of polyacenes, beyond a certain length, the critical length depending on the exchange-correlation potential. This phenomenon may be attributed to an instability with respect to HOMO-LUMO mixing, which suggests a diradical character of long acenes. However, the increase of the S2 operator with acene length questions this simple view. It is shown that this increase cannot be attributed to spin polarization of the inner MOs, and that a second symmetry breaking takes place for the pentadecacene, with four unpaired electrons centered at the first and third quarters of the chain. The spin density distributions of broken-symmetry solutions support a qualitative picture in terms of tetra-methylene hexacenes separated by Clar sextets. A strategy is proposed to identify local symmetry breaking in polyradical systems.

Atomic-scale strain manipulation of a charge density wave

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe2 Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

Nature of lattice distortions in the cubic double perovskite Ba2NaOsO6

We present detailed calculations of the electric field gradient (EFG) using a point charge approximation in ${\mathrm{Ba}}_{2}{\mathrm{NaOsO}}_{6}$, a Mott insulator with strong spin-orbit interaction. Recent $^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR) measurements found that the onset of local point symmetry breaking, likely caused by the formation of quadrupolar order [Chen, Pereira, and Balents, Phys. Rev. B 82, 174440 (2010)], precedes the formation of long range magnetic order in this compound [Lu et al., Nat. Commun. 8, 14407 (2017); Liu et al., Physica B 536, 863 (2018)]. An extension of the static $^{23}\mathrm{Na}$ NMR measurements as a function of the orientation of a 15 T applied magnetic field at 8 K in the magnetically ordered phase is reported. Broken local cubic symmetry induces a nonspherical electronic charge distribution around the Na site and thus finite EFG, affecting the NMR spectral shape. We combine the spectral analysis as a function of the orientation of the magnetic field with calculations of the EFG to determine the exact microscopic nature of the lattice distortions present in low temperature phases of this material. We establish that orthorhombic distortions, constrained along the cubic axes of the perovskite reference unit cell, of oxygen octahedra surrounding Na nuclei are present in the magnetic phase. Other common types of distortions often observed in oxide structures are considered as well.

Investigation of defects dependence of local piezoelectric response on Fe, La-modified (Pb,Sr)TiO3 thin films: A piezoresponse force microscopy study

In this study, undoped-(Pb,Sr)TiO3 and Fe3+, La3+ co-doped (Pb,Sr)TiO3 thin films were investigated at the nanoscale level by piezoresponse force microscopy (PFM), in order to evaluate the impact of doping-induced damages on the ferroelectric and piezoelectric properties. Detailed investigations with nanoscale resolution have revealed occurrence of abnormal domains in writing pattern under forward and reverse bias for (Pb,Sr,La)(Ti,Fe)O3 thin films. Further piezoresponse hysteresis loop measurements show that fully switchable loops were observed under high voltage mediated by defect dipoles and by “ferroelectric-like” polar defects clusters. They have been discussed taking into account charged defect formation with both local changes in the dipole moment and local symmetry breaking effects. In addition, the domain writing and its retention behavior of the undoped-PST and (Pb,Sr,La)(Ti,Fe)O3 thin films were investigated. Undoped-PST films exhibited better stability for both positive and negative domains for a relatively long time in comparison to that observed for (Pb,Sr,La)(Ti,Fe)O3 films.

Orbitally limited pair-density-wave phase of multilayer superconductors

We investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic (Pauli) limiting magnetic field stabilizes a staggered layer dependent pair-density wave phase in the superconducting singlet channel. The high-field pair-density wave phase is separated from the low-field BCS phase by a first-order phase transition. The motivating guiding question in this paper is: what is the minimal necessary Maki parameter $\alpha_M$ for the appearance of the pair-density wave phase of a superconducting trilayer system? To address this problem we generalize the circular cell method for the regular flux-line lattice of a type-II superconductor to include paramagnetic depairing effects. Then, we apply the model to the trilayer system, where each of the layers are characterized by Ginzburg-Landau parameter $\kappa_0$, and a Maki parameter $\alpha_M$. We find that when the spin-orbit Rashba interaction compares to the superconducting condensation energy, the orbitally limited pair-density wave phase stabilizes for Maki parameters $\alpha_M> 10$.

Localized Symmetry Breaking for Tuning Thermal Expansion in ScF3 Nanoscale Frameworks.

The local symmetry, beyond the averaged crystallographic structure, tends to bring unusual performances. Negative thermal expansion is a peculiar physical property of solids. Here, we report the delicate design of the localized symmetry breaking to achieve controllable thermal expansion in ScF3 nanoscale frameworks. Intriguingly, an isotropic zero thermal expansion is concurrently engineered by localized symmetry breaking, with a remarkably low coefficient of thermal expansion of about +4.0 × 10-8/K up to 675 K. This mechanism is investigated by the joint analysis of atomic pair distribution function of synchrotron X-ray total scattering and extended X-ray absorption fine structure spectra. A localized rhombohedral distortion presumably plays a critical role in stiffening ScF3 nanoscale frameworks and concomitantly suppressing transverse thermal vibrations of fluorine atoms. This physical scenario is also theoretically corroborated by the extinction of phonon modes with negative Grüneisen parameters in rhombohedral ScF3. The present work opens an untraditional chemical modification route to achieve controllable thermal expansion by breaking local symmetries in materials.