Chasing the objective upper eyelid symmetry formula; R2, RMSE, POC, MAE, and MSE.

PURPOSE: Investigate the most appropriate mathematical formula to objectively express upper eyelid contour symmetry. METHODS: 62 eyes of 31 patients were included in the study. The upper eyelid contour symmetry of the patients was classified subjectively (independent of MRD1) as poor, acceptable, and good by three oculoplastic specialists (senior, expert, and junior surgeon). Bézier curves of the upper lid contour were drawn with ImageJ software (NIH, Bethesda, MA, USA). Using the algorithms created by Author SKC in Spyder (Python 3.7.9.), the symmetry of the Bézier curves of the left eyelids were obtained according to the y-axis, and the mid-pupils of both eyes were superimposed. The lower curve moved vertically to the equal height of the other curve to equalize MRD1's. R2 (Coefficient of determination), RMSE (Root-mean-square error), MSE (Mean squared error), POC (Percentage of co-efficiency), and MAE (Mean absolute error) were calculated. We evaluated the correlation between these objective formulas and the subjective grading of three surgeons using Spearman's rho (ρ). RESULTS: The correlation coefficient of RMSE and MSE were the same for all surgeons grading. There was a strong correlation between the senior surgeon's subjective scoring (N; poor = 8, acceptable = 16, good = 8) and R2, RMSE, POC, MAE (ρ = 0.643, p < 0.001, ρ = -0.607, p < 0.001, ρ = 0.562, p < 0.001, ρ = -0.517, p < 0.001, respectively). We found a strong relationship between the expert surgeon's subjective scoring (N; poor = 9, acceptable = 13, good:10) and R2 (ρ = 0.611, p < 0.001), RMSE (ρ = -0.549, p < 0.001), POC (ρ = 0.511, p < 0.001), and MAE (ρ = -0.450, p < 0.05). We found a strong correlation between junior surgeon's subjective scoring (N; poor = 6, acceptable = 18, good = 8) and R2, RMSE, and POC (ρ: -0.517, p < 0.001; ρ: -0.470, p < 0.001; ρ: 0.521, p < 0.001; respectively) and moderate correlation between MAE (ρ:-0.394, p < 0.05). The highest correlation is observed with R2. CONCLUSIONS: RMSE, MSE, POC, MAE, and especially R2, may quantitatively express upper eyelid contour symmetry, comparable with the oculoplastic surgeon. The highest correlation was observed between the senior surgeon and R2, and decreases with the experience of the surgeon.

Homotopy, symmetry, and non-Hermitian band topology.

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time (PT) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases inPT-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneousPTsymmetry breaking is captured by Chern-Euler and Chern-Stiefel-Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.

Gait asymmetrical evaluation of lower limb amputees using wearable inertial sensors.

This study presents an analysis and evaluation of gait asymmetry (GA) based on the temporal gait parameters identified using a portable gait event detection system, placed on the lateral side of the shank of both lower extremities of the participants. Assessment of GA was carried out with seven control subjects (CS), one transfemoral amputee (TFA) and one transtibial amputee (TTA) while walking at different speeds on overground (OG) and treadmill (TM). Gait cycle duration (GCD), stance phase duration (SPD), swing phase duration (SwPD), and the sub-phases of the gait cycle (GC) such as Loading-Response (LR), Foot-Flat (FF), and Push-Off (PO), Swing-1 (SW-1) and Swing-2 (SW-2) were evaluated. The results revealed that GCD showed less asymmetry as compared to other temporal parameters in both groups. A significant difference (p < 0.05) was observed between the groups for SPD and SwPD with lower limb amputees (LLA) having a longer stance and shorter swing phase for their intact side compared to their amputated side, resulting, large GA for TFA compared to CS and TTA. The findings could potentially contribute towards a better understanding of gait characteristics in LLA and provide a guide in the design and control of lower limb prosthetics/orthotics.

Total ankle arthroplasty improves discrete and continuous stance phase gait symmetry.

BACKGROUND: Total ankle arthroplasty (TAA) is used to treat symptomatic end-stage ankle arthritis (AA). However, little is known about TAA's effects on gait symmetry. RESEARCH QUESTION: Determine if symmetry changes from before surgery through two years following TAA utilizing the normalized symmetry index (NSI) and statistical parametric mapping (SPM). METHODS: 141 patients with end-stage unilateral AA were evaluated from a previously collected prospective database, where each participant was tested within two weeks of surgery (Pre-Op), one year and two years following TAA. Walking speed, hip extension angle and moment, hip flexion angle, ankle plantarflexion angle and moment, ankle dorsiflexion angle, weight acceptance (GRF1), and propulsive (GRF2) vertical ground reaction forces were calculated for each limb. Gait symmetry was assessed using the NSI. A linear mixed effects model with a single response for each gait symmetry variable was used to examine the fixed effect of follow-up time (Pre-Op, Post-1 yr, Post-2 yr) and the random effect of participant with gait speed as a covariate in the model. A one-dimensional repeated measures analysis of variance (ANOVA) statistical parameter mapping (SPM) was completed to examine differences in the time-series NSI to determine regions of significant differences between follow-up times. RESULTS: Relative to Pre-Op values, GRF1, and GRF2 showed increased symmetry for discrete metrics and the time-series NSI across sessions. Hip extension moment had the largest symmetry improvement. Ankle plantarflexion angle was different between Pre-Op and Post-2 yr (p=0.010); and plantarflexion moment was different between Pre- Op and each post-operative session (p<0.001). The time-series Ankle Angle NSI was greater during the early stance phase in the Pre-Op session compared to Post-2 yr. SIGNIFICANCE: Symmetry across most of the stance phase improved following TAA indicating that TAA successfully improves gait symmetry and future work should determine if these improvements restore symmetry to levels equivalent with health age-match controls.

Crystal structure of tris-{N,N-diethyl-N'-[(4-nitro-phen-yl)(oxo)meth-yl]carbamimido-thio-ato}cobalt(III).

The synthesis, crystal structure, and a Hirshfeld surface analysis of tris-{N,N-diethyl-N'-[(4-nitro-phen-yl)(oxo)meth-yl]carbamimido-thio-ato}cobalt(III) conducted at 180 K are presented. The complex consists of three N,N-diethyl-N'-[(4-nitro-benzene)(oxo)meth-yl]carbamimido-thio-ato ligands, threefold sym-metric-ally bonded about the CoIII ion, in approximately octa-hedral coordination, which generates a triple of individually near planar metallacyclic (Co-S-C-N-C-O) rings. The overall geometry of the complex is determined by the mutual orientation of each metallacycle about the crystallographically imposed threefold axis [dihedral angles = 81.70 (2)°] and by the dihedral angles between the various planar groups within each asymmetric unit [metallacycle to benzene ring = 13.83 (7)°; benzene ring to nitro group = 17.494 (8)°]. The complexes stack in anti-parallel columns about the axis of the space group (P), generating solvent-accessible channels along [001]. These channels contain ill-defined, multiply disordered, partial-occupancy solvent. Atom-atom contacts in the crystal packing predominantly (∼96%) involve hydrogen, the most abundant types being H⋯H (36.6%), H⋯O (31.0%), H⋯C (19.2%), H⋯N (4.8%), and H⋯S (4.4%).

HaMADS3, HaMADS7, and HaMADS8 are involved in petal prolongation and floret symmetry establishment in sunflower (Helianthus annuus L.).

The development of floral organs, crucial for the establishment of floral symmetry and morphology in higher plants, is regulated by MADS-box genes. In sunflower, the capitulum is comprised of ray and disc florets with various floral organs. In the sunflower long petal mutant (lpm), the abnormal disc (ray-like) floret possesses prolongated petals and degenerated stamens, resulting in a transformation from zygomorphic to actinomorphic symmetry. In this study, we investigated the effect of MADS-box genes on floral organs, particularly on petals, using WT and lpm plants as materials. Based on our RNA-seq data, 29 MADS-box candidate genes were identified, and their roles on floral organ development, especially in petals, were explored, by analyzing the expression levels in various tissues in WT and lpm plants through RNA-sequencing and qPCR. The results suggested that HaMADS3, HaMADS7, and HaMADS8 could regulate petal development in sunflower. High levels of HaMADS3 that relieved the inhibition of cell proliferation, together with low levels of HaMADS7 and HaMADS8, promoted petal prolongation and maintained the morphology of ray florets. In contrast, low levels of HaMADS3 and high levels of HaMADS7 and HaMADS8 repressed petal extension and maintained the morphology of disc florets. Their coordination may contribute to the differentiation of disc and ray florets in sunflower and maintain the balance between attracting pollinators and producing offspring. Meanwhile, Pearson correlation analysis between petal length and expression levels of MADS-box genes further indicated their involvement in petal prolongation. Additionally, the analysis of cis-acting elements indicated that these three MADS-box genes may regulate petal development and floral symmetry establishment by regulating the expression activity of HaCYC2c. Our findings can provide some new understanding of the molecular regulatory network of petal development and floral morphology formation, as well as the differentiation of disc and ray florets in sunflower.

A three-dimensional quantitative assessment on bony growth and symmetrical recovery of mandible after decompression for unicystic ameloblastoma.

Unicystic ameloblastoma (UAM) of the jaw can be effectively reduced in volume through decompression, which promotes bone regeneration and restores jaw symmetry. This study quantitatively evaluated changes in mandible volume and symmetry following decompression of mandibular UAM. This study included 17 patients who underwent surgical decompression followed by second-stage curettage for mandibular UAM. Preoperative and postoperative three-dimensional computed tomography (CT) images were collected. Bone volume and the area of cortical perforation were measured to assess bone growth during decompression. Mandibular volumetric symmetry was analyzed by calculating the volumetric ratio of the two sides of the mandible. Twelve pairs of landmarks were identified on the surface of the lesion regions, and their coordinates were used to calculate the mean asymmetry index (AI) of the mandible. Paired t-tests and the Mann-Whitney U test were used for statistical analysis, with p < 0.05 considered indicative of statistical significance. The mean duration of decompression was 9.41 ± 3.28 months. The mean bone volume increased by 8.07 ± 2.41%, and cortical perforation recovery was 71.97 ± 14.99%. The volumetric symmetry of the mandible improved significantly (p < 0.05), and a statistically significant decrease in AI was observed (p < 0.05). In conclusion, UAM decompression enhances bone growth and symmetry recovery of the mandible. The present evaluation technique is clinically useful for quantitatively assessing mandibular asymmetry.

Investigating structural and optoelectronic properties of Cr-substituted ZnSe semiconductors.

The optoelectronic and structural characteristics of the Zn1-xCrxSe (0 ≤ x ≤ 1) semiconductor are reported by employing density functional theory (DFT) within the mBJ potential. The findings revealed that the lattice constant decreases with increasing Cr concentration, although the bulk modulus exhibits the opposite trend. ZnSe is a direct bandgap material; however, a change from direct to indirect electronic bandgap has been seen with Cr presence. This transition is caused by structural alterations by Cr and defects forming, which results in novel optical features, including electronic transitions. The electronic bandgap decreases from 2.769 to 0.216 eV, allowing phonons to participate and improving optical absorption. A higher concentration of Cr boosts infrared absorption and these Cr-based ZnSe (ZnCrSe) semiconductors also cover a wider spectrum in the visible range from red to blue light. Important optical parameters such as reflectance, optical conductivity, optical bandgap, extinction coefficient, refractive index, magnetization factor, and energy loss function are discussed, providing a theoretical understanding of the diverse applications of ZnCrSe semiconductors in photonic and optoelectronic devices.

BMP4 regulates asymmetric Pkd2 distribution in mouse nodal immotile cilia and ciliary mechanosensing required for left-right determination.

BACKGROUND: Mouse nodal immotile cilia mechanically sense the bending direction for left-right (L-R) determination and activate the left-side-specific signaling cascade, leading to increased Nodal activity. Asymmetric distribution of Pkd2, a crucial channel for L-R determination, on immotile cilia has been reported recently. However, the causal relationship between the asymmetric Pkd2 distribution and direction-dependent flow sensing is not well understood. Furthermore, the underlying molecular mechanism directing this asymmetric Pkd2 distribution remains unclear. RESULTS: The effects of several recombinant proteins and inhibitors on the Pkd2 distribution were analyzed using super-resolution microscopy. Notably, bone morphogenetic protein 4 (BMP4) affected the Pkd2 distribution. Additionally, three-dimensional manipulation of nodal immotile cilia using optical tweezers revealed that excess BMP4 caused defects in the mechanosensing ability of the cilia. CONCLUSIONS: Experimental data together with model calculations suggest that BMP4 regulates the asymmetric distribution of Pkd2 in nodal immotile cilia, thereby affecting the ability of these cilia to sense the bending direction for L-R determination. This study, for the first time, provides insight into the relationship between the asymmetric protein distribution in cilia and their function.

Highly Anisotropic Pd2Lab2Lcc2 and Pd2Lab2Lcd2 Type Cages by Heteromeric Completive Self-Sorting.

Pd(II)-based low-symmetry coordination cages possessing anisotropic cavities are of great interest. The common strategies employed to achieve such cages utilize either more than one type of symmetrical ligands (e.g., Laa, Lbb, etc.) or only one type of unsymmetrical ligand (e.g., Lab). To significantly enhance the anisotropy, we have designed two unsymmetrical bidentate ligands i.e., Lab and Lcd, aiming a low-symmetry Pd2Lab2Lcd2-type cage. It was accomplished by high-fidelity integrative self-sorting of two different low-symmetry cages having Pd2Lab4 and Pd4Lcd8-type architectures (homoleptic complexes of the designed ligands). Structural constraints and geometry complementarity in the ligand design drive the non-statistical exclusive self-assembly of the Pd2Lab2Lcd2-type cage. By taking advantage of the complemental geometries between ligands, a low-symmetry Pd2Lab2Lcc2-type cage was also obtained. Heteromeric completive self-sorting of three homoleptic assemblies (Pd2Lab4, Pd4Lcc8 and Pd4Lcd8-type cages) into an exclusive mixture of Pd2Lab2Lcd2 and Pd2Lab2Lcc2-type mixed ligated assemblies was demonstrated through cage-to-cage transformations.

Unicompartmental knee arthroplasty approximates healthy knee kinematics more closely than total knee arthroplasty.

Total knee arthroplasty (TKA) and unicompartmental knee arthroplasty (UKA) are effective surgeries to treat end-stage knee osteoarthritis. Clinicians assume that TKA alters knee kinematics while UKA preserves native knee kinematics; however, few studies of in vivo kinematics have evaluated this assumption. This study used biplane radiography to compare side-to-side tibiofemoral kinematics during chair rise, stair ascent, and walking in 16 patients who received either TKA or UKA. We hypothesized that TKA knees would have significant kinematic changes and increased asymmetry with the contralateral knee, while UKA knee kinematics would not change after surgery and preoperative knee symmetry would be maintained. Native bone and implant motion were tracked using a volumetric model-based tracking technique. Six degrees of freedom kinematics were calculated throughout each motion. Kinematics were compared between the operated and contralateral knees pre- and post-surgery using a linear mixed-effects model. TKA knees became less varus with the tibia more medial, posterior, and distal relative to the femur. UKA knees became less varus with the tibia less lateral on average. Postoperative TKA knees were in less varus than UKA knees on average and at low flexion angles, with an internally rotated tibia during chair rise and stair ascent. At high flexion angles, the tibia was more medial and posterior after TKA than UKA. Side-to-side kinematic symmetry worsened after TKA but was maintained or improved after UKA. Greater understanding of kinematic differences between operated and contralateral knees after surgery may help surgeons understand why some patients remain unsatisfied with their new knees.

Nearly Ideal Random Tiling with Dodecagonal Symmetry from Pentablock Quarterpolymers of the AB1CB2D Type.

Two-dimensional tiling manners as cross-sectional views of cylindrical domain assembly formed by pentablock quarterpolymers of the AB1CB2D type in bulk were investigated. Several binary and ternary blends from three mother polymers having different ϕB1/ϕB2 ratios (ϕB1 and ϕB2 are the volume fractions of the B1 and B2 blocks, respectively) represent nonperiodic but ordered triangle/square tilings, where the N3/N4 ratios (N3 and N4 are the numbers of triangles and squares in the observed area, respectively) are all close enough to the theoretical value of 4/√3 ≑ 2.31 for the dodecagonal quasicrystalline (DDQC) state, irrespective of the total number of polygons. The TEM images, having almost the same N3/N4 ratios, were proved to show 4- and 6-fold symmetries in terms of the angular appearance of equilateral polygon sides via image analyses. Among them, a ternary blend showed a nearly ideal random tiling pattern that is almost equivalent to the theoretically predicted tiling by SCFT. Moreover, the magnitude of phason strain estimated for a TEM image from the ternary blend was proved to be quite small when the observing area is narrow, while it deviates from the ideal quasicrystalline tiling with an increasing number of vertices in the observing area.

'Organ'ising Floral Organ Development.

Flowers are plant structures characteristic of the phylum Angiosperms composed of organs thought to have emerged from homologous structures to leaves in order to specialize in a distinctive function: reproduction. Symmetric shapes, colours, and scents all play important functional roles in flower biology. The evolution of flower symmetry and the morphology of individual flower parts (sepals, petals, stamens, and carpels) has significantly contributed to the diversity of reproductive strategies across flowering plant species. This diversity facilitates attractiveness for pollination, protection of gametes, efficient fertilization, and seed production. Symmetry, the establishment of body axes, and fate determination are tightly linked. The complex genetic networks underlying the establishment of organ, tissue, and cellular identity, as well as the growth regulators acting across the body axes, are steadily being elucidated in the field. In this review, we summarise the wealth of research already at our fingertips to begin weaving together how separate processes involved in specifying organ identity within the flower may interact, providing a functional perspective on how identity determination and axial regulation may be coordinated to inform symmetrical floral organ structures.

Large dynamic scissoring mode displacements coupled to band gap opening in the cubic phase of the methylammonium lead halide perovskites.

Hybrid perovskites are a rapidly growing research area, having reached photovoltaic power conversion efficiencies of over 25 %. There is a increasing consensus that the structures of these materials, and hence their electronic structures, can not be understood purely from the time and space averaged crystal structures observable by conventional methods. We apply a symmetry-motivated analysis method to analyse X-ray pair distribution function data of the cubic phases of the hybrid perovskites MAPb$X_3$ ($X$ = I, Br, Cl). We demonstrate that, even in the cubic phase, the local structure of the inorganic components of MAPb$X_3$ ($X$ = I, Br, Cl), are dominated by scissoring type deformations of the Pb$X_6$ octahedra. We find these modes to have a larger amplitude than equivalent distortions in the $A$-site deficient perovskite ScF$_3$ and demonstrate that they show a significant departure from the harmonic approximation. Calculations performed on an inorganic perovskite analogue, FrPbBr3show that the large amplitudes of the scissoring modes are coupled to a dynamic opening of the electronic band gap. Finally, we use density functional theory calculations to show that the organic MA cations reorientate to accommodate the large amplitude scissoring modes.

The free energy principle induces intracellular compartmentalization.

Living systems at all scales are compartmentalized into interacting subsystems. This paper reviews a mechanism that drives compartmentalization in generic systems at any scale. It first discusses three symmetries of generic physical interactions in a quantum-theoretic description. It then shows that if one of these, a permutation symmetry on the inter-system boundary, is spontaneously broken, the symmetry breaking is amplified by the Free Energy Principle (FEP). It thus shows how compartmentalization generically results from permutation symmetry breaking under the FEP. It finally notes that the FEP asymptotically restores the broken symmetry, showing that the FEP can be regarded as a theory of fluctuations away from a permutation-symmetric boundary, and hence from an entangled joint state of the interacting systems.

A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics.

Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals since. Thermodynamics still has unknown possibilities waiting to be explored. This paper begins with a brief review of Clausius's work on the second law of thermodynamics and a reassessment of the content of Clausius's statement. The review tells that what Clausius originally referred to as the second law of thermodynamics was, in fact, the theorem of equivalence of transformations (TET) in a reversible cycle. On this basis, a new symmetric form of Clausius's TET is proposed. This theorem says that the two transformations, i.e., the transformation of heat to work and the transformation of work from high pressure to low pressure, should be equivalent in a reversible work-to-heat cycle. New thermodynamic cyclic laws are developed on the basis of the cycle with two work reservoirs (two pressures), which enriches the fundamental of the second law of thermodynamics.

Effects of prosthetic stiffness and added mass on metabolic power and asymmetry in female runners with a leg amputation.

Similar to nonamputees, female athletes with unilateral transtibial amputation (TTA) using running-specific leg prostheses (RSPs) may have worse running economy and higher rates of running-related injury than male athletes. Optimizing RSP configuration for female athletes could improve running economy and minimize biomechanical asymmetry, which has been associated with running-related injury. Nine females with a TTA ran at 2.5 m/s while we measured metabolic rates and ground reaction forces. Subjects used an RSP with a manufacturer-recommended stiffness category, one category less stiff and two categories less stiff than recommended. Use of an RSP two categories less stiff resulted in 3.0% lower net metabolic power (P = 0.04), 7.8% lower affected leg stiffness (P = 6.01 × 10-4), increased contact time asymmetry (P = 0.04), and decreased stance average vertical ground reaction force asymmetry (P = 0.04) compared with a recommended stiffness category RSP. Lower RSP stiffness (kN/m) values were associated with lower net metabolic power (P = 0.02), lower affected leg stiffness (P = 1.36 × 10-4), longer affected leg contact time (P = 1.46 × 10-4), and similar affected leg peak and stance-average vertical ground reaction force compared with higher RSP stiffness values. Subjects then used the RSP stiffness category that elicited the lowest net metabolic power with 100 g, 200 g, and 300 g added distally. We found no significant effects of added mass on net metabolic power, biomechanics, or asymmetry. These results suggest that female runners with a TTA could decrease metabolic power during running while minimizing biomechanical asymmetries, which have been associated with running-related injury, by using an RSP two categories less stiff than manufacturer recommended.NEW & NOTEWORTHY Females with unilateral transtibial amputation can improve running performance through reductions in net metabolic power by using a running-specific prosthesis (RSP) that is less stiff than manufacturer-recommended. Lower RSP stiffness values are associated with greater leg stiffness and contact time asymmetry, and lower stance-average vertical ground reaction force asymmetry. However, we found that adding mass to the RSP did not affect net metabolic power and stance-phase biomechanical asymmetries during running.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation.

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

Perfect Zeeman Anisotropy in Rotationally Symmetric Quantum Dots with Strong Spin-Orbit Interaction.

In nanoscale structures with rotational symmetry, such as quantum rings, the orbital motion of electrons combined with a spin-orbit interaction can produce a very strong and anisotropic Zeeman effect. Since symmetry is sensitive to electric fields, ring-like geometries provide an opportunity to manipulate magnetic properties over an exceptionally wide range. In this work, we show that it is possible to form rotationally symmetric confinement potentials inside a semiconductor quantum dot, resulting in electron orbitals with large orbital angular momentum and strong spin-orbit interactions. We find complete suppression of Zeeman spin splitting for magnetic fields applied in the quantum dot plane, similar to the expected behavior of an ideal quantum ring. Spin splitting reappears as orbital interactions are activated with symmetry-breaking electric fields. For two valence electrons, representing a common basis for spin-qubits, we find that modulating the rotational symmetry may offer new prospects for realizing tunable protection and interaction of spin-orbital states.

Magnetic structures in R5Pt2In4 (R = Tb-Tm) investigated by neutron powder diffraction.

Results of the neutron powder diffraction measurements carried out for R5Pt2In4 (R = Tb-Tm) are reported. The compounds crystallize in an orthorhombic crystal structure of the Lu5Ni2In4-type with the rare earth atoms occupying three different sublattices. At low temperatures the rare earth magnetic moments order below the critical temperature equal to 105, 93, 28, 12 and 3.8 K for R = Tb, Dy, Ho, Er and Tm, respectively. With decreasing temperature the rare earth magnetic moments at the 2a and 4g2 sites order first, while the moments at the 4g1 site order at lower temperatures. Ferrimagnetic order along the c axis, described by the propagation vector k1 = [0, 0, 0], develops in Tb5Pt2In4 below the Curie temperature (TC = 108 K). At lower temperatures, an antiferromagnetic component in the ab plane appears. The component is incommensurate with the crystal structure (k2 = [0, 0.66, ½]), but it turns into a commensurate one (k3 = [0, 0, ½]) with decreasing temperature. Antiferromagnetic order along the c axis, described by k4 = [½, 0, 0], is found in Dy5Pt2In4 below the Néel temperature (TN = 93 K). The k4-related component disappears below 80 K and the magnetic structure transforms into a ferro/ferrimagnetic one described by k1 = [0, 0, 0]. Further decrease in temperature leads to the appearance of an incommensurate antiferromagnetic component along the ab plane below 10 K (k2 = [0, 0.45, ½]), which finally turns into a commensurate one (k5 = [0, ½, ½]). In Ho5Pt2In4, a sine-modulated magnetic structure with moments parallel to the c axis (k6 = [⅓,0,0]) is observed below 28 K. With a decrease in temperature, new components, related to k1 = [0, 0, 0] (bc plane) and k4 = [½, 0, 0] (c axis), appear. The coexistence of two orderings - in the ab plane (k1 = [0, 0, 0]) and a modulated one with moments along the b axis (k7 = [kx, 0, 0]) - is found in Er5Pt2In4 below 12 K. Decreasing temperature leads to the order-order transformation of the k1-related component to another one with magnetic moments still constrained to the ab plane and preserved value of the propagation vector (i.e. k1 = [0, 0, 0]). Tm5Pt2In4 orders antiferromagnetically below TN = 4.1 K. Thulium magnetic moments lie in the ab plane, while the magnetic structure is described by k5 = [0, ½ , ½]. The direction of magnetic moments depends on the rare earth element involved and indicates an influence of single ion anisotropy resulting from interaction with the crystalline electric field.