Fourfold Rotation Research Articles

Crystalline finite-size topology

Topological phases stabilized by crystalline point group symmetry protection are a large class of symmetry-protected topological phases subjected to considerable experimental scrutiny. Here, we show that the canonical three-dimensional (3D) crystalline topological insulator protected by time-reversal symmetry T and fourfold rotation symmetry C4 individually or the product symmetry C4T, generically realizes finite-size crystalline topological phases in thin film geometry [a quasi-(3−1)-dimensional, or q(3−1)D, geometry]: response signatures of the 3D bulk topology coexist with topologically protected, quasi-(3−2)D, and quasi-(3−3)D boundary modes within the energy gap resulting from strong hybridization of the Dirac cone surface states of the underlying 3D crystalline topological phase. Importantly, we find qualitative distinctions between these gapless boundary modes and those of strictly 2D crystalline topological states with the same symmetry protection and develop a low-energy, analytical theory of the finite-size topological magnetoelectric response. Published by the American Physical Society 2024

Tunable C4-Symmetry-Broken Metasurfaces Based on Phase Transition of Vanadium Dioxide (VO2).

Coupling is a ubiquitous phenomenon observed in various systems, which profoundly alters the original oscillation state of resonant systems and leads to the unique optical properties of metasurfaces. In this study, we introduce a terahertz (THz) tunable coupling metasurface characterized by a four-fold rotation (C4) symmetry-breaking structural array achieved through the incorporation of vanadium dioxide (VO2). This disruption of the C4 symmetry results in dynamically controlled electromagnetic interactions and couplings between excitation modes. The coupling between new resonant modes modifies the peak of electromagnetic-induced transparency (EIT) within the C4 symmetric metasurfaces, simulating the mutual interference process between modes. Additionally, breaking the C4 symmetry enhances the mirror asymmetry, and imparts distinct chiral properties in the far-field during the experimental process. This research demonstrates promising applications in diverse fields, including biological monitoring, light modulation, sensing, and nonlinear enhancement.

Atomic Structure and Dynamics of Organic-Inorganic Hybrid Perovskite Formamidinium Lead Iodide.

The atomic dynamic behaviors of formamidinium lead iodide [HC(NH2)2PbI3] are critical for understanding and improving photovoltaic performances. However, they remain unclear. Here, we investigate the structural phase transitions and the reorientation dynamics of the formamidinium cation [HC(NH2)2+, FA+] of FAPbI3 using neutron scattering techniques. Two structural phase transitions occur with decreasing temperature, from cubic to tetragonal phase at 285 K and then to another tetragonal at 140 K, accompanied by gradually frozen reorientation of FA cations. The nearly isotropic reorientation in the cubic phase is suppressed to reorientation motions involving a two-fold (C2) rotation along the N···N axis and a four-fold (C4) rotation along the C-H axis in the tetragonal phase, and eventually to local disordered motion as a partial C4 along the C-H axis in another tetragonal phase, thereby indicating an intimate interplay between lattice and orientation degrees of freedom in the hybrid perovskite materials. The present complete atomic structure and dynamics provide a solid standing point to understand and then improve photovoltaic properties of organic-inorganic hybrid perovskites in the future.

Synthesis, crystal structure and properties of chlorido-tetra-kis-(pyridine-3-carbo-nitrile)-thio-cyanato-iron(II).

Reaction of FeCl2·4H2O with KSCN and 3-cyano-pyridine (pyridine-3-carbo-nitrile) in ethanol accidentally leads to the formation of single crystals of Fe(NCS)(Cl)(3-cyano-pyridine)4 or [FeCl(NCS)(C6H4N2)4]. The asymmetric unit of this compound consists of one FeII cation, one chloride and one thio-cyanate anion that are located on a fourfold rotation axis as well as of one 3-cyano-pyridine coligand in a general position. The FeII cations are sixfold coordinated by one chloride anion and one terminally N-bonding thio-cyanate anion in trans-positions and four 3-cyano-pyridine coligands that coordinate via the pyridine N atom to the FeII cations. The complexes are arranged in columns with the chloride anions, with the thio-cyanate anions always oriented in the same direction, which shows the non-centrosymmetry of this structure. No pronounced inter-molecular inter-actions are observed between the complexes. Initially, FeCl2 and KSCN were reacted in a 1:2 ratio, which lead to a sample that contains the title compound as the major phase together with a small amount of an unknown crystalline phase, as proven by powder X-ray diffraction (PXRD). If FeCl2 and KSCN is reacted in a 1:1 ratio, the title compound is obtained as a nearly pure phase. IR investigations reveal that the CN stretching vibration for the thio-cyanate anion is observed at 2074 cm-1, and that of the cyano group at 2238 cm-1, which also proves that the anionic ligands are only terminally bonded and that the cyano group is not involved in the metal coordination. Measurements with thermogravimetry and differential thermoanalysis reveal that the title compound decomposes at 169°C when heated at a rate of 4°C min-1 and that the 3-cyano-pyridine ligands are emitted in two separate poorly resolved steps. After the first step, an inter-mediate compound with the composition Fe(NCS)(Cl)(3-cyano-pyridine)2 of unknown structure is formed, for which the CN stretching vibration of the thio-cyanate anion is observed at 2025 cm-1, whereas the CN stretching vibration of the cyano group remain constant. This strongly indicates that the FeII cations are linked by μ-1,3-bridg-ing thio-cyanate anions into chains or layers.

Hourglass nodal loop phonons in two dimensions jointly supported by fourfold rotation and glide mirror symmetries

Hourglass nodal loop phonons in two dimensions jointly supported by fourfold rotation and glide mirror symmetries

Competing Vortex Topologies in Iron-Based Superconductors.

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

Oxygen vacancies at the origin of pinned moments in oxide interfaces: The example of tetragonal CuO/SrTiO3

Obtaining an accurate theoretical description of the emergent phenomena in oxide heterostructures is a major challenge. Recently, intriguing paramagnetic spin and pinned orbital moments have been discovered by x-ray magnetic circular dichroism measurements at the Cu ${L}_{2,3}$ edge of a tetragonal $\mathrm{CuO}/{\mathrm{SrTiO}}_{3}$ heterostructure. Using first-principles calculations, we propose a scenario that explains both types of moments, based on the formation of oxygen vacancies in the ${\mathrm{TiO}}_{2}$ interface layer. We show the emergence of a paramagnetic two-dimensional electron gas hosted in the interface CuO layer. It is invisible at the Ti ${L}_{2,3}$ edge since the valence of the Ti atoms remains unchanged. Strong structural distortions breaking both the local and global fourfold rotation ${C}_{4}$ symmetries at the interface lead to the in-plane pinning of the Cu orbital moment close to the vacancy. Our results, and in particular the pinning of the orbital moment, may have implications for other systems, especially monoxide/dioxide interfaces with similar metal-oxygen bond length and weak spin-orbit coupling.

Topological defects in a double-mirror quadrupole insulator displace diverging charge

We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a disclination and a parametric defect. Since disclinations necessarily strain the lattice and parametric defects require closed curves in parameter space, both defects break four-fold rotation symmetry, even away from their origin. The Wannier representation of the defects is thus determined by local reflection symmetries. Contrary to the hypothesis, we find that the local charge density decays as \sim 1/r^2~ 1/r2 with distance, leading to a diverging defect charge. Because topological defects are incompatible with four-fold rotation symmetry, we conclude that defect charge quantization is protected by sublattice symmetry, and not higher order topology.

Breakdown of bulk-projected isotropy in surface electronic states of topological Kondo insulator SmB6(001)

The topology and spin-orbital polarization of two-dimensional (2D) surface electronic states have been extensively studied in this decade. One major interest in them is their close relationship with the parities of the bulk (3D) electronic states. In this context, the surface is often regarded as a simple truncation of the bulk crystal. Here we show breakdown of the bulk-related in-plane rotation symmetry in the topological surface states (TSSs) of the Kondo insulator SmB6. Angle-resolved photoelectron spectroscopy (ARPES) performed on the vicinal SmB6(001)-p(2 × 2) surface showed that TSSs are anisotropic and that the Fermi contour lacks the fourfold rotation symmetry maintained in the bulk. This result emphasizes the important role of the surface atomic structure even in TSSs. Moreover, it suggests that the engineering of surface atomic structure could provide a new pathway to tailor various properties among TSSs, such as anisotropic surface conductivity, nesting of surface Fermi contours, or the number and position of van Hove singularities in 2D reciprocal space.

Design, development and characterization of resistive arm based planar and conformal metasurfaces for RCS reduction

This paper reports the design, development and characterization of a broadband, polarization insensitive metasurface absorber in planar, cylindrically bent and 90° dihedral surface geometry. Four metallic patches loaded with eight lumped resistors are used, which has been optimized numerically using CST MICROWAVE STUDIO, as a unit cell of developed metasurface absorber, to achieve 20 dB reflection reduction for 51.21% fractional bandwidth (13.42–22.66 GHz) under normal incidence with 0.12 {lambda }_{L} thickness (where {lambda }_{L} corresponds to lower operating frequency). The numerical findings are also verified analytically using equivalent circuit analysis, which exhibits very good agreement. Polarization-insensitive characteristics are achieved using fourfold rotation symmetry of the designed structure. The fabricated prototype of the designed absorber is experimentally characterized, using free space measurement method and ABmm vector network analyzer (VNA) system, and fairly good agreement with numerical-analytical findings are reported. The major novelty of this study is the design and development of a broadband (13.42–22.66 GHz), polarization insensitive metasurface absorber that provides 20 dB reflection reduction numerically as well as experimentally in the whole band, which to the author’s knowledge has not been observed till now. Also, keeping in mind the radar stealth applications, first time we have demonstrated both numerically and experimentally, different geometrical shapes of conformal metasurfaces that can be practically used in actual scenario.

Rotation symmetry-protected topological phases of fermions

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand, we demonstrate the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through explicit block-state constructions. We find that for the precise correspondence to hold it is necessary to change the central extension structure of the symmetry group by the $\mathbb{Z}_2$ fermion parity. On the other hand, we uncover new classes of intrinsically fermionic SPT phases that are only enabled by interactions, both in 2D and 3D with four-fold rotation. Moreover, several new instances of Lieb-Schultz-Mattis-type theorems for Majorana-type fermionic SPTs are obtained and we discuss their interpretations from the perspective of bulk-boundary correspondence.

Orthorhombic charge density wave on the tetragonal lattice of EuAl4.

EuAl4 possesses the BaAl4 crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge density wave (CDW) transition at T CDW= 145 K and features four consecutive antiferromagnetic phase transitions below 16 K. Here we use single-crystal X-ray diffraction to determine the incommensurately modulated crystal structure of EuAl4 in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q= (0,0,0.1781 (3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the Al atoms as the location of the CDW. The tem-per-ature dependence of the specific heat reveals an anomaly at T CDW= 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl4 leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.

Enhancement of superconductivity by electronic nematicity in cuprate superconductors

ABSTRACT The cuprate superconductors are characterised by numerous ordering tendencies, with the electronically nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimised takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimised reaches its maximum. This dome-like shape nematic-order strength dependence of thus indicates that the electronic nematicity enhances superconductivity. Moreover, this nematic order induces the anisotropy of the electron Fermi surface, where although the original electron Fermi surface contour with the four-fold rotation symmetry is broken up into that with a residual twofold rotation symmetry, this electron Fermi surface contour with the twofold rotation symmetry still is truncated to form the disconnected Fermi arcs with the most spectral weight that locates at around the tips of the Fermi arcs. Concomitantly, these tips of the Fermi arcs connected by the scattering wave vectors construct an octet scattering model, however, the partial scattering wave vectors and their respective symmetry-corresponding partners occur with unequal amplitudes, leading to these electronically ordered states being broken both rotation and translation symmetries. As a natural consequence, the electronic structure is inequivalent between the and directions in momentum space. These anisotropic features of the electronic structure are also confirmed via the result of the autocorrelation of the single-particle excitation spectra, where the breaking of the rotation symmetry is verified by the inequivalence on the average of the electronic structure at the two Bragg scattering sites. The theory also indicates that the order parameter of the electronic nematicity achieves its maximum in the characteristic energy and then decreases rapidly as the energy moves away from the characteristic energy.

Development of Resistive-Ink Based Planar and Conformal Metasurfaces for RCS Reduction

This work reports design, development and characterization of both planar and conformal Metasurfaces using resistive Ink based lossy pattern printed on top of FR-4 dielectric substrate for RADAR stealth application. Different geometrical dimensions of the proposed unit cell have been optimized numerically using CST-Microwave Studio, to achieve 20 dB reflection reduction with 60% fractional bandwidth in frequency range 10.5-19.5 GHz under normal incidence with 0.12λ_L thickness (where λ_L corresponds to lower operating frequency) and 10 dB reflection reduction up to 40° oblique angle of incidence in the given frequency spectrum for both TE and TM polarized wave. An equivalent circuit analytical modelling has also been performed to understand and verify the numerical findings which are nearly in agreement. Polarization insensitive characteristics of developed surfaces is achieved using fourfold rotation symmetry of the designed unit cell. The designed absorbers are fabricated in form of planar, cylindrically bent and 90° dihedral Metasurfaces and are characterized using ABmm Vector Network Analyzer (VNA) system and free space measurement method. A thorough different experimental measurements are performed and it is found that measured characteristics are in agreement with numerical-analytical findings.

Classification of Dirac points with higher-order Fermi arcs

Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display "higher order Fermi arcs," which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher order Fermi arcs. When higher order Fermi arcs do exist, they obey either a $\mathbb{Z}_2$ (four-fold rotation axis) or $\mathbb{Z}_3$ (three- or six-fold rotation axis) group structure. Finally, we build two models with six-fold symmetry to illustrate the cases with and without higher order Fermi arcs. We predict higher order Fermi arcs in Na$_3$Bi.

Design, development and characterization of wide incidence angle and polarization insensitive metasurface absorber based on resistive-ink for X and Ku band RCS reduction

This article deals with the design, development and characterization of a broadband, wide incidence angle and polarization-insensitive metasurface, which consists of periodic resistive-ink pattern printed on top of FR-4 dielectric substrate as a RADAR absorber. Geometrical dimensions of the proposed unit cell have been optimized numerically using CST-Microwave Studio to achieve 99% absorptivity for X and Ku frequency spectrum (8–18 GHz) under the normal angle of incidence and to achieve almost 90% absorptivity under the oblique angle of incidence up to 50° within X-Band to Ku-Band spectrum. Furthermore, it is reported that by having fourfold rotation symmetry, the designed structure is insensitive to the polarization of the incident wave. An equivalent circuit analytical modeling has also been performed to understand and verify numerical findings that are nearly in agreement. The designed absorber is fabricated and characterized using ABmm VNA and free space measurement method, for both normal and oblique angle of incidence, and it is found that measured characteristics are in agreement with numerical-analytical findings. Furthermore, the monostatic and bistatic Radar Cross Section reduction capability of the designed absorbing structure for both planar and curved surface (cylinder) is studied extensively to assess its potential application in X-Band to Ku-Band Spectrum.

Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems.

We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle, which is an integer multiple of 2π, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the effective surface Dirac fermion(s) in the presence of a pseudomagnetic flux induced by disclinations. Furthermore, we find that our results have a field theoretic description, and the corresponding geometric response actions (e.g., the Euclidean Wen-Zee action) enrich the topological field theory of non-Hermitian systems.

Thermodynamic electric quadrupole moments of nematic phases from first-principles calculations

The electronic nematic phase emerging with spontaneous rotation symmetry breaking is a central issue of modern condensed matter physics. In particular, various nematic phases in iron-based superconductors and high-$T_{\rm c}$ cuprate superconductors are extensively studied recently. Electric quadrupole moments (EQMs) are one of the order parameters characterizing these nematic phases in a unified way, and elucidating EQMs is a key to understanding these nematic phases. However, the quantum-mechanical formulation of the EQMs in crystals is a nontrivial issue because the position operators are non-periodic and unbound. Recently, the EQMs have been formulated by local thermodynamics, and such {\it thermodynamic EQMs} may be used to characterize the fourfold rotation symmetry breaking in materials. In this paper, we calculate the thermodynamic EQMs in iron-based superconductors LaFeAsO and FeSe as well as a cuprate superconductor La$_2$CuO$_4$ by a first-principles calculation. We show that owing to the orbital degeneracy the EQMs in iron-based superconductors are mainly determined by the geometric properties of wave functions. This result is in sharp contrast to the cuprate superconductor, in which the EQMs are dominated by distortion of the Fermi surface.

Noncentrosymmetric topological Dirac semimetals in three dimensions

Topological Dirac semimetals are a class of semimetals that host symmetry-protected Dirac points near the Fermi level, which arise due to a band inversion of the conduction and valence bands. In this work, we study the less explored class of \emph{noncentrosymmetric} topological Dirac semimetals in three dimensions. We identify the noncentrosymmetric crystallographic point groups required to stabilize fourfold degenerate band crossings and derive model Hamiltonians for all distinct types of band inversions allowed by symmetry. Using these model Hamiltonians, which emphasize the physical nature of the allowed couplings, we establish the generic electronic phase diagram noncentrosymmetric Dirac semimetals and show that it generically includes phases with coexistent Weyl point nodes or Weyl line nodes. In particular, for one specific type of band inversion in sixfold symmetric systems we show that Weyl line nodes are always present. Based on first-principles calculations, we predict that BiPd$_2$O$_4$ is a noncentrosymmetric Dirac semimetal under 20 Gpa pressure and hosts topological type-II Dirac points on the fourfold rotation axis. Furthermore, we propose that the hexagonal polar alloy LiZnSb$_{x}$Bi$_{1-x}$ realizes a Dirac semimetal with coexistent Weyl points. Interestingly, the emergence and location of the Weyl points is highly tunable and can be controlled by the alloy concentration $x$. More generally, our results not only establish band-inverted noncentrosymmetric systems as a broad and versatile class of topological semimetals, but also provide a framework for studying the quantum nonlinear Hall effect and nonlinear optical properties in the Dirac semimetals.

Active polarization-independent plasmon-induced transparency metasurface with suppressed magnetic attenuation.

A tunable polarization-independent plasmon-induced transparency (PIT) metasurface based on connected half-ring and split-ring resonators is proposed to working in the terahertz band. We analyze the PIT effect in metasurfaces comprising of ring resonator and split ring resonator. Due to the magnetic attenuation caused by the reverse current between the two resonators, the relative position of the ring resonator and the split-ring resonator greatly affects the strength of the PIT effect. Magnetic attenuation weakens the dark mode of the split ring resonator. Through simulation and experiment, it is found that connecting the ring resonator and split-ring resonator can avoid magnetic attenuation and achieve a stronger PIT window. Furthermore, the fourfold rotation structure of the connected half-ring and split-ring resonator on silicon substrate achieves an optically controlled polarization-independent PIT effect. The design would provide significant guidance in multifunctional active devices, such as modulators and switches in terahertz communication.